knn_full_submit.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "knn-full-submit.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "DfU9gBvVdnWA"
      },
      "source": [
        "import datetime\n",
        "import gc\n",
        "import random\n",
        "import time\n",
        "\n",
        "import numpy\n",
        "import pandas\n",
        "import scipy\n",
        "from scipy import sparse\n",
        "import matplotlib.pyplot as plt\n",
        "import IPython.display as disp\n",
        "\n",
        "class Progress:\n",
        "    \"\"\"Wrapper for IPython.display.ProgressBar with improved performance\"\"\"\n",
        "\n",
        "    def __init__(self, total):\n",
        "        self.bar = disp.ProgressBar(total)\n",
        "        self.total = total\n",
        "        self.progress = 0\n",
        "        self.last = 0\n",
        "        self.start = time.monotonic_ns()\n",
        "    def inc(self, delta=1):\n",
        "        self.progress += delta\n",
        "        if time.monotonic_ns() - self.last > 1e8:\n",
        "            self.bar.progress = self.progress\n",
        "            self.bar.update()\n",
        "            self.last = time.monotonic_ns()\n",
        "    def __enter__(self):\n",
        "        return self\n",
        "    def __exit__(self, exc_type, exc_value, tb):\n",
        "        self.bar.progress = self.progress\n",
        "        self.bar.update()\n",
        "        print(f\"Completed {self.progress}/{self.total} in {(time.monotonic_ns() - self.start) / 1000000}ms\")\n",
        "        return False\n",
        "\n",
        "class Timer:\n",
        "    def __init__(self, name):\n",
        "        self.name = name\n",
        "    \n",
        "    def __enter__(self):\n",
        "        self.start = time.monotonic_ns()\n",
        "        print(f\"Task: {self.name}\")\n",
        "\n",
        "    def __exit__(self, exc_type, exc_value, tb):\n",
        "        end = time.monotonic_ns()\n",
        "        time_ns = end - self.start\n",
        "        print(f\"Took {time_ns / 1000000}ms\")\n",
        "        return False"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sF43KZfGd4vs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2bf1ae7d-efe5-4cc1-d4bf-d890a825f9de"
      },
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mounted at /content/drive\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IUBdKi0Pd6AT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "229403ec-8116-41a2-8299-a1e2f2c0b9c1"
      },
      "source": [
        "!test -d dataset || unzip /content/drive/Shareddrives/'STAT4609 Netflix'/dataset.zip -d dataset"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Archive:  /content/drive/Shareddrives/STAT4609 Netflix/dataset.zip\n",
            "  inflating: dataset/README          \n",
            "  inflating: dataset/combined_data_1.txt  \n",
            "  inflating: dataset/combined_data_2.txt  \n",
            "  inflating: dataset/combined_data_3.txt  \n",
            "  inflating: dataset/combined_data_4.txt  \n",
            "  inflating: dataset/movie_titles.csv  \n",
            "  inflating: dataset/probe.txt       \n",
            "  inflating: dataset/qualifying.txt  \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "36ivpwyyd7yv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9da5ce73-c22a-4dc8-a50c-fab71c4e90a2"
      },
      "source": [
        "!cp /content/drive/Shareddrives/'STAT4609 Netflix'/preprocess-dataset /usr/local/bin\n",
        "!chmod +x /usr/local/bin/preprocess-dataset\n",
        "!test -f dataset/output.npy || (cd dataset && preprocess-dataset)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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            "tcmalloc: large alloc 1879048192 bytes == 0x5630aae9c000 @  0x7fe83163a2a4 0x56303750c120 0x56303750c265 0x56303750af2a 0x5630375095de 0x56303750b956 0x56303750b96c 0x56303752630a 0x56303750b855 0x7fe830bfbbf7 0x563037507e3e\n",
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            "tcmalloc: large alloc 3758096384 bytes == 0x56311ae9c000 @  0x7fe83163a2a4 0x56303750c120 0x56303750c265 0x56303750af2a 0x563037509698 0x56303750b956 0x56303750b96c 0x56303752630a 0x56303750b855 0x7fe830bfbbf7 0x563037507e3e\n",
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          "name": "stdout"
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      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sceZ7Gc3d8lZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ae2ebdf0-77b5-4ba9-fdbc-10cb985778a2"
      },
      "source": [
        "COL_USER = 0\n",
        "COL_MOVIE = 1\n",
        "COL_RATINGS = 2\n",
        "COL_YEAR = 3\n",
        "COL_DOY = 4\n",
        "COL_DOW = 5\n",
        "COL_PROBED = 6\n",
        "\n",
        "with Timer(\"Loading data...\"):\n",
        "    data = numpy.load(\"dataset/output.npy\")\n",
        "    data_size = data.shape[0]\n",
        "\n",
        "with Timer(\"Counting users and movies\"):\n",
        "    user_count = numpy.max(data[:, COL_USER]) + 1\n",
        "    movie_count = numpy.max(data[:, COL_MOVIE]) + 1\n",
        "\n",
        "with Timer(\"Copying train/test split\"):\n",
        "    train = data[data[:, 6] == 0, :3].copy()\n",
        "    evaluation = data[data[:, 6] == 1, :3].copy()\n",
        "\n",
        "# Free the memory used to hold the whole dataset\n",
        "del data\n",
        "gc.collect()\n",
        "\n",
        "print(f\"Train/test size: {train.shape[0]}/{evaluation.shape[0]}\")\n",
        "\n",
        "evaluation_results = []"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Task: Loading data...\n",
            "Took 4088.67364ms\n",
            "Task: Counting users and movies\n",
            "Took 559.444552ms\n",
            "Task: Copying train/test split\n",
            "Took 4882.736761ms\n",
            "Train/test size: 99072112/1408395\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oAr65FapeJoy"
      },
      "source": [
        "class KnnRecommend:\n",
        "    def __init__(self, metric, aggregate, k, q, batch_size=1024):\n",
        "        \"\"\"Arguments:\n",
        "        metric: a function taking a size n vector and a size q*n matrix, returning the distances of the vector to each of the q rows\n",
        "        aggregate: a function that takes in a vector of ratings and weights and aggregates them to a single rating\n",
        "        k: the number of neighbours to use, k <= q\n",
        "        q: the number of users to select neighbours from\n",
        "        batch_size: number of rows to process in each batch; does not affect results\"\"\"\n",
        "        self.metric = metric\n",
        "        self.aggregate = aggregate\n",
