HyperGraph.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4f7c2d27-614e-475a-a3d9-c235f12b5607",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "import scipy as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "65362d04-b31d-46f8-a996-356375611f0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "310e11ad-b9f3-4d5a-80e0-d44412023c42",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    z = np.exp(-x)\n",
    "\n",
    "    return 1 / (1 + z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4fd0521a-2f81-4645-875d-a7a16fd7f499",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loading Iris Datasets:\n",
    "iris = sns.load_dataset(\"iris\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5d803164-2cc7-4c21-8067-cd88a8001779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a2a10993-ba9f-4781-a4b8-79c1f1ba18a9",
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.copy().iloc[:, :-2].values\n",
    "y = pd.get_dummies(iris.copy().iloc[:, -1]).values\n",
    "\n",
    "n = X.shape[0]\n",
    "m = X.shape[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "384e0c56-3f75-4f68-bd2d-6e90177c2be7",
   "metadata": {},
   "outputs": [],
   "source": [
    "I_n = np.eye(n, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "878770e0-1e2d-4d8d-a10b-86ce190aa30c",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = np.linalg.inv(X @ X.T + I_n) @ X @ X.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aa658822-b382-4765-987c-ec4a04602778",
   "metadata": {},
   "outputs": [],
   "source": [
    "A = 0.5*(np.abs(Z) + np.abs(Z.T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4f1fb9bb-fe2b-49c6-b327-641a1ec5e794",
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4860f790-ebc4-49c6-a84e-232d63fa15af",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-11-68ce05380a4f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     13\u001b[0m     \u001b[0munique2\u001b[0m  \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mh\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mH_preprocess\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[0mmask1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msort\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_preprocess\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mu\u001b[0m \u001b[1;32min\u001b[0m \u001b[0munique\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m     \u001b[0mmask2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msort\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_preprocess\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mu\u001b[0m \u001b[1;32min\u001b[0m \u001b[0munique2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     16\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m     \u001b[0mmask\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmask1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m&\u001b[0m \u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmask2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-11-68ce05380a4f>\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[0;32m     13\u001b[0m     \u001b[0munique2\u001b[0m  \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0marray\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtuple\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mh\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mflatten\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mh\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mH_preprocess\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[0mmask1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msort\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_preprocess\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mu\u001b[0m \u001b[1;32min\u001b[0m \u001b[0munique\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 15\u001b[1;33m     \u001b[0mmask2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msort\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mH_preprocess\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mT\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mu\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mu\u001b[0m \u001b[1;32min\u001b[0m \u001b[0munique2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     16\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m     \u001b[0mmask\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmask1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m&\u001b[0m \u001b[0mset\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmask2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<__array_function__ internals>\u001b[0m in \u001b[0;36margmax\u001b[1;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\AIML\\lib\\site-packages\\numpy\\core\\fromnumeric.py\u001b[0m in \u001b[0;36margmax\u001b[1;34m(a, axis, out)\u001b[0m\n\u001b[0;32m   1193\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1194\u001b[0m     \"\"\"\n\u001b[1;32m-> 1195\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_wrapfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'argmax'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mout\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mout\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1196\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1197\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\.conda\\envs\\AIML\\lib\\site-packages\\numpy\\core\\fromnumeric.py\u001b[0m in \u001b[0;36m_wrapfunc\u001b[1;34m(obj, method, *args, **kwds)\u001b[0m\n\u001b[0;32m     55\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     56\u001b[0m     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 57\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mbound\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     58\u001b[0m     \u001b[1;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     59\u001b[0m         \u001b[1;31m# A TypeError occurs if the object does have such a method in its\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "hyper_edges_list = []\n",
