Principal component analysis (PCA).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "mYv6Kmf0aaOu"
   },
   "source": [
    "# Principal Component Analisis\n",
    "\n",
    "Welcome to your next lab! In this assignment you will explore problem of reducing dimensionality of data and restoring it back using your PCA model.\n",
    "\n",
    "\n",
    "**You will learn to:**\n",
    "- Build the general architecture of a learning algorithm with OOP in mind:\n",
    "    - Helper functions\n",
    "        - Normalization\n",
    "        - Eigendecomposition\n",
    "    - PCA Class\n",
    "        - Transform\n",
    "        - Restore"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xqGSGVTXaaOx"
   },
   "source": [
    "## 1 - Packages ##\n",
    "\n",
    "First, let's run the cell below to import all the packages that you will need during this assignment. \n",
    "- [numpy](www.numpy.org) is the fundamental package for scientific computing with Python.\n",
    "- [matplotlib](http://matplotlib.org) is a famous library to plot graphs in Python.\n",
    "- [PIL](https://pypi.org/project/PIL/) is the Python Imaging Library.\n",
    "- [mpl_toolkits](https://matplotlib.org/mpl_toolkits/index.html) collections of application-specific functions that extend Matplotlib."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "caEUwSVIaaOy"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image\n",
    "\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WT1gorpfaaO6"
   },
   "source": [
    "## 2 - Overview of the Problem set ##\n",
    "\n",
    "**Problem Statement**: \n",
    "In this assignment we have an image as dataset. We will reduce its dimensionality using our algorithm. Here it is represented as array with dimension (1280, 960)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "G1AgYQ8gaaO8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = Image.open('cat2.jpeg')\n",
    "img = img.convert('L', colors=256)\n",
    "img = np.array(img, dtype=np.uint8)\n",
    "imgplot = plt.imshow(img, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "E1pvBRfoaaPC"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of image: (1280, 960)\n"
     ]
    }
   ],
   "source": [
    "print('Shape of image:', img.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hWk35GejaaPH"
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "Shape of image: (1280, 960)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "r7vkukJ3aaPK"
   },
   "source": [
    "But firstly we will check performance of PCA on simple synthetic dataset, which includes 13 examples with 3 features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6bO68NN_aaPL"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of input data: (13, 3)\n"
     ]
    }
   ],
   "source": [
    "X = np.asarray([[12, 15, 20, 24, 27, 30, 63, 8, 67, 43, 11, 15, 67], \n",
    "                [34, 31, 29, 88, 76, 80, 89, 53, 48, 66, 45, 50, 85], \n",
    "                [45, 50, 43, 60, 65, 59, 89, 53, 43, 31, 33, 40, 80]]).T\n",
    "print('Shape of input data:', X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sd6IJIvUaaPS"
   },
   "source": [
    "**Expected output:**\n",
    "    \n",
    "Shape of input data: (13, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FVEWrxh0aaPT"
   },
   "source": [
    "Let's visualize it:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jwZVMqTSaaPW"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "plt.rcParams['legend.fontsize'] = 10   \n",
    "ax.plot(X.T[0,:], X.T[1,:], X.T[2,:], 'o', markersize=8, color='blue', alpha=0.5, label='Initial')\n",
    "\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "LM61ZQPvaaPc"
   },
   "source": [
    "## 3 -  Principal Component Analisis. General Architecture\n",
    "**Mathematical expression of the algorithm**:\n",
    "\n",
    "Principal Component Analysis (PCA) is a simple linear transformation technique that is used in numerous applications, such as stock market predictions, the analysis of gene expression data, and many more. \n",
    "\n",
    "Steps of the algorithm:\n",
    "- Standardize the data;\n",
    "- Obtain the Eigenvectors and Eigenvalues from the covariance matrix;\n",
    "- Sort eigenvalues in descending order and choose the $k$ eigenvectors that correspond to the $k$ largest eigenvalues where $k$ is the number of dimensions of the new feature subspace $(k≤$n_features);\n",