        "        self.k = k\n",
        "        self.q = q\n",
        "        self.batch_size = batch_size\n",
        "    def fit(self, ratings):\n",
        "        raise Exception(\"Uninitialized function\")\n",
        "    def predict_rating(self, user_id, movie_id):\n",
        "        raise Exception(\"Uninitialized function\")\n",
        "    def evaluate(self):\n",
        "        raise Exception(\"Uninitialized function\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zjSCBn4flPCd"
      },
      "source": [
        "class DataLoader:\n",
        "    def __init__(self, csr, q):\n",
        "        self.csr = csr.astype(numpy.float64)\n",
        "        self.ptr = 0\n",
        "\n",
        "        self._output = numpy.empty((csr.shape[0], q))\n",
        "\n",
        "    def set_batch_size(self, batch_size):\n",
        "        self.batch_size = batch_size\n",
        "        self.buf = numpy.empty((batch_size, self.csr.shape[1]))\n",
        "\n",
        "    def __iter__(self):\n",
        "        return self\n",
        "    def __next__(self):\n",
        "        end = min(self.ptr + self.batch_size, self.csr.shape[0])\n",
        "        num_rows = end - self.ptr\n",
        "        self.last_start = self.ptr\n",
        "        self.last_end = end\n",
        "        if num_rows == 0:\n",
        "            raise StopIteration\n",
        "        self.csr[self.ptr:end, :].toarray(out=self.buf[:num_rows, :])\n",
        "        self.buf[self.buf == 0] = numpy.nan\n",
        "        self.ptr = end\n",
        "        return self.buf[:num_rows, :]\n",
        "\n",
        "    def output(self, vec):\n",
        "        self._output[self.last_start:self.last_end] = vec\n",
        "\n",
        "    def get_output(self):\n",
        "        return self._output"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pU6HNGIlg0fx"
      },
      "source": [
        "def _fit(self, ratings):\n",
        "    gc.collect()\n",
        "\n",
        "    # express as a sparse matrix such that coo[user, movie] = rating\n",
        "    with Timer(\"Counting users and movies\"):\n",
        "        user_count = ratings[:, COL_USER].max() + 1\n",
        "        movie_count = ratings[:, COL_MOVIE].max() + 1\n",
        "    \n",
        "    with Timer(\"Repacking ratings to COO format\"):\n",
        "        ratings_col = ratings[:, COL_RATINGS].astype(numpy.float64)\n",
        "        user_col = ratings[:, COL_USER]\n",
        "        movie_col = ratings[:, COL_MOVIE]\n",
        "        coo = scipy.sparse.coo_matrix((ratings_col, (user_col, movie_col)), shape=(user_count, movie_count))\n",
        "    with Timer(\"Repacking ratings to CSR format\"):\n",
        "        ratings = coo.tocsr()\n",
        "        \n",
        "    with Timer(\"Choosing top Q users\"):\n",
        "        user_rating_counts = numpy.asarray((ratings != 0).sum(axis=1)).reshape(-1)\n",
        "        top_q_users = numpy.argsort(-user_rating_counts)[:self.q]\n",
        "        \n",
        "    with Timer(\"Computing movie mean ratings\"):\n",
        "        movie_rating_counts = numpy.asarray((ratings != 0).sum(axis=0)).reshape(-1)\n",
        "        movie_means = numpy.asarray(ratings.sum(axis=0) / movie_rating_counts).reshape(-1)\n",
        "\n",
        "    with Timer(\"Extracting top q ratings\"):\n",
        "        top_q_ratings = ratings[top_q_users, :].toarray().astype(numpy.float64)\n",
        "        top_q_ratings[top_q_ratings == 0] = numpy.nan\n",
        "    with Timer(\"Computing distance matrix\"):\n",
        "        with Progress(user_count) as progress:\n",
        "            loader = DataLoader(ratings, self.q)\n",
        "            loader.set_batch_size(self.batch_size)\n",
        "            self.metric(loader, top_q_ratings, movie_means, progress)\n",
        "        distmat = loader.get_output()\n",
        "\n",
        "    with Timer(\"Sorting distances\"):\n",
        "        neighbours = numpy.argsort(distmat, axis=1)\n",
        "\n",
        "    self.distmat = distmat # m * q (float)\n",
        "    self.neighbours = neighbours # m * q (int 0..q)\n",
        "    self.top_q_users = top_q_users # q (int 0..m)\n",
        "    self.top_q_ratings = top_q_ratings # q * n (float)\n",
        "    self.movie_means = movie_means # n (float)\n",
        "\n",
        "KnnRecommend.fit = _fit"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3-RfIvbJyuFD"
      },
      "source": [
        "def _predict(self, um):\n",
        "    \"\"\"um is an n*2 matrix.\n",
        "    The first column is the user ID.\n",
        "    The second column is the movie ID.\n",
        "    Returns a size n vector of predicted ratings.\"\"\"\n",
        "\n",
        "    def imp(model, um):\n",
        "        probes = um.shape[0]\n",
        "        users = um[:, 0]\n",
        "        movies = um[:, 1]\n",
        "    \n",
        "        # neighbour_cols[i, j] is the user ID of the jth neighbour of the ith probed user\n",
        "        neighbour_cols = model.neighbours[users, :model.k]\n",
        "        # neighbour_indices[i, j] is the index of the distance of the jth neighbour of the ith probed user in distmat\n",
        "        neighbour_indices = neighbour_cols + numpy.arange(probes).reshape((-1, 1)) * model.distmat.shape[1]\n",
        "        # distances[i, j] is the distance between the ith probed user and his jth neighbour\n",
        "        distances = model.distmat[users, :].take(neighbour_indices)\n",
        "        # neighbour_ratings[i, j] is the rating on the ith probed movie by the jth neighbour of the ith probed user\n",
        "        neighbour_ratings = model.top_q_ratings[neighbour_cols.transpose(), movies].transpose()\n",
        "        return model.aggregate(neighbour_ratings, distances, model.movie_means[movies])\n",
        "\n",
        "    output = numpy.empty(um.shape[0])\n",
        "    ptr = 0\n",
        "    nan_count = 0\n",
        "    with Progress(um.shape[0]) as progress:\n",
        "        while ptr < um.shape[0]:\n",
        "            end = min(ptr + self.batch_size, um.shape[0])\n",
        "            batch_output, nan_count_comp = imp(self, um[ptr:end, :])\n",
        "            output[ptr:end] = batch_output\n",
        "            progress.inc(delta=end - ptr)\n",
        "            ptr = end\n",
        "            nan_count += nan_count_comp\n",
        "\n",
        "    if nan_count > 0:\n",
        "        print(f\"{nan_count} entries have no non-NAN neighbours\")\n",
        "\n",
        "    return output\n",
        "\n",
        "KnnRecommend.predict = _predict"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jJjipg3F2P_w"
