cluster analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv(r'C:\\Users\\shiva\\Desktop\\Mini project\\Clustering\\accredited_clg_3.csv')\n",
    "df1=pd.read_csv(r'C:\\Users\\shiva\\Desktop\\Mini project\\Clustering\\Unaccredited_clg_2.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['college_institution_id', 'name', 'university_id', 'district_code',\n",
       "       'state_code', 'city', 'autonomous', 'girl_exclusive',\n",
       "       'infrastructure_id', 'is_accredited', 'offers_scholarship',\n",
       "       'offers_loan', 'accreditation_id', 'accreditation_body', 'score',\n",
       "       'max_score', 'has_score', 'Total_Students', 'courses', 'c_Agriculture',\n",
       "       'c_Area_Studies', 'c_Arts', 'c_Commerce',\n",
       "       'c_Criminology_&_Forensic_Science', 'c_Cultural_Studies',\n",
       "       'c_Defence_Studies', 'c_Design', 'c_Disability_Studies', 'c_Education',\n",
       "       'c_Engineering_&_Technology', 'c_Fashion_Technology', 'c_Fine_Arts',\n",
       "       'c_Fisheries_Science', 'c_Foreign_Language', 'c_Gandhian_Studies',\n",
       "       'c_Home_Science', 'c_IT_&_Computer', 'c_Indian_Language',\n",
       "       'c_Journalism_&_Mass_Communication', 'c_Law',\n",
       "       'c_Library_&_Information_Science', 'c_Linguistics', 'c_Management',\n",
       "       'c_Marine_Science_/_Oceanography', 'c_Medical_Science',\n",
       "       'c_Oriental_Learning', 'c_Physical_Education', 'c_Religious_Studies',\n",
       "       'c_Science', 'c_Social_Science', 'c_Social_Work',\n",
       "       'c_Veterinary_&_Animal_Sciences', 'c_Women_Studies',\n",
       "       'infrastructure_score', 'Accr_Score_Percentage', 'Total_Teachers',\n",
       "       'student_to_teacher'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "accr_infra_score=df.loc[:,['college_institution_id','infrastructure_score']]\n",
    "unaccr_infra_score=df1.loc[:,['college_institution_id','infrastructure_score']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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>college_institution_id</th>\n",
       "      <th>infrastructure_score</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34211</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>52688</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>39714</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11142</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9082</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>43057</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>39522</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7611</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>27346</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>44599</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>18453</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>42143</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>50254</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>29418</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>18829</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>40845</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>8779</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>39843</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>39665</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>36491</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>19377</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>45957</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>39147</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>6567</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1351</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>7291</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>7487</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>41491</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>8305</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>18193</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5382</th>\n",
       "      <td>24898</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5383</th>\n",
       "      <td>39723</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5384</th>\n",
       "      <td>39660</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5385</th>\n",
       "      <td>39809</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5386</th>\n",
       "      <td>16610</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5387</th>\n",
       "      <td>10025</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5388</th>\n",
       "      <td>29098</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5389</th>\n",
       "      <td>40292</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5390</th>\n",
       "      <td>40299</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5391</th>\n",
       "      <td>39838</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5392</th>\n",
       "      <td>47557</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5393</th>\n",
       "      <td>39644</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5394</th>\n",
       "      <td>11003</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5395</th>\n",
       "      <td>28651</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5396</th>\n",
       "      <td>11242</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5397</th>\n",
       "      <td>11195</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5398</th>\n",
       "      <td>39345</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5399</th>\n",
       "      <td>11084</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5400</th>\n",
       "      <td>11101</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5401</th>\n",
       "      <td>11115</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5402</th>\n",
       "      <td>16537</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5403</th>\n",
       "      <td>11058</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5404</th>\n",
       "      <td>16535</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5405</th>\n",
       "      <td>21018</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5406</th>\n",
       "      <td>11085</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5407</th>\n",
       "      <td>39564</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5408</th>\n",
       "      <td>11001</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5409</th>\n",
       "      <td>39593</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5410</th>\n",
       "      <td>38396</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5411</th>\n",
       "      <td>12479</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5412 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      college_institution_id  infrastructure_score\n",
