08_Principal_Component_Analysis.ipynb

{
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  {
   "cell_type": "markdown",
   "id": "31215afa",
   "metadata": {
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   },
   "source": [
    "# Principal Component Analysis\n",
    "\n",
    "Principal component analysis (PCA) is a technique that transforms high-dimensions data into lower-dimensions while retaining as much information as possible.\n",
    "\n",
    "<table><tr>\n",
    "    <td><img src=\"https://i.postimg.cc/TPZxdTNr/PCA1.png\" width=\"417\"/> </td>\n",
    "    <td> <img src=\"https://i.postimg.cc/NFxvkms4/PCA2.png\" width=\"500\"/></td>\n",
    "</tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Curse of Dimensionality  \n",
    "\n",
    "Dimensionality in a dataset becomes a severe impediment to achieve a reasonable efficiency for most algorithms. Increasing the number of features does not always improve accuracy. When data does not have enough features, the model is likely to underfit, and when data has too many features, it is likely to overfit. Hence it is called the curse of dimensionality. The curse of dimensionality is an astonishing paradox for data scientists, based on the exploding amount of n-dimensional spaces — as the number of dimensions, n, increases.\n",
    "\n",
    "<img src=\"https://i.postimg.cc/Yqbw46y2/curse.jpg\" width=\"400\"/>"
   ]
  },
  {
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   "id": "dd10acd9",
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   "source": [
    "There are two techniques to make dimensionality reduction:\n",
    "\n",
    "* Feature Selection\n",
    "* Feature Extraction\n",
    "\n",
    "<img src=\"https://i.postimg.cc/4xmjmr9w/vs.png\" width=\"500\"/>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "### Feature Selection\n",
    "n feature selection, usually, a subset of original features is selected.\n",
    "<img src=\"https://i.postimg.cc/7LzcN0X2/feature-selection.png\" width=\"300\"/>\n",
    "\n",
    "### Feature Extraction\n",
    "In feature extraction, a set of new features are found. That is found through some mapping from the existing features. Moreover, mapping can be either linear or non-linear.\n",
    "<img src=\"https://i.postimg.cc/4yWF354r/feature-extraction.png\" width=\"300\"/>"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "## Principal Component Analysis (PCA)\n",
    "\n",
    "Principal Component Analysis (PCA) is an exploratory approach to reduce the data set's dimensionality to 2D or 3D, used in exploratory data analysis for making predictive models. Principal Component Analysis is a `linear` transformation of data set that defines a new coordinate rule such that:\n",
    "\n",
    "   * The highest variance by any projection of the data set appears to lays on the first axis.\n",
    "   * The second biggest variance on the second axis, and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcc831cd",
   "metadata": {
    "id": "bcc831cd"
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   "source": [
    "> 💥 In the eyes of PCA, variance is an objective and mathematical way to quantify the amount of information in our data.\n",
    "**Variance is information.**\n",
    "\n",
    "<img src=\"https://i.postimg.cc/X7DzSQz5/variance.jpg\" width=\"400\"/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b91ddfa0",
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   "source": [
    ">**✨ Additional infornamtion:**  \n",
    "    **Autoencoders** are neural networks that stack numerous non-linear transformations to reduce input into a low-dimensional latent space (layers). The aim of an autoencoder is to learn a lower-dimensional representation (encoding) for a higher-dimensional data, typically for dimensionality reduction, by training the network to capture the most important parts of the input image."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71cc3462",
   "metadata": {
    "id": "t1_I7MrAOEUd"
   },
   "source": [
    "# PCA for Data Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e9dfe47",
   "metadata": {
    "id": "9e9dfe47"
   },
   "source": [
    "### PCA and KNN on IRIS dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b27cd76d",
   "metadata": {
    "id": "b27cd76d"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import plotly.express as px\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA\n",
    "import warnings \n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "798c551b",
   "metadata": {
    "id": "798c551b"
   },
   "outputs": [],
   "source": [
    "iris = load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6ffaa887",
   "metadata": {
    "id": "6ffaa887"
   },
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "259c5700",
   "metadata": {
    "id": "259c5700"
   },
   "outputs": [],
   "source": [
    "iris.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "89938f0f",
   "metadata": {