      },
      "source": [
        "def _evaluate(self):\n",
        "    gc.collect()\n",
        "    self.fit(train)\n",
        "    pred = self.predict(evaluation[:, [COL_USER, COL_MOVIE]])\n",
        "    target = evaluation[:, COL_RATINGS]\n",
        "    rmse = numpy.sqrt(((pred - target) ** 2).mean())\n",
        "    evaluation_results.append((self.aggregate, self.metric, self.k, self.q, rmse))\n",
        "    return rmse\n",
        "\n",
        "KnnRecommend.evaluate = _evaluate"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "slpjiW1f24xY"
      },
      "source": [
        "class Metric:\n",
        "    \"\"\"For all methods, loader is DataLoader instance, mat is a q*n rating matrix,\n",
        "    means is a size n vector of mean ratings,\n",
        "    and output is a function to assign results to.\"\"\"\n",
        "\n",
        "    def p_norm(p):\n",
        "        def impl(loader, mat, means, progress, p):\n",
        "            q, n = mat.shape\n",
        "            mat_1qn = mat.reshape((1, q, n))\n",
        "    \n",
        "            delta_buf = numpy.empty((loader.batch_size, q, n))\n",
        "            norm_buf = numpy.empty((loader.batch_size, q))\n",
        "            for batch in loader:\n",
        "                b = batch.shape[0] # usually this is loader.batch_size, but this is smaller in the last batch\n",
        "                batch = batch.reshape((b, 1, n))\n",
        "\n",
        "                delta = delta_buf[:b, :, :]\n",
        "                numpy.subtract(mat_1qn, batch, out=delta)\n",
        "                numpy.abs(delta, out=delta)\n",
        "                numpy.power(delta, p, out=delta)\n",
        "\n",
        "                norm = norm_buf[:b, :]\n",
        "                numpy.sum(delta, axis=2, out=norm)\n",
        "                \n",
        "                loader.output(norm)\n",
        "\n",
        "        return lambda loader, mat, means, progress: impl(loader, mat, means, progress, p)\n",
        "\n",
        "    def cosine_mean(loader, mat, means, progress):\n",
        "        q = mat.shape[0]\n",
        "\n",
        "        ret = numpy.empty(q)\n",
        "        mat = mat - means.reshape((1, -1))\n",
        "        nan_indices = numpy.where(numpy.isnan(mat))\n",
        "        mat[nan_indices] = numpy.take(means, nan_indices[1]) # assume average if rating is unknown\n",
        "        norm_mat = numpy.linalg.norm(mat, axis=1)\n",
        "        mat_nq = mat.transpose()\n",
        "\n",
        "        # preallocate `inner` to improve performance\n",
        "        inner_buf = numpy.empty((loader.batch_size, q))\n",
        "\n",
        "        nan_bools_buf = numpy.empty((loader.batch_size, mat.shape[1]), dtype=bool)\n",
        "\n",
        "        for batch in loader:\n",
        "            b = batch.shape[0]\n",
        "            inner = inner_buf[:b, :]\n",
        "            batch -= means.reshape((1, -1))\n",
        "\n",
        "            nan_bools = nan_bools_buf[:b, :]\n",
        "            # numpy.isnan(batch, out=nan_bools)\n",
        "            # batch[nan_bools] = 0 # impute with means\n",
        "            numpy.matmul(batch, mat_nq, out=inner)\n",
        "            norm_batch = numpy.linalg.norm(batch, axis=1)\n",
        "            inner /= norm_batch.reshape((-1, 1))\n",
        "            inner /= norm_mat.reshape((1, -1))\n",
        "            loader.output(inner)\n",
        "            progress.inc(delta=b)\n",
        "\n",
        "        return ret"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kA3BAyloUrud"
      },
      "source": [
        "class Aggregate:\n",
        "    \"\"\"For all methods, ratings is a p*q rating matrix,\n",
        "    distances is a p*q distance matrix,\n",
        "    means is a size-p mean rating vector\"\"\"\n",
        "\n",
        "    def baseline(ratings, distances, means):\n",
        "        return means, 0\n",
        "\n",
        "    def average(ratings, distances, means):\n",
        "        ret = numpy.nanmean(ratings, axis=1)\n",
        "        nan_indices = numpy.isnan(ret)\n",
        "\n",
        "        nan_count = nan_indices.sum()\n",
        "        ret[nan_indices] = means[nan_indices]\n",
        "        return ret, nan_count"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0dK4N0pr2au4"
      },
      "source": [
        "## Example shown for Q = 300 and Q = 400\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_D4j0V-YetXT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "1dc90541-9226-4aad-dc08-e32ac0b3f071"
      },
      "source": [
        "rmse_q300 = []\n",
        "for k in [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,300]:\n",
        "  model = KnnRecommend(Metric.cosine_mean, Aggregate.average, k, 300,batch_size =526)\n",
        "  rmse = model.evaluate()\n",
        "  rmse_q300.append(rmse)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Task: Counting users and movies\n",
            "Took 276.023694ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 714.3765ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8424.450239ms\n",
            "Task: Choosing top Q users\n",
            "Took 533.711151ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 701.117918ms\n",
            "Task: Extracting top q ratings\n",
            "Took 65.876651ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 239088.519688ms\n",
            "Took 239090.93952ms\n",
            "Task: Sorting distances\n",
            "Took 3378.089287ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 1992.310285ms\n",
            "1369 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 274.674332ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 739.419266ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8882.902059ms\n",
            "Task: Choosing top Q users\n",
            "Took 596.395646ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 710.750682ms\n",
            "Task: Extracting top q ratings\n",
            "Took 65.100866ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 238027.814165ms\n",
            "Took 238030.105586ms\n",
            "Task: Sorting distances\n",
            "Took 1580.675373ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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          "metadata": {
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        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 2471.966497ms\n",
            "1052 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 279.603861ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 760.85129ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 9093.237716ms\n",
