Testing2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4b93cf5b-abb1-4cc8-9b21-f9d8adb882b9",
   "metadata": {},
   "source": [
    "# Testing 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "974aa857-d38b-4c5c-aa5f-665fe452b903",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "821490c9-84b6-472d-b850-a2df59c7fc1b",
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      input1  input2  input3  input4  input5  input6  input7  input8  input9  \\\n",
       "0          0       1       6      15      12       1       0       0       0   \n",
       "1          0       0      10      16       6       0       0       0       0   \n",
       "2          0       0       8      15      16      13       0       0       0   \n",
       "3          0       0       0       3      11      16       0       0       0   \n",
       "4          0       0       5      14       4       0       0       0       0   \n",
       "...      ...     ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "5615       0       0       4      10      13       6       0       0       0   \n",
       "5616       0       0       6      16      13      11       1       0       0   \n",
       "5617       0       0       1      11      15       1       0       0       0   \n",
       "5618       0       0       2      10       7       0       0       0       0   \n",
       "5619       0       0      10      14       8       1       0       0       0   \n",
       "\n",
       "      input10  ...  input56  input57  input58  input59  input60  input61  \\\n",
       "0           7  ...        0        0        0        6       14        7   \n",
       "1           7  ...        0        0        0       10       16       15   \n",
       "2           1  ...        0        0        0        9       14        0   \n",
       "3           0  ...        0        0        0        0        1       15   \n",
       "4           0  ...        0        0        0        4       12       14   \n",
       "...       ...  ...      ...      ...      ...      ...      ...      ...   \n",
       "5615        1  ...        0        0        0        2       14       15   \n",
       "5616        0  ...        0        0        0        6       16       14   \n",
       "5617        0  ...        0        0        0        2        9       13   \n",
       "5618        0  ...        0        0        0        5       12       16   \n",
       "5619        2  ...        0        0        1        8       12       14   \n",
       "\n",
       "      input62  input63  input64  class  \n",
       "0           1        0        0      0  \n",
       "1           3        0        0      0  \n",
       "2           0        0        0      7  \n",
       "3           2        0        0      4  \n",
       "4           7        0        0      6  \n",
       "...       ...      ...      ...    ...  \n",
       "5615        9        0        0      9  \n",
       "5616        6        0        0      0  \n",
       "5617        6        0        0      8  \n",
       "5618       12        0        0      9  \n",
       "5619       12        1        0      8  \n",
       "\n",
       "[5620 rows x 65 columns]"
      ],
      "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>input1</th>\n      <th>input2</th>\n      <th>input3</th>\n      <th>input4</th>\n      <th>input5</th>\n      <th>input6</th>\n      <th>input7</th>\n      <th>input8</th>\n      <th>input9</th>\n      <th>input10</th>\n      <th>...</th>\n      <th>input56</th>\n      <th>input57</th>\n      <th>input58</th>\n      <th>input59</th>\n      <th>input60</th>\n      <th>input61</th>\n      <th>input62</th>\n      <th>input63</th>\n      <th>input64</th>\n      <th>class</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>1</td>\n      <td>6</td>\n      <td>15</td>\n      <td>12</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>7</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>14</td>\n      <td>7</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>16</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>7</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>16</td>\n      <td>15</td>\n      <td>3</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0</td>\n      <td>0</td>\n      <td>8</td>\n      <td>15</td>\n      <td>16</td>\n      <td>13</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>9</td>\n      <td>14</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>3</td>\n      <td>11</td>\n      <td>16</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>15</td>\n      <td>2</td>\n      <td>0</td>\n      <td>0</td>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0</td>\n      <td>0</td>\n      <td>5</td>\n      <td>14</td>\n      <td>4</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>4</td>\n      <td>12</td>\n      <td>14</td>\n      <td>7</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>5615</th>\n      <td>0</td>\n      <td>0</td>\n      <td>4</td>\n      <td>10</td>\n      <td>13</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>14</td>\n      <td>15</td>\n      <td>9</td>\n      <td>0</td>\n      <td>0</td>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>5616</th>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>16</td>\n      <td>13</td>\n      <td>11</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>16</td>\n      <td>14</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5617</th>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>11</td>\n      <td>15</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>9</td>\n      <td>13</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>5618</th>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>10</td>\n      <td>7</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>5</td>\n      <td>12</td>\n      <td>16</td>\n      <td>12</td>\n      <td>0</td>\n      <td>0</td>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>5619</th>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>14</td>\n      <td>8</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>8</td>\n      <td>12</td>\n      <td>14</td>\n      <td>12</td>\n      <td>1</td>\n      <td>0</td>\n      <td>8</td>\n    </tr>\n  </tbody>\n</table>\n<p>5620 rows × 65 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "source": [
