Testing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "018e2c76-4dbb-49a7-ad57-56d0c73e11ed",
   "metadata": {},
   "source": [
    "# Just testing the datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bad26bdd-0dff-4892-a8ac-c74685d3cb3f",
   "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": "b01d57c3-bedf-4aee-b6a2-42b225db78d1",
   "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": "0bc9014d-877f-4384-b70c-f0c8a9b127aa",
   "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": "1386412a-993c-4f7d-b1e3-05bfbde5745d",
   "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]"
      ],
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     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "source": [
    "data_labels=optdigits_df.iloc[:,64:]\n",
    "data_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f1227087-224c-4dee-bb72-79dc7c13d7cd",
   "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": "a8095414-0913-4bab-939b-36a07f085514",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Principal_Component_Analysis(X):\n",
    "    X_standard,X_mean,X_cov=normalising_function(X)\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",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3dd5b71e-5d25-452c-9b3b-bcfde1537ca6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#importing libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "iris = load_iris() #dataset is stored in iris \n",
    "class PCA: #defining a class called PCA\n",
    "    def __init__(self, n_components): #constructor \n",
    "        self.n_components = n_components # no. of components\n",
    "        self.components = None\n",
    "        self.mean = None\n",
    "\n",
    "    def fit(self, X): #fit method\n",
    "        # Mean centering\n",
    "        self.mean = np.mean(X, axis=0)\n",
    "        X = X - self.mean\n",
    "\n",
    "        cov = np.cov(X.T)\n",
    "\n",
    "        eigenvalues, eigenvectors = np.linalg.eig(cov)\n",
    "\n",
    "        eigenvectors = eigenvectors.T\n",
    "        #print(eigenvalues)\n",
    "        idxs = np.argsort(eigenvalues)[::-1]\n",
    "        eigenvalues = eigenvalues[idxs]\n",
    "        #print(eigenvalues)\n",
    "        eigenvectors = eigenvectors[idxs]\n",
    "\n",
    "        self.components = eigenvectors[0:self.n_components]\n",
    "\n",
    "    def transform(self, X): #transform method\n",
    "        # project data\n",
    "        X = X - self.mean\n",
    "        return np.dot(X, self.components.T)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cb313186-37f3-4350-80fe-4fe89565e804",
   "metadata": {},
   "outputs": [
    {
     "output_type": "error",
     "ename": "NameError",
     "evalue": "name 'X_train' is not defined",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-8-4fff3f0f718d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mX_standard\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mX_mean\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mX_cov\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnormalising_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mX_standard\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'X_train' is not defined"
     ]
    }
   ],
   "source": [
    "X_standard,X_mean,X_cov=normalising_function(X_train)\n",
    "X_standard"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b87c1996-5c59-4cf5-8b98-0bc1ce756b00",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, Y_train, Y_test = train_test_split(data_features,data_labels, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5cdae23e-74ea-4db3-8f9d-a9051fad4aa7",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "      input1  input2  input3  input4  input5  input6  input7  input8  input9  \\\n",
       "579        0       2      12      16      14       1       0       0       0   \n",
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       "...      ...     ...     ...     ...     ...     ...     ...     ...     ...   \n",
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       "5157       0       0       0      14      11       0       0       0       0   \n",
       "\n",
       "      input10  ...  input55  input56  input57  input58  input59  input60  \\\n",
       "579        12  ...       11        0        0        1       14       16   \n",
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       "2025        0  ...        0        0        0        0        7       16   \n",
       "4251        0  ...        0        0        0        0        0        3   \n",