            "Task: Choosing top Q users\n",
            "Took 550.453627ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 724.088026ms\n",
            "Task: Extracting top q ratings\n",
            "Took 66.45548ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 238018.378207ms\n",
            "Took 238020.24798ms\n",
            "Task: Sorting distances\n",
            "Took 1572.174158ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 3041.166339ms\n",
            "866 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 279.109596ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 748.369871ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8870.960166ms\n",
            "Task: Choosing top Q users\n",
            "Took 543.486121ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 716.452806ms\n",
            "Task: Extracting top q ratings\n",
            "Took 65.759934ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 238567.145959ms\n",
            "Took 238568.183806ms\n",
            "Task: Sorting distances\n",
            "Took 1600.187497ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 4144.291337ms\n",
            "471 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 280.39139ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 744.947874ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8808.170153ms\n",
            "Task: Choosing top Q users\n",
            "Took 541.981065ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 716.411635ms\n",
            "Task: Extracting top q ratings\n",
            "Took 66.743062ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237774.477696ms\n",
            "Took 237775.456724ms\n",
            "Task: Sorting distances\n",
            "Took 1562.260614ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
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            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 4725.46253ms\n",
            "414 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 269.792631ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 742.210392ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8520.023948ms\n",
            "Task: Choosing top Q users\n",
            "Took 549.585753ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 703.954522ms\n",
            "Task: Extracting top q ratings\n",
            "Took 66.937389ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237359.129269ms\n",
            "Took 237361.116298ms\n",
            "Task: Sorting distances\n",
            "Took 1574.286577ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 5542.466828ms\n",
            "356 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 276.857853ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 770.109596ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8565.64533ms\n",
            "Task: Choosing top Q users\n",
            "Took 530.670458ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 713.262141ms\n",
            "Task: Extracting top q ratings\n",
            "Took 67.252546ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          }
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        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237381.852639ms\n",
            "Took 237381.975641ms\n",
            "Task: Sorting distances\n",
            "Took 1569.043753ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "tags": []
          }
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        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 6075.290122ms\n",
            "350 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 276.461318ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 743.079786ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8446.614328ms\n",
            "Task: Choosing top Q users\n",
            "Took 537.490373ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 720.019797ms\n",
            "Task: Extracting top q ratings\n",
            "Took 65.685736ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 238057.722183ms\n",
            "Took 238060.18627ms\n",
            "Task: Sorting distances\n",
            "Took 1560.957558ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 6866.925321ms\n",
            "350 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 274.292059ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 756.517903ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8723.18483ms\n",
            "Task: Choosing top Q users\n",
            "Took 540.982359ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 710.408292ms\n",
            "Task: Extracting top q ratings\n",
            "Took 66.505202ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 238154.641533ms\n",
            "Took 238156.729053ms\n",
            "Task: Sorting distances\n",
            "Took 1567.968459ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
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          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 7634.384489ms\n",
            "332 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 267.123944ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 731.219532ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8673.124451ms\n",
            "Task: Choosing top Q users\n",
            "Took 535.105221ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 709.174337ms\n",
            "Task: Extracting top q ratings\n",
            "Took 64.621497ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237482.669683ms\n",
            "Took 237484.030533ms\n",
            "Task: Sorting distances\n",
            "Took 1590.266453ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 8188.230135ms\n",
            "324 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 266.79213ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 728.882041ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8373.977728ms\n",
            "Task: Choosing top Q users\n",
            "Took 539.046001ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 718.99193ms\n",
            "Task: Extracting top q ratings\n",
            "Took 66.077856ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237770.672933ms\n",
            "Took 237773.975989ms\n",
            "Task: Sorting distances\n",
            "Took 1568.24635ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 8960.509803ms\n",
            "52 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 265.742069ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 722.412235ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 8566.648159ms\n",
            "Task: Choosing top Q users\n",
            "Took 556.636223ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 705.420555ms\n",