    "optdigits_df=pd.read_csv('optdigits_csv.csv')\n",
    "optdigits_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "91eace18-4a1e-4a86-87f0-d7569310b226",
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      input1  input2  input3  input4  input5  input6  input7  input8  input9  \\\n",
       "0          0       1       6      15      12       1       0       0       0   \n",
       "1          0       0      10      16       6       0       0       0       0   \n",
       "2          0       0       8      15      16      13       0       0       0   \n",
       "3          0       0       0       3      11      16       0       0       0   \n",
       "4          0       0       5      14       4       0       0       0       0   \n",
       "...      ...     ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "5615       0       0       4      10      13       6       0       0       0   \n",
       "5616       0       0       6      16      13      11       1       0       0   \n",
       "5617       0       0       1      11      15       1       0       0       0   \n",
       "5618       0       0       2      10       7       0       0       0       0   \n",
       "5619       0       0      10      14       8       1       0       0       0   \n",
       "\n",
       "      input10  ...  input55  input56  input57  input58  input59  input60  \\\n",
       "0           7  ...        0        0        0        0        6       14   \n",
       "1           7  ...        3        0        0        0       10       16   \n",
       "2           1  ...        0        0        0        0        9       14   \n",
       "3           0  ...        0        0        0        0        0        1   \n",
       "4           0  ...       12        0        0        0        4       12   \n",
       "...       ...  ...      ...      ...      ...      ...      ...      ...   \n",
       "5615        1  ...        4        0        0        0        2       14   \n",
       "5616        0  ...        1        0        0        0        6       16   \n",
       "5617        0  ...        0        0        0        0        2        9   \n",
       "5618        0  ...        2        0        0        0        5       12   \n",
       "5619        2  ...        8        0        0        1        8       12   \n",
       "\n",
       "      input61  input62  input63  input64  \n",
       "0           7        1        0        0  \n",
       "1          15        3        0        0  \n",
       "2           0        0        0        0  \n",
       "3          15        2        0        0  \n",
       "4          14        7        0        0  \n",
       "...       ...      ...      ...      ...  \n",
       "5615       15        9        0        0  \n",
       "5616       14        6        0        0  \n",
       "5617       13        6        0        0  \n",
       "5618       16       12        0        0  \n",
       "5619       14       12        1        0  \n",
       "\n",
       "[5620 rows x 64 columns]"
      ],
      "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>input1</th>\n      <th>input2</th>\n      <th>input3</th>\n      <th>input4</th>\n      <th>input5</th>\n      <th>input6</th>\n      <th>input7</th>\n      <th>input8</th>\n      <th>input9</th>\n      <th>input10</th>\n      <th>...</th>\n      <th>input55</th>\n      <th>input56</th>\n      <th>input57</th>\n      <th>input58</th>\n      <th>input59</th>\n      <th>input60</th>\n      <th>input61</th>\n      <th>input62</th>\n      <th>input63</th>\n      <th>input64</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>1</td>\n      <td>6</td>\n      <td>15</td>\n      <td>12</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>7</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>14</td>\n      <td>7</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>16</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>7</td>\n      <td>...</td>\n      <td>3</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>16</td>\n      <td>15</td>\n      <td>3</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>0</td>\n      <td>0</td>\n      <td>8</td>\n      <td>15</td>\n      <td>16</td>\n      <td>13</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>9</td>\n      <td>14</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>3</td>\n      <td>11</td>\n      <td>16</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>15</td>\n      <td>2</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>0</td>\n      <td>0</td>\n      <td>5</td>\n      <td>14</td>\n      <td>4</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>12</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>4</td>\n      <td>12</td>\n      <td>14</td>\n      <td>7</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>5615</th>\n      <td>0</td>\n      <td>0</td>\n      <td>4</td>\n      <td>10</td>\n      <td>13</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>...