sparsecluster_demo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "dbaa89e8",
   "metadata": {},
   "source": [
    "# sparsecluster demo"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6765b59b",
   "metadata": {},
   "source": [
    "`sparsecluster` is a wrapper around `pynndescent` for efficient construction of nearest-neighbor graphs and `gbbs` for graph-based hierarchical clustering. the basic idea is to use an approximate distance matrix as input for linkage, in order to allow for clustering of large (and sparse) datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "18481afc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sparsecluster\n",
    "import fastcluster\n",
    "from matplotlib import pyplot as plt\n",
    "import scipy.cluster.hierarchy\n",
    "import sklearn.cluster\n",
    "import scipy.cluster\n",
    "import sklearn.datasets\n",
    "import pandas as pd\n",
    "import time\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d699e555",
   "metadata": {},
   "source": [
    "## simple demo example"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14bfa3f2",
   "metadata": {},
   "source": [
    "for initial demo, use a random matrix for 10 samples and 5 features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a922ca69",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "X=np.random.rand(10,5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f95ae9dc",
   "metadata": {},
   "source": [
    "as baseline, we construct a full distance matrix using `scipy.spatial.distance.pdist` and an exact linkage using `fastcluster`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8ba18afc",
   "metadata": {},
   "outputs": [],
   "source": [
    "metric='euclidean'\n",
    "d0 = scipy.spatial.distance.pdist(X, metric=metric)\n",
    "Z0s = fastcluster.linkage(d0, metric=metric, method='single')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b52011f",
   "metadata": {},
   "source": [
    "now we use `sparsecluster` to construct distances and linkages for either 10 neighbors (i.e., the full matrix) or 5 neighbors (an approximation). during nearest-neighbor descent, we can store additional distances for `n_backup` non-nearest neighbors. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "69444ba2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z1s,d1 = sparsecluster.linkage(X, metric=metric, method='single', n_neighbors=10, return_distance=True)\n",
    "Z2s,d2 = sparsecluster.linkage(X, metric=metric, method='single', n_neighbors=5, n_backup=0, return_distance=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ed37c020",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '5 nearest neighbors')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(1,3,figsize=(12,4))\n",
    "axs[0].imshow(scipy.spatial.distance.squareform(d0), cmap=plt.cm.viridis, vmin=0, vmax=d0.max())\n",
    "axs[0].set_title('full distance matrix')\n",
    "axs[1].imshow(d1.todense(), cmap=plt.cm.viridis, vmin=0, vmax=d0.max())\n",
    "axs[1].set_title('10 nearest neighbors')\n",
    "axs[2].imshow(d2.todense(), cmap=plt.cm.viridis, vmin=0, vmax=d0.max())\n",
    "axs[2].set_title('5 nearest neighbors')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e70ea26",
   "metadata": {},
   "source": [
    "even though the sparse approximation is missing entries for larger distances, the resulting dendrograms (using single linkage) are equivalent, possibly up to a re-ordering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b934ed91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '5 neighbors')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(1,3,figsize=(6,5),sharex=True)\n",
    "L0=scipy.cluster.hierarchy.dendrogram(Z0s,ax=axs[0],orientation='right')\n",
    "L1=scipy.cluster.hierarchy.dendrogram(Z1s,ax=axs[1],orientation='right')\n",
    "L2=scipy.cluster.hierarchy.dendrogram(Z2s,ax=axs[2],orientation='right')\n",
    "axs[0].set_title('full matrix')\n",
    "axs[1].set_title('10 neighbors')\n",
    "axs[2].set_title('5 neighbors')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "353eb174",
   "metadata": {},
   "source": [
    "try the same thing with complete or weighted linkage (but skipping the re-calculation of the distance matrices): 5 nearest neighbors is not always enough"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "22ceede0",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z0c = fastcluster.linkage(d0, metric=metric, method='complete')\n",
    "Z1c = sparsecluster.linkage(X, dist=d1, metric=metric, method='complete', n_neighbors=10)\n",