       "0                      34211                    14\n",
       "1                      52688                     9\n",
       "2                      39714                    10\n",
       "3                      11142                     5\n",
       "4                       9082                     2\n",
       "5                      43057                    23\n",
       "6                      39522                    15\n",
       "7                       7611                    14\n",
       "8                      27346                    14\n",
       "9                      44599                     8\n",
       "10                     18453                    11\n",
       "11                     42143                    10\n",
       "12                     50254                    10\n",
       "13                     29418                    18\n",
       "14                     18829                     6\n",
       "15                     40845                    10\n",
       "16                      8779                     7\n",
       "17                     39843                     7\n",
       "18                     39665                    12\n",
       "19                     36491                    17\n",
       "20                     19377                     4\n",
       "21                     45957                    12\n",
       "22                     39147                     4\n",
       "23                      6567                     5\n",
       "24                      1351                    16\n",
       "25                      7291                     6\n",
       "26                      7487                     8\n",
       "27                     41491                     7\n",
       "28                      8305                     4\n",
       "29                     18193                     8\n",
       "...                      ...                   ...\n",
       "5382                   24898                    12\n",
       "5383                   39723                     9\n",
       "5384                   39660                    11\n",
       "5385                   39809                     9\n",
       "5386                   16610                    17\n",
       "5387                   10025                    13\n",
       "5388                   29098                    11\n",
       "5389                   40292                    10\n",
       "5390                   40299                    14\n",
       "5391                   39838                    17\n",
       "5392                   47557                    15\n",
       "5393                   39644                     9\n",
       "5394                   11003                    11\n",
       "5395                   28651                    20\n",
       "5396                   11242                     4\n",
       "5397                   11195                    11\n",
       "5398                   39345                    12\n",
       "5399                   11084                    15\n",
       "5400                   11101                    14\n",
       "5401                   11115                    13\n",
       "5402                   16537                    17\n",
       "5403                   11058                    17\n",
       "5404                   16535                    17\n",
       "5405                   21018                     8\n",
       "5406                   11085                     8\n",
       "5407                   39564                     7\n",
       "5408                   11001                    11\n",
       "5409                   39593                     6\n",
       "5410                   38396                     6\n",
       "5411                   12479                    10\n",
       "\n",
       "[5412 rows x 2 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "infra_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unaccr_infra_score.infrastructure_score.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=np.array(accr_infra_score['infrastructure_score'])\n",
    "x1=list(unaccr_infra_score.infrastructure_score.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x)\n",
    "plt.ylabel('Number of colleges')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x1)\n",
    "plt.ylabel('No. of colleges')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_norm=preprocessing.normalize([x])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.014102  , 0.00906557, 0.01007286, ..., 0.00604372, 0.00604372,\n",
       "        0.01007286]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x_norm[0])\n",
    "plt.ylabel('Number of colleges')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import NearestNeighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "nbrs=NearestNeighbors(n_neighbors=2,algorithm='ball_tree').fit(x_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "distances,indices=nbrs.kneighbors(x_norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.mixture import GaussianMixture"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_reshape=x.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[14],\n",
       "       [ 9],\n",
       "       [10],\n",
       "       ...,\n",
       "       [ 6],\n",
       "       [ 6],\n",
       "       [10]], dtype=int64)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_reshape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "gmm = GaussianMixture(n_components=5, covariance_type='full').fit(x_reshape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction_gmm = gmm.predict(x_reshape)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 1, ..., 2, 2, 1], dtype=int64)"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_gmm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "probs = gmm.predict_proba(x_reshape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.43932885e-03, 6.11245938e-01, 1.45733891e-02, 3.63309158e-01,\n",
       "        1.43218632e-03],\n",
       "       [9.36491591e-04, 3.94802624e-01, 6.03073189e-01, 9.03300200e-05,\n",
       "        1.09736497e-03],\n",
       "       [1.37718864e-03, 6.38535124e-01, 3.58215459e-01, 8.79971141e-04,\n",
       "        9.92257166e-04],\n",
       "       ...,\n",
       "       [2.46501016e-04, 1.90828321e-02, 9.79102855e-01, 1.02298791e-08,\n",
       "        1.56780137e-03],\n",
       "       [2.46501016e-04, 1.90828321e-02, 9.79102855e-01, 1.02298791e-08,\n",
       "        1.56780137e-03],\n",
       "       [1.37718864e-03, 6.38535124e-01, 3.58215459e-01, 8.79971141e-04,\n",
       "        9.92257166e-04]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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