            "Task: Extracting top q ratings\n",
            "Took 67.110479ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 236865.165182ms\n",
            "Took 236866.925449ms\n",
            "Task: Sorting distances\n",
            "Took 1560.467024ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 9336.350209ms\n",
            "34 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 256.071208ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 701.513633ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 7715.063419ms\n",
            "Task: Choosing top Q users\n",
            "Took 536.952158ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 705.515906ms\n",
            "Task: Extracting top q ratings\n",
            "Took 65.899527ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 236541.141306ms\n",
            "Took 236542.21343ms\n",
            "Task: Sorting distances\n",
            "Took 1568.474551ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 10154.207587ms\n",
            "24 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 262.300701ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 699.102817ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 7632.302605ms\n",
            "Task: Choosing top Q users\n",
            "Took 532.621114ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 709.101319ms\n",
            "Task: Extracting top q ratings\n",
            "Took 60.933488ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237165.03291ms\n",
            "Took 237166.103083ms\n",
            "Task: Sorting distances\n",
            "Took 1586.652131ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 10896.024262ms\n",
            "9 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 267.31508ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 706.152674ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 7758.858674ms\n",
            "Task: Choosing top Q users\n",
            "Took 531.193361ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 700.772246ms\n",
            "Task: Extracting top q ratings\n",
            "Took 61.221463ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237975.419558ms\n",
            "Took 237977.296389ms\n",
            "Task: Sorting distances\n",
            "Took 1615.982224ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 11641.091158ms\n",
            "9 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 262.463098ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 717.365105ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 7609.214961ms\n",
            "Task: Choosing top Q users\n",
            "Took 521.359131ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 701.365405ms\n",
            "Task: Extracting top q ratings\n",
            "Took 60.292389ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 237609.41721ms\n",
            "Took 237611.263106ms\n",
            "Task: Sorting distances\n",
            "Took 1589.904842ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 12171.862571ms\n",
            "9 entries have no non-NAN neighbours\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "llXtJer7e2EG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e979619a-f6ef-4887-b427-cd1e566c4d8b"
      },
      "source": [
        "print(rmse_q300)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.404534079770204, 1.2823973117635439, 1.247372393289325, 1.1959231786321178, 1.189881280446423, 1.177705262948518, 1.167758882780713, 1.1527838530728955, 1.1542050113909228, 1.1678293427312367, 1.1662597354720212, 1.1769096906557126, 1.174123219198517, 1.1700075927386806, 1.1690441575089083, 1.1702632616032251]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qZsRcwNZe4Vc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "6cc8db8c-b708-403d-bb2a-4d7eb0ca698a"
      },
      "source": [
        "rmse_q400 = []\n",
        "for k in [10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,400]:\n",
        "  model = KnnRecommend(Metric.cosine_mean, Aggregate.average, k, 400,batch_size =526)\n",
        "  rmse = model.evaluate()\n",
        "  rmse_q400.append(rmse)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Task: Counting users and movies\n",
            "Took 273.149515ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 721.143697ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 7605.584206ms\n",
            "Task: Choosing top Q users\n",
            "Took 525.747403ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 698.391994ms\n",
            "Task: Extracting top q ratings\n",
            "Took 76.280479ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 280892.644212ms\n",
            "Took 280895.045712ms\n",
            "Task: Sorting distances\n",
            "Took 5333.522666ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 2200.847533ms\n",
            "1069 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 267.746819ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 697.627259ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10730.049613ms\n",
            "Task: Choosing top Q users\n",
            "Took 525.61927ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 692.508772ms\n",
            "Task: Extracting top q ratings\n",
            "Took 74.972774ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282234.582873ms\n",
            "Took 282236.48945ms\n",
            "Task: Sorting distances\n",
            "Took 2123.522908ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 2732.998698ms\n",
            "832 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 272.916481ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 712.086971ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10701.492281ms\n",
            "Task: Choosing top Q users\n",
            "Took 520.730503ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 689.698466ms\n",
            "Task: Extracting top q ratings\n",
            "Took 74.478016ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 281518.650701ms\n",
            "Took 281520.052468ms\n",
            "Task: Sorting distances\n",
            "Took 2113.100834ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 3244.120142ms\n",
            "766 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 265.934397ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 709.420637ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10487.124204ms\n",
            "Task: Choosing top Q users\n",
            "Took 530.163435ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 703.991604ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.914309ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 281700.822981ms\n",
            "Took 281701.897936ms\n",
            "Task: Sorting distances\n",