    "Z2c = sparsecluster.linkage(X, dist=d2, metric=metric, method='complete', n_neighbors=5)\n",
    "\n",
    "Z0w = fastcluster.linkage(d0, metric=metric, method='weighted')\n",
    "Z1w = sparsecluster.linkage(X, dist=d1, metric=metric, method='weighted', n_neighbors=10)\n",
    "Z2w = sparsecluster.linkage(X, dist=d2, metric=metric, method='weighted', n_neighbors=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d505bea0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'weighted linkage')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x576 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(2,3,figsize=(6,8))\n",
    "\n",
    "L0=scipy.cluster.hierarchy.dendrogram(Z0c,ax=axs[0,0],orientation='right')\n",
    "L1=scipy.cluster.hierarchy.dendrogram(Z1c,ax=axs[0,1],orientation='right')\n",
    "L2=scipy.cluster.hierarchy.dendrogram(Z2c,ax=axs[0,2],orientation='right')\n",
    "\n",
    "L0=scipy.cluster.hierarchy.dendrogram(Z0w,ax=axs[1,0],orientation='right')\n",
    "L1=scipy.cluster.hierarchy.dendrogram(Z1w,ax=axs[1,1],orientation='right')\n",
    "L2=scipy.cluster.hierarchy.dendrogram(Z2w,ax=axs[1,2],orientation='right')\n",
    "\n",
    "axs[0,0].set_title('full matrix')\n",
    "axs[0,1].set_title('10 neighbors')\n",
    "axs[0,2].set_title('5 neighbors')\n",
    "\n",
    "axs[1,0].set_title('full matrix')\n",
    "axs[1,1].set_title('10 neighbors')\n",
    "axs[1,2].set_title('5 neighbors')\n",
    "\n",
    "axs[0,0].set_ylabel(\"complete linkage\")\n",
    "axs[1,0].set_ylabel(\"weighted linkage\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e4c837b",
   "metadata": {},
   "source": [
    "## how many neighbors are needed?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "323e9b9b",
   "metadata": {},
   "source": [
    "use the `digits` dataset to compare the `sparsecluster` linkages to the `fastcluster` linkages "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "663bf8a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = sklearn.datasets.load_digits()\n",
    "X, y = digits.data, digits.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "50ba5ea7",
   "metadata": {},
   "outputs": [],
   "source": [
    "nc=10\n",
    "metric='cosine'\n",
    "\n",
    "fastcluster_linkage = {}\n",
    "for method in (\"single\", \"complete\", \"weighted\"):\n",
    "    fastcluster_linkage[method] = fastcluster.linkage(X, method=method, metric=metric)\n",
    "    \n",
    "sparsecluster_linkage = {}\n",
    "for nfrac in [.01, .02, .05, .1, .2, .5]:\n",
    "    for bfrac in [0, 1, 5]:\n",
    "        nn = int(nfrac*X.shape[0])\n",
    "        for r in range(3):\n",
    "            Zs, ds = sparsecluster.linkage(X, metric=metric, method='single', \n",
    "                                           n_neighbors=nn, n_backup=bfrac*nn, \n",
    "                                           n_jobs=8, random_state=r,\n",
    "                                           return_distance=True)\n",
    "            \n",
    "            Zc = sparsecluster.linkage(X, dist=ds, metric=metric, method='complete')           \n",
    "            Zw = sparsecluster.linkage(X, dist=ds, metric=metric, method='weighted')           \n",
    "\n",
    "            sparsecluster_linkage[('single',nfrac, bfrac, r)] = Zs\n",
    "            sparsecluster_linkage[('complete',nfrac, bfrac, r)] = Zc\n",
    "            sparsecluster_linkage[('weighted',nfrac, bfrac, r)] = Zw"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d517a0d6",
   "metadata": {},
   "source": [
    "we use \"cophenetic distances\" (i.e., distances along the tree) to compare the linkages. here's a scatter plot of cophenetic distances for fastcluster vs. sparsecluster linkage (10% neighbors calculated). for single linkage, the results are identical, for average or complete linkage they are similar for small distances and more divergent for larger ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "66792ae0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x252 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axs=plt.subplots(1,3,figsize=(10,3.5), sharex=True, sharey=True)\n",
    "for n,method in enumerate(['single','weighted','complete']):\n",
    "    d1=scipy.cluster.hierarchy.cophenet(fastcluster_linkage[method])\n",
    "    d2=scipy.cluster.hierarchy.cophenet(sparsecluster_linkage[(method,.01,1,0)])\n",
    "    axs[n].plot(d1,d2,'.')\n",
    "    if n==1:\n",
    "        axs[n].set_xlabel('cophenetic distances in fastcluster linkage')\n",
    "    if n==0:\n",