       "...       ...  ...      ...      ...      ...      ...      ...      ...   \n",
       "905         6  ...       11        0        0        0       10       16   \n",
       "5192        0  ...       11        0        0        0        1       11   \n",
       "3980        0  ...        0        0        0        0       13        9   \n",
       "235         0  ...        4        0        0        0        2       10   \n",
       "5157        0  ...        0        0        0        0        1       14   \n",
       "\n",
       "      input61  input62  input63  input64  \n",
       "579        16       12        3        0  \n",
       "19         15        3        0        0  \n",
       "3610       14        5        0        0  \n",
       "2025        0        0        0        0  \n",
       "4251       15       13        0        0  \n",
       "...       ...      ...      ...      ...  \n",
       "905        16        7        0        0  \n",
       "5192       12        4        0        0  \n",
       "3980        0        0        0        0  \n",
       "235        16       10        0        0  \n",
       "5157       16        4        0        0  \n",
       "\n",
       "[4496 rows x 64 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train"
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   "cell_type": "code",
   "execution_count": 8,
   "id": "8d851cf9-1ada-4bef-a2f2-e2931c623105",
   "metadata": {},
   "outputs": [
    {
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       "      class\n",
       "579       3\n",
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       "3610      8\n",
       "2025      7\n",
       "4251      1\n",
       "...     ...\n",
       "905       9\n",
       "5192      6\n",
       "3980      7\n",
       "235       0\n",
       "5157      1\n",
       "\n",
       "[4496 rows x 1 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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    "Y_train"
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  {
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   "execution_count": 9,
   "id": "fa7abb67-5820-4ad3-b210-f1260f0ca764",
   "metadata": {},
   "outputs": [
    {
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       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>1124 rows × 64 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      input1  input2  input3  input4  input5  input6  input7  input8  input9  \\\n",
       "5291       0       0       0       4      14      14       1       0       0   \n",
       "3496       0       0       0       1      13      12       1       0       0   \n",
       "2078       0       0       6      14      16      13       0       0       0   \n",
       "4824       0       0       0       1      15       2       0       0       0   \n",
       "440        0       0       5      13       1       0       0       0       0   \n",
       "...      ...     ...     ...     ...     ...     ...     ...     ...     ...   \n",
       "3196       0       0       2      10      16      12       0       0       0   \n",
       "4078       0       0       5      14      15       2       0       0       0   \n",
       "4096       0       0       4      12      16      10       0       0       0   \n",
       "4221       0       0       7      13       3       0       0       0       0   \n",
       "4991       0       0       0       0      13      12       0       0       0   \n",
       "\n",
       "      input10  ...  input55  input56  input57  input58  input59  input60  \\\n",
       "5291        0  ...        3        0        0        0        0        2   \n",
       "3496        0  ...        4        0        0        0        0        0   \n",
       "2078        6  ...        0        0        0        0        2       12   \n",
       "4824        0  ...        0        0        0        0        0        2   \n",
       "440         0  ...        5        0        0        0        4       14   \n",
       "...       ...  ...      ...      ...      ...      ...      ...      ...   \n",
       "3196        2  ...        3        0        0        0        1       11   \n",
       "4078        0  ...        0        0        0        0        6       16   \n",
       "4096        0  ...        0        0        0        0        6       12   \n",
       "4221        0  ...       16        3        0        0        6       15   \n",
       "4991        0  ...        0        0        0        0        0        0   \n",
       "\n",
       "      input61  input62  input63  input64  \n",