    "id": "89938f0f"
   },
   "outputs": [],
   "source": [
    "X_df = pd.DataFrame(X, columns=iris.feature_names)\n",
    "y_df = pd.DataFrame(y, columns=[\"label\"])\n",
    "X_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2f028d9e",
   "metadata": {
    "id": "2f028d9e",
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "px.scatter_matrix(X_df, color=y, title='Scatter Matrix of Features', height=800, )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a34e35da",
   "metadata": {
    "id": "a34e35da"
   },
   "outputs": [],
   "source": [
    "px.pie(y_df, names=\"label\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "81a0671b",
   "metadata": {
    "id": "81a0671b"
   },
   "outputs": [],
   "source": [
    "df = pd.concat([X_df, y_df], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "734c46f7",
   "metadata": {
    "id": "734c46f7"
   },
   "outputs": [],
   "source": [
    "px.imshow(df.corr())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1904d32f",
   "metadata": {
    "id": "1904d32f"
   },
   "source": [
    ">**❗ NOTE:** One of the biggest aims of these sort of plots and EDAs are to identify features that are not much helpful in explaining the target outcome. The SepalWidthCm feature seems to be less relevant in explaining the target class as compared to the other features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "884625a8",
   "metadata": {
    "id": "884625a8"
   },
   "outputs": [],
   "source": [
    "X_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b179741",
   "metadata": {
    "id": "1b179741"
   },
   "source": [
    "### Train Test split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f6c12da6",
   "metadata": {
    "id": "f6c12da6"
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4213b64",
   "metadata": {
    "id": "e4213b64"
   },
   "source": [
    "### Standardizing the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9684f22",
   "metadata": {
    "id": "e9684f22"
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93c54ae6",
   "metadata": {
    "id": "93c54ae6"
   },
   "source": [
    "### Apply PCA to transform iris dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "92e5e64b",
   "metadata": {
    "id": "92e5e64b"
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=4)\n",
    "X_train_pca = pca.fit_transform(X_train)\n",
    "X_test_pca = pca.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4711ad17",
   "metadata": {
    "id": "4711ad17"
   },
   "source": [
    "> The `explained_variance_ratio_` tells us how much of the total variance is explained by each principal component."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e7d53f9",
   "metadata": {
    "id": "1e7d53f9"
   },
   "outputs": [],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04615085",
   "metadata": {
    "id": "04615085"
   },
   "outputs": [],
   "source": [
    "px.bar(x= [\"pca-1\", \"pca-2\", \"pca-3\", \"pca-4\"] ,y = pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a9b0d6d",
   "metadata": {
    "id": "9a9b0d6d"
   },
   "source": [
    "> As we can see from the above plot :  \n",
    ">* The first component covers 72.962% of the original datas information with a loss of ~ 28%.\n",
    ">* The second component covers 22.850% of the original datas information with a loss of ~ 78%.\n",
    ">* Both the first and second principal components are enough to cover ~ 95% with a loss of ~ 5%.\n",
    "> The third and fourth components can be safely ignored because they only contribute to ~3% and 0.5% of original datas information."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c12d163",
   "metadata": {
    "id": "9c12d163"
   },
   "source": [
    "💥 **Since the first two principal components have high variance we will select them for dimensionality reduction.**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d08134a",
   "metadata": {
    "id": "2d08134a"
   },
   "source": [
    "### Plotting the 2 principal components with maximum variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b4969544",
   "metadata": {
    "id": "b4969544"
   },
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "pca.fit(X_train)\n",
    "X_train_pca = pca.transform(X_train)\n",
    "X_test_pca = pca.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "303130c4",
   "metadata": {
    "id": "303130c4"
   },
   "outputs": [],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6750f2f8",
   "metadata": {
    "id": "6750f2f8"
   },
   "outputs": [],
   "source": [
    "px.bar(x= [\"pca-1\", \"pca-2\"] ,y = pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e174ff74",
   "metadata": {
    "id": "e174ff74"
   },
   "outputs": [],
   "source": [
    "X_train_pca_df = pd.DataFrame(X_train_pca,columns=['PCA-1','PCA-2'])\n",
    "X_train_pca_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79c620e7",
   "metadata": {
    "id": "79c620e7"
   },
   "outputs": [],
   "source": [