    "        axs[n].set_ylabel('cophenetic distances in sparsecluster linkage')\n",
    "    axs[n].set_title(method)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5e72a24",
   "metadata": {},
   "source": [
    "more systematically, we can calculate the correlation between these cophenetic distances for different linkage methods and different number of neighbors and backup distances stored: for single linkage, the two methods give identical results, while for weighted or complete linkage, only small cophenetic distances are correctly reproduced. including backup distances helps especially for few neighbors and weighted linkage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a5736a57",
   "metadata": {},
   "outputs": [],
   "source": [
    "cc=dict((k,scipy.stats.pearsonr(scipy.cluster.hierarchy.cophenet(fastcluster_linkage[k[0]]),\n",
    "                                scipy.cluster.hierarchy.cophenet(sparsecluster_linkage[k]))[0]) \n",
    "        for k in sparsecluster_linkage.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1495da7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 442.375x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g=sns.relplot(data=pd.Series(cc).reset_index().rename({'level_1': 'fraction neighbors',\n",
    "                                                     'level_2': 'n_backup',\n",
    "                                                     'level_0': 'method',\n",
    "                                                     0: 'correlation'},axis=1),     \n",
    "            x='fraction neighbors',y='correlation',style='n_backup',hue='method', kind='line')\n",
    "g.ax.set_xscale('log')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd00cea5",
   "metadata": {},
   "source": [
    "## benchmarking time and memory usage"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c73ca8c",
   "metadata": {},
   "source": [
    "use the `20newsgroups_vectorized` sparse dataset for benchmarking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5fc0447f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<11314x130107 sparse matrix of type '<class 'numpy.float64'>'\n",
       "\twith 1787565 stored elements in Compressed Sparse Row format>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext memory_profiler\n",
    "\n",
    "data,labels = sklearn.datasets.fetch_20newsgroups_vectorized(subset='train',\n",
    "                                                             data_home='.',\n",
    "                                                             return_X_y=True)\n",
    "data_dense=np.asarray(data.todense())\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ea837bb",
   "metadata": {},
   "source": [
    "here's time and memory usage for `sparsecluster`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "769359b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "peak memory: 7001.49 MiB, increment: 1468.89 MiB\n",
      "CPU times: user 42min 56s, sys: 1min 5s, total: 44min 1s\n",
      "Wall time: 6min 35s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "%memit Zs = sparsecluster.linkage(data, metric='cosine', method='single',  n_neighbors=100, n_backup=500, n_jobs=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "488adc5f",
   "metadata": {},
   "source": [
    "here's time and memory usage for `sparsecluster`, but with dense input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e0bd47d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "peak memory: 14599.66 MiB, increment: 7598.12 MiB\n",
      "CPU times: user 10h 59min 40s, sys: 10min 32s, total: 11h 10min 13s\n",
      "Wall time: 1h 26min 56s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "%memit Zs = sparsecluster.linkage(data_dense, metric='cosine', method='single',  n_neighbors=100, n_backup=500, n_jobs=8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc69dd9",
   "metadata": {},
   "source": [
    "here's time and memory usage for `fastcluster`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5681ff89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "peak memory: 13570.23 MiB, increment: 0.00 MiB\n",
      "CPU times: user 4h 9min 18s, sys: 11min 40s, total: 4h 20min 59s\n",
      "Wall time: 1h 11min 56s\n"
     ]
    }
   ],
   "source": [
    "%%time \n",
    "%memit Z0 = fastcluster.linkage(data_dense, metric='cosine', method='single')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57a340a0",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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