       "5291       16       14        0        0  \n",
       "3496       11       16        5        0  \n",
       "2078       12        0        0        0  \n",
       "4824       16        5        0        0  \n",
       "440        16       13        0        0  \n",
       "...       ...      ...      ...      ...  \n",
       "3196       14        6        0        0  \n",
       "4078       16        8        0        0  \n",
       "4096        0        0        0        0  \n",
       "4221        6        9        9        1  \n",
       "4991       15       11        0        0  \n",
       "\n",
       "[1124 rows x 64 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f9af4199-7d21-4344-8810-e6da8d495d74",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "      class\n",
       "5291      8\n",
       "3496      1\n",
       "2078      8\n",
       "4824      4\n",
       "440       6\n",
       "...     ...\n",
       "3196      3\n",
       "4078      8\n",
       "4096      7\n",
       "4221      2\n",
       "4991      1\n",
       "\n",
       "[1124 rows x 1 columns]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "26dc5104-8f9d-449f-b9bf-9f36ecf7c9dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of Training Data =  (4496, 64)\n",
      "Shape of Training Labels =  (4496, 1)\n",
      "Shape of Testing Data =  (1124, 64)\n",
      "Shape of Testing Labels =  (1124, 1)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of Training Data = \", X_train.shape)\n",
    "print(\"Shape of Training Labels = \",Y_train.shape)\n",
    "print(\"Shape of Testing Data = \",X_test.shape)\n",
    "print(\"Shape of Testing Labels = \",Y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "de9c158d-8dc3-42ca-85fe-0b98ddbaa00b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  2, 12, 16, 14,  1,  0,  0],\n",
       "       [ 0, 12, 12,  8, 16,  7,  0,  0],\n",
       "       [ 0,  2,  1,  1, 16,  8,  0,  0],\n",
       "       [ 0,  0,  2, 14, 16, 10,  0,  0],\n",
       "       [ 0,  0,  1, 11, 12, 16,  7,  0],\n",
       "       [ 0,  0,  0,  0,  0, 15, 12,  0],\n",
       "       [ 0,  3, 13,  6,  4, 16, 11,  0],\n",
       "       [ 0,  1, 14, 16, 16, 12,  3,  0]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "firstimage=X_train.iloc[0,:].to_numpy().reshape(8,8)\n",
    "firstimage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "a911abf2-e82f-4a27-964e-f51c184e67af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f076d2a9a30>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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   ],
   "source": [
    "plt.imshow(firstimage)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a1ccc221-b594-4524-b432-7ce41f48570f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label of this first image :  3\n"
     ]
    }
   ],
   "source": [
    "print(\"Label of this first image : \",int(Y_train.iloc[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1ab1c503-eef5-49ae-9d64-307173bb9a75",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d1553408-2dbc-4f2a-a6ca-fc2e8eb15fa7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  1.88758124,  1.4060955 , ...,  0.89897115,\n",
       "         0.2087321 , -0.18225272],\n",
       "       [ 0.        , -0.34279071, -1.15325352, ..., -0.6455248 ,\n",
       "        -0.52120789, -0.18225272],\n",
       "       [ 0.        , -0.34279071,  0.12642099, ..., -0.30230348,\n",
       "        -0.52120789, -0.18225272],\n",
       "       ...,\n",
       "       [ 0.        , -0.34279071,  0.97953733, ..., -1.16035679,\n",
       "        -0.52120789, -0.18225272],\n",
       "       [ 0.        , -0.34279071, -0.30013718, ...,  0.55574983,\n",
       "        -0.52120789, -0.18225272],\n",
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       "        -0.52120789, -0.18225272]])"
      ]
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     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f69e739-ab30-429d-a26f-85050ef9edf8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "ee61e242-282e-4e7e-ba2a-e45ccc1bfe26",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type :  <class 'numpy.ndarray'> Shape :  (4496, 64)\n"
     ]
    }
   ],
   "source": [
    "print(\"Type : \", type(X_standard), \"Shape : \", X_standard.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "63e93a2d-d83b-4185-b9e0-dfa0f6f2dab5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type :  <class 'numpy.ndarray'> Shape :  (64,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Type : \", type(X_mean), \"Shape : \", X_mean.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "27cd6cbe-a828-4f6c-9aa2-5c79aff40620",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Type :  <class 'numpy.ndarray'> Shape :  (64, 64)\n"