</td>\n      <td>4</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>14</td>\n      <td>15</td>\n      <td>9</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5616</th>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>16</td>\n      <td>13</td>\n      <td>11</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>6</td>\n      <td>16</td>\n      <td>14</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5617</th>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>11</td>\n      <td>15</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>9</td>\n      <td>13</td>\n      <td>6</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5618</th>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>10</td>\n      <td>7</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>...</td>\n      <td>2</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>5</td>\n      <td>12</td>\n      <td>16</td>\n      <td>12</td>\n      <td>0</td>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5619</th>\n      <td>0</td>\n      <td>0</td>\n      <td>10</td>\n      <td>14</td>\n      <td>8</td>\n      <td>1</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>...</td>\n      <td>8</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>8</td>\n      <td>12</td>\n      <td>14</td>\n      <td>12</td>\n      <td>1</td>\n      <td>0</td>\n    </tr>\n  </tbody>\n</table>\n<p>5620 rows × 64 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "source": [
    "data_features=optdigits_df.iloc[:,:64]\n",
    "data_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "16468339-5880-4be8-9502-1c86a9abe715",
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "      class\n",
       "0         0\n",
       "1         0\n",
       "2         7\n",
       "3         4\n",
       "4         6\n",
       "...     ...\n",
       "5615      9\n",
       "5616      0\n",
       "5617      8\n",
       "5618      9\n",
       "5619      8\n",
       "\n",
       "[5620 rows x 1 columns]"
      ],
      "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>class</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>7</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>4</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>6</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>5615</th>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>5616</th>\n      <td>0</td>\n    </tr>\n    <tr>\n      <th>5617</th>\n      <td>8</td>\n    </tr>\n    <tr>\n      <th>5618</th>\n      <td>9</td>\n    </tr>\n    <tr>\n      <th>5619</th>\n      <td>8</td>\n    </tr>\n  </tbody>\n</table>\n<p>5620 rows × 1 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "data_labels=optdigits_df.iloc[:,64:]\n",
    "data_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cca51f90-5fc6-406c-a6a0-53d01cb3f215",
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalising_function(X):\n",
    "    X_standard=StandardScaler().fit_transform(X)\n",
    "    X_mean=np.mean(X_standard,axis=0)\n",
    "    X_cov=(X_standard - X_mean).T.dot((X_standard - X_mean))/(X_standard.shape[0]-1)\n",
    "    return X_standard,X_mean,X_cov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2fbe4aa9-6e43-436c-b54f-dd643d43cb3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Principal_Component_Analysis(X):\n",
    "    X_standard,X_mean,X_cov=normalising_function(X)\n",
    "    \n",
    "    X_standard=X_standard-X_standard.mean(axis=0)\n",
    "    \n",
    "    fig=plt.figure(figsize=(10,10))\n",
    "    sns.heatmap(pd.DataFrame(X_cov))\n",
    "    plt.show()\n",
    "    \n",
    "    eigenvalues, eigenvectors = np.linalg.eig(X_cov)\n",
    "    \n",
    "    unsorted_eigen_value_vector_pair=[(np.abs(eigenvalues[i]),eigenvectors[:,i]) for i in range(len(eigenvalues))]\n",
    "    sorted_eigen_value_vector_pair=sorted(unsorted_eigen_value_vector_pair, reverse=True, key=lambda x:x[0])\n",
    "\n",
    "    fig=plt.figure(figsize=(15,4))\n",
    "    sns.heatmap(pd.DataFrame([pair[1] for pair in sorted_eigen_value_vector_pair[0:21]]),annot=False,cmap='coolwarm',vmin=-0.5,vmax=0.5)\n",
    "    plt.ylabel(\"Ranked Eigen Values\")\n",
    "    plt.xlabel(\"Eigen Vector Components\")\n",
    "    plt.show()\n",
    "    \n",
    "    lam_sum=sum(eigenvalues)\n",
    "    explained_variance=[(lam_k/lam_sum) for lam_k in sorted(eigenvalues,reverse=True)]\n",
    "    \n",
    "    plt.figure(figsize=(6,4))\n",
    "    plt.bar(range(len(explained_variance)),explained_variance,alpha=0.5,align='center',label='Individual Explained variance $\\lambda_{k}$')\n",
    "    plt.ylabel('Explained variance ratio')\n",
    "    plt.xlabel('Ranked Principal Components')\n",
    "    plt.title('Scree Graph')\n",
    "    plt.legend(loc='best')\n",
    "    plt.tight_layout()\n",
    "    \n",
    "    \n",
    "    fig = plt.figure(figsize=(6,4))\n",
    "    ax1 = fig.add_subplot(111)\n",
    "    ax1.plot(np.cumsum(explained_variance))\n",
    "    ax1.set_ylim([0,1.0])\n",
    "    ax1.set_xlabel('Number of Principal Components')\n",
    "    ax1.set_ylabel('Cumulative explained variance')\n",
    "    ax1.set_title('Explained Variance')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "    print(\"Choosing 5 Principal Components explains : \",np.cumsum(explained_variance)[5], \"% of variance\")\n",
    "    print(\"Choosing 25 Principal Components explains : \",np.cumsum(explained_variance)[25], \"% of variance\")\n",
    "    print(\"Choosing 32 Principal Components explains : \",np.cumsum(explained_variance)[32], \"% of variance\")\n",
    "\n",
    "    print([(j, np.cumsum(explained_variance)[j]) for j in range(len(explained_variance[:64]))])\n",
    "\n",
    "    matW = np.hstack( pair[1].reshape(64,1) for pair in sorted_eigen_value_vector_pair[0:32])#[0:4] originally\n",
    "    print(matW.shape)\n",
    "\n",
    "    Z = X_standard.dot(matW)\n",
    "    #Z = matW.T.dot(X_standard.T)\n",
    "    print(Z.shape)\n",
    "    \n",
    "    return Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e7bbd6ac-7fa7-41fe-a3c4-cf87fe8434ca",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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