    "n = X.shape[0]\n",
    "for i in range(n):\n",
    "    dist = np.linalg.norm(X[i] - X, axis=1)\n",
    "    hyper_edge = np.zeros(n)\n",
    "    hyper_edge[np.argsort(dist)[:k + 1]] = 1\n",
    "    hyper_edges_list.append(hyper_edge.reshape(-1, 1))\n",
    "    \n",
    "H_preprocess = np.hstack(hyper_edges_list)\n",
    "while True:\n",
    "    shape_pre = H_preprocess.shape\n",
    "    unique = np.array(list(set(tuple(h.flatten()) for h in H_preprocess)))\n",
    "    unique2  = np.array(list(set(tuple(h.flatten()) for h in H_preprocess.T)))\n",
    "    mask1 = np.sort([np.argmax(np.sum(H_preprocess == u, axis=1)) for u in unique])\n",
    "    mask2 = np.sort([np.argmax(np.sum(H_preprocess.T == u, axis=1)) for u in unique2])\n",
    "    \n",
    "    mask = list(set(mask1) & set(mask2))\n",
    "    \n",
    "    H_preprocess = H_preprocess[mask]\n",
    "    H_preprocess = H_preprocess[:, mask]\n",
    "    \n",
    "    if np.linalg.cond(H_preprocess) < 1/sys.float_info.epsilon:\n",
    "        H = H_preprocess\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "906e2203-04be-4e6a-881d-ca28c934dcb3",
   "metadata": {},
   "outputs": [],
   "source": [
    "H_preprocess.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5e00015c-8cf7-4362-aca0-10bf4cf268c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "H.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17f39b02-0541-4800-a05d-5ad81196e57c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "size = H.shape[0]\n",
    "D_v = np.eye(size) * H.sum(axis= 1)\n",
    "D_e = np.eye(size) * H.sum(axis= 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5cb3acc2-0ec8-49b8-8922-664c82028634",
   "metadata": {},
   "outputs": [],
   "source": [
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9a5a6e6b-d713-4630-957a-a333dd105e84",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.array(list(set(tuple(h.flatten()) for h in H))).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d4bdb6d3-8e3c-4bfa-8f44-6ba5b49c3538",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.array(list(set(tuple(h.flatten()) for h in H.T))).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ef9e027e-f755-4175-bbca-3b76f9ecbfa2",
   "metadata": {},
   "outputs": [],
   "source": [
    "H[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a6cfd9ac-37c7-466f-a966-c6cef007ad12",
   "metadata": {},
   "outputs": [],
   "source": [
    "D_v_inv = np.linalg.inv(D_v)\n",
    "D_e_inv = np.linalg.inv(D_e)\n",
    "D_v_inv_frac = sp.linalg.fractional_matrix_power(D_v, -0.5)\n",
    "D_e_inv_frac = sp.linalg.fractional_matrix_power(D_e, -0.5)\n",
    "H_inv = np.linalg.inv(H)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8070283-a06a-4433-a516-d5efa6870c37",
   "metadata": {},
   "outputs": [],
   "source": [
    "H.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1f84796-da95-4c3a-a030-7930accb24d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "S = D_v_inv_frac @ H @ D_e_inv @ H_inv @ D_v_inv_frac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b3c0de31-5c77-4ec3-81ff-496a1137ed59",
   "metadata": {},
   "outputs": [],
   "source": [
    "# X = X[mask]\n",
    "# y = y[mask]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "77c17159-181a-41ac-b26f-bcaf74fe5d19",
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 20\n",
    "Theta = np.random.normal(size=(m, L))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2e05ad16-c254-45d0-9718-c9be95b5334d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Z = sigmoid(S @ X @ Theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c39edb0-e503-4403-85fb-5422cb0d6d72",
   "metadata": {},
   "outputs": [],
   "source": [
    "I = np.eye(L, L)\n",
    "M = np.eye(size, size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc1584c8-685d-451f-9291-e338990d8722",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = np.linalg.inv(Z.T @ S.T @ M @ S @ Z + I) @ Z.T @ S.T @ M @ y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7185b3b-0f67-447a-afec-f4c8daed629e",
   "metadata": {},
   "outputs": [],
   "source": [
    "beta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2dadd3e0-a614-459e-aa0e-8f84ac19c786",
   "metadata": {},
   "outputs": [],
   "source": [
    "sum(np.argmax(S @ Z @ beta, axis=1) == np.argmax(y, axis=1)) / y.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "616dc806-9cad-4cf7-a326-304245802a85",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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