            "Took 2122.766144ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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          },
          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 4227.77901ms\n",
            "733 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 266.49487ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 710.753465ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10531.241032ms\n",
            "Task: Choosing top Q users\n",
            "Took 529.528308ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 703.859976ms\n",
            "Task: Extracting top q ratings\n",
            "Took 73.107876ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282306.263562ms\n",
            "Took 282307.433701ms\n",
            "Task: Sorting distances\n",
            "Took 2121.730931ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 5000.516656ms\n",
            "710 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 270.290884ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 729.648097ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10961.285141ms\n",
            "Task: Choosing top Q users\n",
            "Took 525.632142ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 704.131155ms\n",
            "Task: Extracting top q ratings\n",
            "Took 76.54071ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
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          },
          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 283531.452366ms\n",
            "Took 283533.239042ms\n",
            "Task: Sorting distances\n",
            "Took 2135.040972ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 5575.553601ms\n",
            "694 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 264.840199ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 705.291749ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10377.368373ms\n",
            "Task: Choosing top Q users\n",
            "Took 524.760418ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 704.653678ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.783198ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
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          },
          "metadata": {
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          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 281608.242935ms\n",
            "Took 281609.276885ms\n",
            "Task: Sorting distances\n",
            "Took 2118.981518ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 6324.500799ms\n",
            "586 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 269.415363ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 711.163524ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10360.420965ms\n",
            "Task: Choosing top Q users\n",
            "Took 536.820907ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 700.611996ms\n",
            "Task: Extracting top q ratings\n",
            "Took 73.02666ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
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            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 281946.935219ms\n",
            "Took 281948.038218ms\n",
            "Task: Sorting distances\n",
            "Took 2130.690763ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
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          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 6990.912359ms\n",
            "573 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 276.007563ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 708.851493ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 11417.213592ms\n",
            "Task: Choosing top Q users\n",
            "Took 521.284723ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 693.737455ms\n",
            "Task: Extracting top q ratings\n",
            "Took 75.409715ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
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            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282376.033714ms\n",
            "Took 282376.889229ms\n",
            "Task: Sorting distances\n",
            "Took 2108.971388ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 7625.808582ms\n",
            "520 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 414.51041ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 699.233712ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10708.205897ms\n",
            "Task: Choosing top Q users\n",
            "Took 527.920905ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 698.397809ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.18866ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282243.984913ms\n",
            "Took 282245.144449ms\n",
            "Task: Sorting distances\n",
            "Took 2113.568067ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 8236.813105ms\n",
            "503 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 267.469217ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 706.301728ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10697.122042ms\n",
            "Task: Choosing top Q users\n",
            "Took 527.177725ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 695.034615ms\n",
            "Task: Extracting top q ratings\n",
            "Took 73.374249ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282262.587919ms\n",
            "Took 282263.715854ms\n",
            "Task: Sorting distances\n",
            "Took 2098.278563ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 9057.918141ms\n",
            "474 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 270.553269ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 713.013154ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 10666.973531ms\n",
            "Task: Choosing top Q users\n",
            "Took 529.051941ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 701.415367ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.937834ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 283637.420389ms\n",
            "Took 283639.543745ms\n",
            "Task: Sorting distances\n",
            "Took 2113.109704ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 9689.588528ms\n",
            "446 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 393.243503ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 715.14173ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 12868.196687ms\n",
            "Task: Choosing top Q users\n",
            "Took 530.899682ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 694.890764ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.766373ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