     ]
    }
   ],
   "source": [
    "print(\"Type : \", type(X_cov), \"Shape : \", X_cov.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa7818c7-acfe-4790-a85d-f771b88101e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "fig=plt.figure(figsize=(10,10))\n",
    "sns.heatmap(pd.DataFrame(X_cov))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "67444d89-e66d-4b35-b540-5cd617e5a50d",
   "metadata": {},
   "outputs": [],
   "source": [
    "eigenvalues, eigenvectors = np.linalg.eig(X_cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b8ab2550-1ec0-4c79-8761-4403b4bbb96f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of Eigen Values :  (64,)\n",
      "Shape of Eigen Vectors :  (64, 64)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of Eigen Values : \", eigenvalues.shape)\n",
    "print(\"Shape of Eigen Vectors : \", eigenvectors.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "926ff569-0d65-493d-80db-e5cbaeef28f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "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])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "22e65c05-5f23-4bf9-bb92-304302e8671f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        -0.05493151, -0.14104259, -0.15266851, -0.07676771]))"
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   "cell_type": "code",
   "execution_count": 25,
   "id": "0b58ba95-a8e0-4c65-be53-ecbd65843e1e",
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   "outputs": [
    {
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       "        -0.24513243, -0.2041636 , -0.14093627, -0.05698891]))"
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     "execution_count": 25,
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   "execution_count": 26,
   "id": "fc437fea-f1a1-4ee5-9780-6f801188c287",
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    {
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       "         0.16681917,  0.2172426 , -0.03918722, -0.02444608, -0.00534784,\n",
       "         0.06678308, -0.19161317, -0.12620978,  0.17047224,  0.03037697,\n",
       "        -0.09802528, -0.01277628, -0.03538428,  0.056413  ,  0.12578006,\n",
       "         0.06877889, -0.00602681, -0.11664066, -0.09251002]))"
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     "execution_count": 26,
     "metadata": {},
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    "sorted_eigen_value_vector_pair[2]"
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  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "b6c99676-75f2-41fc-af9c-67ddcaac102b",
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "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()"
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  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "958679f9-c7ac-40d0-a00e-1edfc71036f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "lam_sum=sum(eigenvalues)\n",
    "explained_variance=[(lam_k/lam_sum) for lam_k in sorted(eigenvalues,reverse=True)]"
   ]
  },
  {
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   "execution_count": 29,
   "id": "66c05128-3742-4d84-9f94-8c84cf6361a1",
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       " 0.004868557004021335,\n",
       " 0.004482144411450576,\n",
       " 0.004342729283128952,\n",
       " 0.004073564278123213,\n",
       " 0.003940974517830927,\n",
       " 0.0035087305926510275,\n",
       " 0.003436427247216412,\n",
       " 0.003227144822304323,\n",
       " 0.003125541144112858,\n",
       " 0.0028331002666132565,\n",
       " 0.002630340024403161,\n",
       " 0.0025817633815100587,\n",
       " 0.0024989289320360452,\n",
       " 0.002250240565214113,\n",
       " 0.0022289935776074682,\n",
       " 0.002088976258122881,\n",
       " 0.0018718096619846144,\n",
       " 0.0018342567607264038,\n",
       " 0.0016902979168203,\n",
       " 0.0015283971746942976,\n",
       " 0.0014345718172772243,\n",
       " 0.001258611773866785,\n",
       " 0.0010722736462698342,\n",
       " 0.0009290011187443603,\n",
       " 0.0,\n",
       " 0.0]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explained_variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "745e88ae-495b-4883-9487-f2522206c739",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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     "output_type": "display_data"
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   ],