    "px.scatter(X_train_pca_df, x=\"PCA-1\", y=\"PCA-2\", color= y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "734c4d98",
   "metadata": {
    "id": "734c4d98"
   },
   "outputs": [],
   "source": [
    "X_train_pca.shape, X_test_pca.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "608f4951",
   "metadata": {
    "id": "608f4951"
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "scores = cross_val_score(knn, X_train, y_train, cv=5)\n",
    "print(\"score before dimension reduction:\",scores.mean())   \n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "scores = cross_val_score(knn, X_train_pca, y_train, cv=5)\n",
    "print(\"score after dimension reduction:\",scores.mean())   "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fd24a76",
   "metadata": {
    "id": "9fd24a76"
   },
   "source": [
    "### Plotting the 3 principal components with maximum variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "07389dbc",
   "metadata": {
    "id": "07389dbc"
   },
   "outputs": [],
   "source": [
    "pca3D = PCA(n_components=3)\n",
    "pca3D.fit(X_train)\n",
    "X_train_pca3D = pca3D.transform(X_train)\n",
    "X_test_pca3D = pca3D.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d3649c7f",
   "metadata": {
    "id": "d3649c7f"
   },
   "outputs": [],
   "source": [
    "pca3D.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42754f3b",
   "metadata": {
    "id": "42754f3b"
   },
   "outputs": [],
   "source": [
    "X_train_pca3D_df = pd.DataFrame(X_train_pca3D,columns=['PCA-1','PCA-2', 'PCA-3'])\n",
    "X_train_pca3D_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "010be4c9",
   "metadata": {
    "id": "010be4c9"
   },
   "outputs": [],
   "source": [
    "px.scatter_3d(X_train_pca3D_df, x=\"PCA-1\", y=\"PCA-2\",z=\"PCA-3\", color= y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0d2f5a3",
   "metadata": {
    "id": "d0d2f5a3"
   },
   "outputs": [],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "scores = cross_val_score(knn, X_train, y_train, cv=5)\n",
    "print(\"score before dimension reduction:\",scores.mean())   \n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "scores = cross_val_score(knn, X_train_pca, y_train, cv=5)\n",
    "print(\"score after dimension reduction to 2D:\",scores.mean())  \n",
    "\n",
    "knn = KNeighborsClassifier()\n",
    "scores = cross_val_score(knn, X_train_pca3D, y_train, cv=5)\n",
    "print(\"score after dimension reduction to 3D:\",scores.mean())  "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3297ddf",
   "metadata": {
    "id": "3bddc40f"
   },
   "source": [
    "# PCA to Speed-up Machine Learning Algorithms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7f9c8b91",
   "metadata": {
    "id": "7f9c8b91"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import plotly.express as px\n",
    "from sklearn.decomposition import PCA\n",
    "from time import time\n",
    "import warnings \n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "88aad05d",
   "metadata": {
    "id": "88aad05d"
   },
   "outputs": [],
   "source": [
    "train_df = pd.read_csv(\"./dataset/mnist_train.csv\", dtype=np.uint8)\n",
    "test_df = pd.read_csv(\"./dataset/mnist_test.csv\", dtype=np.uint8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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    "colab": {
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     "height": 235
    },
    "id": "f07e1108",
    "outputId": "0265cad8-1fd9-4063-db14-cd3c2a45ad4d"
   },
   "outputs": [
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       "      <td>0</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</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>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 785 columns</p>\n",
       "</div>\n",
       "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-af595cfb-1f0a-4f69-ae0c-99d83dfd891a')\"\n",
       "              title=\"Convert this dataframe to an interactive table.\"\n",
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       "      height: 32px;\n",
       "      padding: 0 0 0 0;\n",
       "      width: 32px;\n",
       "    }\n",
       "\n",
       "    .colab-df-convert:hover {\n",
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       "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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       "\n",
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       "\n",
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       "        const buttonEl =\n",
       "          document.querySelector('#df-af595cfb-1f0a-4f69-ae0c-99d83dfd891a button.colab-df-convert');\n",
       "        buttonEl.style.display =\n",
       "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
       "\n",
       "        async function convertToInteractive(key) {\n",
       "          const element = document.querySelector('#df-af595cfb-1f0a-4f69-ae0c-99d83dfd891a');\n",
       "          const dataTable =\n",