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              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 283728.67979ms\n",
            "Took 283729.718253ms\n",
            "Task: Sorting distances\n",
            "Took 2119.23184ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 10519.260744ms\n",
            "388 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 271.535165ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 706.901541ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 12262.325905ms\n",
            "Task: Choosing top Q users\n",
            "Took 522.409295ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 709.03265ms\n",
            "Task: Extracting top q ratings\n",
            "Took 71.763392ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 283524.854132ms\n",
            "Took 283526.149105ms\n",
            "Task: Sorting distances\n",
            "Took 2119.3062ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 11013.889205ms\n",
            "68 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 270.276015ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 699.210642ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 11756.845545ms\n",
            "Task: Choosing top Q users\n",
            "Took 526.888823ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 704.260772ms\n",
            "Task: Extracting top q ratings\n",
            "Took 74.085271ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282772.407776ms\n",
            "Took 282774.535168ms\n",
            "Task: Sorting distances\n",
            "Took 2120.812012ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 11723.936151ms\n",
            "55 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 265.671932ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 702.985642ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 12829.253482ms\n",
            "Task: Choosing top Q users\n",
            "Took 537.712504ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 694.129348ms\n",
            "Task: Extracting top q ratings\n",
            "Took 75.150367ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282845.880163ms\n",
            "Took 282847.890357ms\n",
            "Task: Sorting distances\n",
            "Took 2137.902912ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 12312.604062ms\n",
            "28 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 1292.796045ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 719.584157ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 11395.121405ms\n",
            "Task: Choosing top Q users\n",
            "Took 529.438199ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 698.796116ms\n",
            "Task: Extracting top q ratings\n",
            "Took 71.533775ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282633.738466ms\n",
            "Took 282635.124274ms\n",
            "Task: Sorting distances\n",
            "Took 2133.196413ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
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              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 12904.277548ms\n",
            "7 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 288.153397ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 707.867525ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 11115.433186ms\n",
            "Task: Choosing top Q users\n",
            "Took 525.367261ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 697.993017ms\n",
            "Task: Extracting top q ratings\n",
            "Took 71.859629ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 282207.823847ms\n",
            "Took 282209.762117ms\n",
            "Task: Sorting distances\n",
            "Took 2114.296436ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 13819.789732ms\n",
            "7 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 298.844775ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 715.666351ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 12063.455667ms\n",
            "Task: Choosing top Q users\n",
            "Took 538.061796ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 698.983366ms\n",
            "Task: Extracting top q ratings\n",
            "Took 77.136703ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 284513.813587ms\n",
            "Took 284514.863704ms\n",
            "Task: Sorting distances\n",
            "Took 2140.313656ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 14446.812076ms\n",
            "6 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 951.095531ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 713.27132ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 11701.145299ms\n",
            "Task: Choosing top Q users\n",
            "Took 522.799431ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 689.649939ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.061489ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 281592.908539ms\n",
            "Took 281594.050682ms\n",
            "Task: Sorting distances\n",
            "Took 2118.142289ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 15499.415526ms\n",
            "6 entries have no non-NAN neighbours\n",
            "Task: Counting users and movies\n",
            "Took 369.158735ms\n",
            "Task: Repacking ratings to COO format\n",
            "Took 718.135975ms\n",
            "Task: Repacking ratings to CSR format\n",
            "Took 12211.908667ms\n",
            "Task: Choosing top Q users\n",
            "Took 530.244729ms\n",
            "Task: Computing movie mean ratings\n",
            "Took 704.672565ms\n",
            "Task: Extracting top q ratings\n",
            "Took 72.714876ms\n",
            "Task: Computing distance matrix\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='480189' value='480189'></progress>"
            ],
            "text/plain": [
              "[============================================================] 480189/480189"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 480189/480189 in 283714.513229ms\n",
            "Took 283715.58523ms\n",
            "Task: Sorting distances\n",
            "Took 2120.59696ms\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<progress style='width:60ex' max='1408395' value='1408395'></progress>"
            ],
            "text/plain": [
              "[============================================================] 1408395/1408395"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:10: RuntimeWarning: Mean of empty slice\n",
            "  # Remove the CWD from sys.path while we load stuff.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "Completed 1408395/1408395 in 15524.168412ms\n",