    "- Construct the projection matrix $W$ from the selected $k$ eigenvectors;\n",
    "- Transform the original dataset $X$ via $W$ to obtain a $k$-dimensional feature subspace $Y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "cdhebXYbaaPf"
   },
   "source": [
    "### 3.1 -  Eigendecomposition: Computing Eigenvectors and Eigenvalues, \n",
    "\n",
    "**Standardizing the data**\n",
    "\n",
    "Whether to standardize the data prior to a PCA on the covariance matrix depends on the measurement scales of the original features. Since PCA yields a feature subspace that maximizes the variance along the axes, it makes sense to standardize the data, especially, if it was measured on different scales. \n",
    "\n",
    "Let's transform the data onto unit scale, which is a requirement for the optimal performance of many machine learning algorithms. We will do it using standard score:\n",
    "$$z = \\frac{x - \\mu}{\\sigma}\\tag{1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0ZxJqj47aaPg"
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: normalize\n",
    "\n",
    "def normalize(X):\n",
    "    \"\"\"\n",
    "    Normalise data before processing\n",
    "    \n",
    "    Arguments:\n",
    "    X -- matrix of input features of shape (n_examples, n_features)\n",
    "    \n",
    "    Returns:\n",
    "    X_norm -- normalized matrix of shape (n_examples, n_features)\n",
    "    norm_parameters -- matrix of normalization parameters, such as mean and std by columns;\n",
    "        shape (2, n_features)\n",
    "        \n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ### \n",
    "\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    return X_norm, norm_parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3mIontZ7aaPn"
   },
   "outputs": [],
   "source": [
    "norm_test, norm_pars_test = normalize(X)\n",
    "print('Normalized:')\n",
    "print(norm_test[0])\n",
    "print('Parameters:')\n",
    "print(norm_pars_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AWQFoMvlaaPy"
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:60%\">\n",
    "    <tr>\n",
    "        <td style=\"width:10%\"><b>Normalized:</b></td>\n",
    "       <td> [-0.89985013 -1.19521931 -0.49137306]</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><b>Parameters:</b></td>\n",
    "       <td>[[30.92307692 59.53846154 53.15384615]<br>\n",
    " [21.02914292 21.36717607 16.59400334]]</td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "_UN07P2jaaP2"
   },
   "source": [
    "The eigenvectors and eigenvalues of a covariance (or correlation) matrix represent the \"core\" of a PCA: The eigenvectors (principal components) determine the directions of the new feature space, and the eigenvalues determine their magnitude. In other words, the eigenvalues explain the variance of the data along the new feature axes.\n",
    "\n",
    "**Covariance Matrix**\n",
    "\n",
    "The classic approach to PCA is to perform the eigendecomposition on the covariance matrix $Σ$, which is a $n_{features}×n_{features}$ matrix where each element represents the covariance between two features.\n",
    "\n",
    "We can summarize the calculation of the covariance matrix via the following matrix equation:\n",
    "$$C = \\frac{1}{N} \\sum_{n=1}^{N} (x(n)_i – {\\bar{x}}_i)(x(n)_j – {\\bar{x}}_j)\\tag{2}$$\n",
    "where $\\bar{x}$ is the mean vector ${\\bar{x}} = \\sum\\limits_{k=1}^n x_{k}$.\n",
    "The mean vector is a $n_{features}$-dimensional vector where each value in this vector represents the sample mean of a feature column in the dataset.\n",
    "\n",
    "\n",
    "**Correlation Matrix**\n",
    "\n",
    "A correlation matrix is used if the variances of individual variates differ much, or if the units of measurement of the individual variates differ.\n",
    "\n",
    "$$R_{ij} = \\frac{c_{ij}}{\\sqrt{c_{ii}c_{jj}}},\\tag{3}$$\n",
    "where $c$ - elements of covariation matrix.\n",
    "\n",
    "\n",
    "**SVD**\n",
    "\n",
    "While the eigendecomposition of the covariance or correlation matrix may be more intuitiuve, most PCA implementations perform a Singular Vector Decomposition (SVD) to improve the computational efficiency. \n",
    "\n",
    "To perform SVD in the right way we need to transpose the input matrix, so $X^T$ will have dimension $n_{features}×n_{samples}$. Let us assume that it is centered, i.e. column means have been subtracted and are now equal to zero.\n",