       "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
       "                                                     [key], {});\n",
       "          if (!dataTable) return;\n",
       "\n",
       "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
       "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
       "            + ' to learn more about interactive tables.';\n",
       "          element.innerHTML = '';\n",
       "          dataTable['output_type'] = 'display_data';\n",
       "          await google.colab.output.renderOutput(dataTable, element);\n",
       "          const docLink = document.createElement('div');\n",
       "          docLink.innerHTML = docLinkHtml;\n",
       "          element.appendChild(docLink);\n",
       "        }\n",
       "      </script>\n",
       "    </div>\n",
       "  </div>\n",
       "  "
      ],
      "text/plain": [
       "   label  1x1  1x2  1x3  1x4  1x5  1x6  1x7  1x8  1x9  ...  28x19  28x20  \\\n",
       "0      5    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
       "1      0    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
       "2      4    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
       "3      1    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
       "4      9    0    0    0    0    0    0    0    0    0  ...      0      0   \n",
       "\n",
       "   28x21  28x22  28x23  28x24  28x25  28x26  28x27  28x28  \n",
       "0      0      0      0      0      0      0      0      0  \n",
       "1      0      0      0      0      0      0      0      0  \n",
       "2      0      0      0      0      0      0      0      0  \n",
       "3      0      0      0      0      0      0      0      0  \n",
       "4      0      0      0      0      0      0      0      0  \n",
       "\n",
       "[5 rows x 785 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a010ab93",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 394
    },
    "id": "a010ab93",
    "outputId": "1b3d5a4f-7982-469c-a1a1-3680b6a5cbac"
   },
   "outputs": [
    {
     "data": {
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>3.956189</td>\n",
       "      <td>2.839845</td>\n",
       "      <td>1.686770</td>\n",
       "      <td>1.678283</td>\n",
       "      <td>0.3466</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0000</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>254.000000</td>\n",
       "      <td>253.000000</td>\n",
       "      <td>253.000000</td>\n",
       "      <td>254.000000</td>\n",
       "      <td>62.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "          const element = document.querySelector('#df-270e30af-723a-4b10-9b36-f628c5218f1b');\n",
       "          const dataTable =\n",
       "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
       "                                                     [key], {});\n",
       "          if (!dataTable) return;\n",
       "\n",
       "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
       "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
       "            + ' to learn more about interactive tables.';\n",
       "          element.innerHTML = '';\n",
       "          dataTable['output_type'] = 'display_data';\n",
       "          await google.colab.output.renderOutput(dataTable, element);\n",
       "          const docLink = document.createElement('div');\n",
       "          docLink.innerHTML = docLinkHtml;\n",
       "          element.appendChild(docLink);\n",
       "        }\n",
       "      </script>\n",
       "    </div>\n",
       "  </div>\n",
       "  "
      ],
      "text/plain": [
       "              label      1x1      1x2      1x3      1x4      1x5      1x6  \\\n",
       "count  60000.000000  60000.0  60000.0  60000.0  60000.0  60000.0  60000.0   \n",
       "mean       4.453933      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "std        2.889270      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "min        0.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "25%        2.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "50%        4.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "75%        7.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "max        9.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "\n",
       "           1x7      1x8      1x9  ...         28x19         28x20  \\\n",
       "count  60000.0  60000.0  60000.0  ...  60000.000000  60000.000000   \n",
       "mean       0.0      0.0      0.0  ...      0.200433      0.088867   \n",
       "std        0.0      0.0      0.0  ...      6.042472      3.956189   \n",
       "min        0.0      0.0      0.0  ...      0.000000      0.000000   \n",
       "25%        0.0      0.0      0.0  ...      0.000000      0.000000   \n",
       "50%        0.0      0.0      0.0  ...      0.000000      0.000000   \n",
       "75%        0.0      0.0      0.0  ...      0.000000      0.000000   \n",