            "6 entries have no non-NAN neighbours\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ltgrMsBqfOJi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "40362c97-b231-480c-ffa8-9a46b3842be2"
      },
      "source": [
        "print(rmse_q400)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[1.433590870102874, 1.2435172900361502, 1.1940331027321116, 1.1825383536026703, 1.1745982573006954, 1.1683504929113735, 1.156811907488939, 1.1551567372936684, 1.1495411500416959, 1.1455476181774291, 1.1528535725494062, 1.158229238360067, 1.1627607272889398, 1.1564238000756273, 1.1663871323491555, 1.1641582974200089, 1.1632882048025546, 1.1607840375553615, 1.1585566350665832, 1.1578543673898085, 1.1592108635844491]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tZad_I0I2VUH"
      },
      "source": [
        "## Plot for RMSE"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LzhVjwjX2QGV"
      },
      "source": [
        "# plot\n",
        "# Since the training requires a long period of time, several google colab have been opened for training for each. Here is the collection of the resuit in list form\n",
        "\n",
        "b1024_q50 = [1.6391911090678126,1.3290757293832074, 1.229060916237895,1.2261753857708095, 1.1882200178770508, 1.215842018139431, 1.2386128807610244]\n",
        "\n",
        "b1024_q100 = [1.5647302569277624, 1.3260066653156044, 1.27198415759572, 1.2292377468016062, 1.2366169509844283, 1.2215330568310059]\n",
        "b256_q100 = [1.5647302569277624, 1.3260066653156044, 1.27198415759572, 1.2292377468016062, 1.2366169509844283, 1.2215330568310059]\n",
        "b526_q100 = [1.5647302569277624, 1.3260066653156044, 1.27198415759572, 1.2292377468016062, 1.2366169509844283, 1.2215330568310059]\n",
        "\n",
        "b1024_q200 = [1.4445087149858504, 1.334292225065238, 1.2281310210295484, 1.1990614168758105, 1.194342770805917, 1.172909858836841, 1.1591807085419106, 1.186584171075952, 1.186277799028361, 1.1876403254525656, 1.1910147135435265]\n",
        "b526_q200 = [1.4445087149858504, 1.334292225065238, 1.2281310210295484, 1.1990614168758105, 1.194342770805917, 1.172909858836841, 1.1591807085419106, 1.186584171075952, 1.186277799028361, 1.1876403254525656, 1.1910147135435265]\n",
        "\n",
        "b1024_q300 = [1.404534079770204, 1.2823973117635439, 1.247372393289325, 1.1959231786321178, 1.189881280446423, 1.177705262948518, 1.167758882780713, 1.1527838530728955, 1.1542050113909228, 1.1678293427312367, 1.1662597354720212, 1.1769096906557126, 1.174123219198517, 1.1700075927386806, 1.1690441575089083, 1.1702632616032251]\n",
        "b526_q300 = [1.404534079770204, 1.2823973117635439, 1.247372393289325, 1.1959231786321178, 1.189881280446423, 1.177705262948518, 1.167758882780713, 1.1527838530728955, 1.1542050113909228, 1.1678293427312367, 1.1662597354720212, 1.1769096906557126, 1.174123219198517, 1.1700075927386806, 1.1690441575089083, 1.1702632616032251]\n",
        "\n",
        "b1024_q400 = [1.433590870102874, 1.2435172900361502, 1.1940331027321116, 1.1825383536026703, 1.1745982573006954, 1.1683504929113735, 1.156811907488939, 1.1551567372936684, 1.1495411500416959, 1.1455476181774291, 1.1528535725494062, 1.158229238360067, 1.1627607272889398, 1.1564238000756273, 1.1663871323491555, 1.1641582974200089, 1.1632882048025546, 1.1607840375553615, 1.1585566350665832, 1.1578543673898085, 1.1592108635844491]\n",
        "b_526_q400 = [1.433590870102874, 1.2435172900361502, 1.1940331027321116, 1.1825383536026703, 1.1745982573006954, 1.1683504929113735, 1.156811907488939, 1.1551567372936684, 1.1495411500416959, 1.1455476181774291, 1.1528535725494062, 1.158229238360067, 1.1627607272889398, 1.1564238000756273, 1.1663871323491555, 1.1641582974200089, 1.1632882048025546, 1.1607840375553615, 1.1585566350665832, 1.1578543673898085, 1.1592108635844491]\n",
        "\n",
        "b_q500 = [1.5647302569277624,1.2700443654251998,1.2215330568310059,1.2215330568310059,1.2215330568310059,1.2215330568310059,1.2215330568310059]"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "MRLvgaRM2kpL",
        "outputId": "74b07e59-b5df-460b-a7d6-0fa5641ccde2"
      },
      "source": [
        "# plot directly with K and Q values\n",
        "import matplotlib.pyplot as plt\n",
        "plt.figure()\n",
        "fig, ax = plt.subplots() \n",
        "ax.plot([5,10,20,25,30,40,50],b1024_q50, label = \"Q = 50\")\n",
        "ax.plot([10,30,50,70,90,100],b1024_q100, label = \"Q = 100\")\n",
        "ax.plot([10,30,50,70,90,110,130,150,170,190,200],b1024_q200, label = \"Q = 200\")\n",
        "ax.plot([10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,300],b1024_q300, label = \"Q = 300\")\n",
        "ax.plot([10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,400],b1024_q400, label = \"Q = 400\")\n",
        "ax.plot([10,60,110,250,290,340,460],b_q500, label = \"Q = 500\")\n",
        "plt.xlabel(\"Size of K\")\n",
        "plt.ylabel(\"RMSE\")\n",
        "plt.title(\"RMSE value for batch size = 1024\")\n",
        "plt.legend()\n"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f56af971990>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 329
        },
        "id": "4Ke6ei3D2nNR",
        "outputId": "1fe2d9a5-a7a1-48bf-faa2-f95658fea3eb"
      },
      "source": [
        "# calculate the ratio of K/Q for better interpretation\n",
        "\n",
        "def ratio_func(rmselist,num):\n",
        "  ratio = []\n",
        "  for i in rmselist:  \n",
        "    ratio.append(i/num)\n",
        "  return ratio  \n",
        "\n",
        "ratio_50 = ratio_func([5,10,20,25,30,40,50],50)\n",
        "ratio_100 = ratio_func([10,30,50,70,90,100],100)\n",
        "ratio_200 = ratio_func([10,30,50,70,90,110,130,150,170,190,200],200)\n",
        "ratio_300 = ratio_func([10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,300],300)\n",
        "ratio_400 = ratio_func([10,30,50,70,90,110,130,150,170,190,210,230,250,270,290,310,330,350,370,390,400],400)\n",
        "ratio_500 = ratio_func([10,60,110,250,290,340,460],500)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.figure()\n",
        "fig, ax = plt.subplots() \n",
        "ax.plot(ratio_50,b1024_q50, label = \"Q = 50\")\n",
        "ax.plot(ratio_100,b1024_q100, label = \"Q = 100\")\n",
        "ax.plot(ratio_200,b1024_q200, label = \"Q = 200\")\n",
        "ax.plot(ratio_300,b1024_q300, label = \"Q = 300\")\n",
        "ax.plot(ratio_400,b1024_q400, label = \"Q = 400\")\n",
        "ax.plot(ratio_500,b_q500, label = \"Q = 500\")\n",
        "plt.xlabel(\"Ratio of K and Q (K/Q)\")\n",
        "plt.ylabel(\"RMSE\")\n",
        "plt.title(\"RMSE value\")\n",
        "plt.legend()\n"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f56a98c1590>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}