   "source": [
    "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",
    "\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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2a47ce08-5479-4cc2-9f24-0161d43d7aa3",
   "metadata": {},
   "outputs": [
    {
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "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()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "21911d49-c6ba-471a-9666-6f4c2c2cb189",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Choosing 5 Principal Components explains :  0.44788459167920175 % of variance\n",
      "Choosing 25 Principal Components explains :  0.8503018959346693 % of variance\n",
      "Choosing 32 Principal Components explains :  0.9072946487012427 % of variance\n"
     ]
    }
   ],
   "source": [
    "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\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "5d7c3c18-d999-4319-843f-093bff38cb3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0.11682856310706477), (1, 0.2179519452967183), (2, 0.2950898916201752), (3, 0.3540255824064435), (4, 0.40286418469256735), (5, 0.44788459167920175), (6, 0.4864985136013183), (7, 0.5208688510750301), (8, 0.5493651286137203), (9, 0.5760963346571213), (10, 0.6024028007707409), (11, 0.6269253878108845), (12, 0.6501650460408502), (13, 0.6712121624245815), (14, 0.6913480458549419), (15, 0.7107271708140528), (16, 0.7288908707329962), (17, 0.7466251109991546), (18, 0.7627650767206148), (19, 0.778081344923097), (20, 0.792759283409862), (21, 0.8061212329595004), (22, 0.8184656105441421), (23, 0.8297722118473683), (24, 0.840275091156037), (25, 0.8503018959346693), (26, 0.8593319958734082), (27, 0.8682820881791236), (28, 0.8768894872962204), (29, 0.8851031150896008), (30, 0.8928680235383554), (31, 0.9002070856137177), (32, 0.9072946487012427), (33, 0.9136109449031029), (34, 0.9197224480327781), (35, 0.9256980475753813), (36, 0.9311383395813451), (37, 0.9362626238232701), (38, 0.9411311808272914), (39, 0.945613325238742), (40, 0.9499560545218709), (41, 0.9540296187999942), (42, 0.9579705933178251), (43, 0.9614793239104761), (44, 0.9649157511576925), (45, 0.9681428959799968), (46, 0.9712684371241097), (47, 0.9741015373907229), (48, 0.9767318774151261), (49, 0.9793136407966362), (50, 0.9818125697286723), (51, 0.9840628102938864), (52, 0.9862918038714938), (53, 0.9883807801296167), (54, 0.9902525897916014), (55, 0.9920868465523277), (56, 0.993777144469148), (57, 0.9953055416438423), (58, 0.9967401134611196), (59, 0.9979987252349863), (60, 0.9990709988812562), (61, 1.0000000000000004), (62, 1.0000000000000004), (63, 1.0000000000000004)]\n"
     ]
    }
   ],
   "source": [
    "print([(j, np.cumsum(explained_variance)[j]) for j in range(len(explained_variance[:64]))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f41cb0e7-c63c-4db6-983e-70344e4171b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(64, 32)\n",
      "<ipython-input-34-9274d5fccee0>:1: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  matW = np.hstack( pair[1].reshape(64,1) for pair in sorted_eigen_value_vector_pair[0:32])#[0:4] originally\n"
     ]
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f67adb71-caa6-4119-bac7-aaf6722f0e45",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4496, 32)\n"
     ]
    }
   ],
   "source": [
    "Z = X_standard.dot(matW)\n",
    "#Z = matW.T.dot(X_standard.T)\n",
    "print(Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "3604736e-3902-4f7d-845f-994c583159bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-4.68984633,  5.68405028, -0.98747352, ...,  0.73961335,\n",
       "         0.81079369, -0.4451384 ],\n",
       "       [ 0.46828809,  1.68189166,  1.39368625, ...,  1.3549725 ,\n",
       "        -2.58895779,  0.63884044],\n",
       "       [ 2.15289531,  0.88235876,  0.04787519, ..., -1.99782126,\n",
       "         3.13776076, -5.02807144],\n",
       "       ...,\n",
       "       [-0.03961872, -0.29000184,  0.3516749 , ...,  1.02981   ,\n",
       "        -0.1854482 , -1.01751432],\n",
       "       [-0.13395758, -0.5387159 , -0.52934364, ...,  0.40962813,\n",
       "        -0.72505847,  0.18310449],\n",
       "       [-0.17723578, -0.19673928,  0.33037332, ...,  0.61418073,\n",
       "        -0.48776592,  0.36210787]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73f4dc45-5e28-41d0-95c1-ca06ae33d8ab",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1548da5e-1adb-483e-b3d8-5bcffa4f9990",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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