       "max        0.0      0.0      0.0  ...    254.000000    254.000000   \n",
       "\n",
       "              28x21         28x22         28x23       28x24    28x25    28x26  \\\n",
       "count  60000.000000  60000.000000  60000.000000  60000.0000  60000.0  60000.0   \n",
       "mean       0.045633      0.019283      0.015117      0.0020      0.0      0.0   \n",
       "std        2.839845      1.686770      1.678283      0.3466      0.0      0.0   \n",
       "min        0.000000      0.000000      0.000000      0.0000      0.0      0.0   \n",
       "25%        0.000000      0.000000      0.000000      0.0000      0.0      0.0   \n",
       "50%        0.000000      0.000000      0.000000      0.0000      0.0      0.0   \n",
       "75%        0.000000      0.000000      0.000000      0.0000      0.0      0.0   \n",
       "max      253.000000    253.000000    254.000000     62.0000      0.0      0.0   \n",
       "\n",
       "         28x27    28x28  \n",
       "count  60000.0  60000.0  \n",
       "mean       0.0      0.0  \n",
       "std        0.0      0.0  \n",
       "min        0.0      0.0  \n",
       "25%        0.0      0.0  \n",
       "50%        0.0      0.0  \n",
       "75%        0.0      0.0  \n",
       "max        0.0      0.0  \n",
       "\n",
       "[8 rows x 785 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e184412e",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "e184412e",
    "outputId": "6b8f81f2-e097-45aa-d678-b39044168d7b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 60000 entries, 0 to 59999\n",
      "Columns: 785 entries, label to 28x28\n",
      "dtypes: uint8(785)\n",
      "memory usage: 44.9 MB\n"
     ]
    }
   ],
   "source": [
    "train_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "IXMrIfocQXj-",
   "metadata": {
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     "height": 542
    },
    "id": "IXMrIfocQXj-",
    "outputId": "e766a831-0c30-4745-9e61-5df05070e31d"
   },
   "outputs": [
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       "</body>\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.pie(train_df, names=\"label\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9f3a5e3b",
   "metadata": {
    "id": "9f3a5e3b"
   },
   "outputs": [],
   "source": [
    "X_train = train_df.drop(['label'], axis=1)\n",
    "y_train = train_df['label']\n",
    "X_test = test_df.drop(['label'], axis=1)\n",
    "y_test = test_df['label']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6f0f984c",
   "metadata": {
    "id": "6f0f984c"
   },
   "outputs": [],
   "source": [
    "del train_df\n",
    "del test_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "01609f89",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "01609f89",
    "outputId": "2c152b42-e2e4-4852-d44d-42d1557bb604"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_train_shape: (60000, 784)\n",
      "Y_train_shape: (60000,)\n",
      "X_test_shape: (10000, 784)\n",
      "Y_test_shape: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"X_train_shape:\",X_train.shape)\n",
    "print(\"Y_train_shape:\",y_train.shape)\n",
    "print(\"X_test_shape:\",X_test.shape)\n",
    "print(\"Y_test_shape:\",y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "96926664",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "96926664",
    "outputId": "5e9c3560-781f-4fa6-c1c3-c951cc8f309f"
   },
   "outputs": [
    {
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       "</body>\n",
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "instance_index = 7890 \n",
    "matrix_conv=X_train.iloc[instance_index].to_numpy().reshape(28,28)\n",
    "px.imshow(matrix_conv)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5c42920",
   "metadata": {
    "id": "c5c42920"
   },
   "source": [
    "## Standardizing the features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "da91108d",
   "metadata": {
    "id": "da91108d"
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0cf7afd",
   "metadata": {
    "id": "a0cf7afd"
   },
   "source": [
    "## Apply PCA to transform MNIST dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18f408d5",
   "metadata": {
    "id": "iGJrvDssRuyo"
   },
   "source": [
    "### Let’s see a Choosing the number of components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "qTLLSXuoSKPp",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 542
    },
    "id": "qTLLSXuoSKPp",
    "outputId": "18c1f819-6a18-4be4-b734-16b49c4a4668"
   },
   "outputs": [
    {
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "pca.fit(X_train)\n",
    "dataframe = pd.DataFrame({'number of components':range(1, len(pca.explained_variance_ratio_)+1) , 'cumulative explained variance':np.cumsum(pca.explained_variance_ratio_)})\n",
    "px.line(dataframe, x=\"number of components\" ,y=\"cumulative explained variance\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "d33a1d87",
   "metadata": {
    "id": "d33a1d87"
   },
   "outputs": [],
   "source": [
    "pca = PCA(0.95)\n",
    "pca.fit(X_train)\n",
    "X_train_pca = pca.transform(X_train)\n",
    "X_test_pca = pca.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "mqVCIDNLOoFc",
   "metadata": {
    "id": "mqVCIDNLOoFc"
   },
   "source": [
    ">**❗ NOTE:** Notice the code has .95 for the number of components parameter. It means that scikit-learn choose the minimum number of principal components such that 95% of the variance is retained."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "DQh1KQpUVce3",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "DQh1KQpUVce3",
    "outputId": "69d96431-e19b-4991-dc7e-28e66bc7ed7c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "331"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93aba9fa",
   "metadata": {
    "id": "rTTvYM0dNee_"
   },
   "source": [
    "### Apply SVM to the Transformed Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "M-GO14n2PQVr",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 394
    },
    "id": "M-GO14n2PQVr",
    "outputId": "b4b5fef0-9182-4788-c344-c41f56ae9482"
   },
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "ignored",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-23-cfbca8e09990>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mt0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtime\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0msvc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSVC\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkernel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'linear'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0msvc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train_pca\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_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      6\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"Time (Seconds): {time() - t0}\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0my_pred\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msvc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test_pca\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sklearn/svm/_base.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, X, y, sample_weight)\u001b[0m\n\u001b[1;32m    253\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    254\u001b[0m         \u001b[0mseed\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mrnd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miinfo\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"i\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 255\u001b[0;31m         \u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msample_weight\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolver_type\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrandom_seed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mseed\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    256\u001b[0m         \u001b[0;31m# see comment on the other call to np.iinfo in this file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    257\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/sklearn/svm/_base.py\u001b[0m in \u001b[0;36m_dense_fit\u001b[0;34m(self, X, y, sample_weight, solver_type, kernel, random_seed)\u001b[0m\n\u001b[1;32m    331\u001b[0m             \u001b[0mepsilon\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mepsilon\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    332\u001b[0m             \u001b[0mmax_iter\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax_iter\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 333\u001b[0;31m             \u001b[0mrandom_seed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrandom_seed\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    334\u001b[0m         )\n\u001b[1;32m    335\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "from sklearn.metrics import accuracy_score\n",
    "t0 = time()\n",
    "svc = SVC(kernel='rbf')\n",
    "svc.fit(X_train_pca, y_train)\n",
    "print(f\"Time (Seconds): {time() - t0}\")\n",
    "y_pred = svc.predict(X_test_pca)\n",
    "\n",
    "print(f\"Accuracy score : {accuracy_score(y_test, y_pred)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "uP84p-H0PQeL",
   "metadata": {
    "id": "uP84p-H0PQeL"
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVC\n",
    "from sklearn.metrics import accuracy_score\n",
    "t0 = time()\n",
    "svc = SVC(kernel='rbf')\n",
    "svc.fit(X_train, y_train)\n",
    "print(f\"Time (Seconds): {time() - t0}\")\n",
    "y_pred = svc.predict(X_test)\n",
    "\n",
    "print(f\"Accuracy score : {accuracy_score(y_test, y_pred)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "_ip88JG3PQgj",
   "metadata": {
    "id": "_ip88JG3PQgj"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ciO4f6nEPQjF",
   "metadata": {
    "id": "ciO4f6nEPQjF"
   },
   "outputs": [],
   "source": []
  }
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