    "\n",
    "Then the $n_{features}×n_{features}$ covariance matrix $C$ is given by $$C=X^TX/(n_{samples}−1).\\tag{4}$$ It is a symmetric matrix and so it can be diagonalized: $$C = ULU^T,\\tag{5}$$\n",
    "where $U$ is a matrix of eigenvectors (each column is an eigenvector) and $L$ is a diagonal matrix with eigenvalues $λ_i$ in the decreasing order on the diagonal. The eigenvectors are called principal axes or principal directions of the data. Projections of the data on the principal axes are called principal components, also known as PC scores; these can be seen as new, transformed, variables. The $j$-th principal component is given by $j$-th column of $X^TV$. The coordinates of the $i$-th data point in the new PC space are given by the $i$-th row of $UX^T$.\n",
    "\n",
    "If we now perform singular value decomposition of $X^T$, we obtain a decomposition\n",
    "$$X^T=USV^T,\\tag{6}$$\n",
    "where $U$ is a unitary matrix and $S$ is the diagonal matrix of singular values $s_i$. From here one can easily see that $$C = USV^TVSU^T/(n_{samples}-1) = U \\frac{S^2}{n_{samples}-1}U^T,\\tag{7}$$\n",
    "meaning that right singular vectors $U$ are principal directions and that singular values are related to the eigenvalues of covariance matrix via $λ_i=s^2_i/(n_{samples}−1)\\tag{8}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZxHUD411aaP4"
   },
   "outputs": [],
   "source": [
    "# GRADED CLASS: Eigendecomposition\n",
    "\n",
    "class Eigendecomposition():\n",
    "        \n",
    "    def covariance(self, X):\n",
    "        \"\"\"\n",
    "        Calculates eigenvectors and eigenvalues of covariance matrix\n",
    "        Arguments:\n",
    "        \n",
    "        X -- normalized input matrix with shape (n_examples, n_features) \n",
    "        \n",
    "        Returnes:\n",
    "        \n",
    "        eig_vals -- array of eigenvalues with shape (n_features, )\n",
    "        eig_vecs -- matrix of eigenvectors with shape (n_features, n_features)\n",
    "        \"\"\"\n",
    "        \n",
    "        ### START CODE HERE ###\n",
    "        \n",
    "        ### END CODE HERE ###\n",
    "        return e_val, e_vect\n",
    "    \n",
    "    def correlation(self, X):\n",
    "        \"\"\"\n",
    "        Calculates eigenvectors and eigenvalues of correlation matrix\n",
    "        Arguments:\n",
    "        \n",
    "        X -- normalized input matrix with shape (n_examples, n_features) \n",
    "        \n",
    "        Returnes:\n",
    "        \n",
    "        eig_vals -- array of eigenvalues with shape (n_features, )\n",
    "        eig_vecs -- matrix of eigenvectors with shape (n_features, n_features)\n",
    "        \"\"\"\n",
    "        \n",
    "        ### START CODE HERE ###\n",
    "        \n",
    "        ### END CODE HERE ###\n",
    "        return e_val, e_vect\n",
    "    \n",
    "    def svd(self, X):\n",
    "        \"\"\"\n",
    "        Calculates eigenvectors and eigenvalues by svd\n",
    "        Arguments:\n",
    "        \n",
    "        X -- normalized input matrix with shape (n_examples, n_features)\n",
    "        \n",
    "        Returnes:\n",
    "        \n",
    "        eig_vals -- array of eigenvalues with shape (n_features, )\n",
    "        eig_vecs -- matrix of eigenvectors with shape (n_features, n_features)\n",
    "        \"\"\"\n",
    "        \n",
    "        ### START CODE HERE ###\n",
    "\n",
    "        ### END CODE HERE ###\n",
    "        return e_val, e_vect\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1wvKwcXMaaQE"
   },
   "outputs": [],
   "source": [
    "cov_vals, cov_vects = Eigendecomposition().covariance(norm_test)\n",
    "\n",
    "for ev in cov_vects:\n",
    "    np.testing.assert_array_almost_equal(1.0, np.linalg.norm(ev))\n",
    "print('Everything ok!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "MSRrHUP9aaQN"
   },
   "outputs": [],
   "source": [
    "cor_vals, cor_vects = Eigendecomposition().correlation(norm_test)\n",
    "\n",
    "for ev in cor_vects:\n",
    "    np.testing.assert_array_almost_equal(1.0, np.linalg.norm(ev))\n",
    "print('Everything ok!')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "z1VS00guaaQd"
   },
   "outputs": [],
   "source": [
    "svd_vals, svd_vects = Eigendecomposition().svd(norm_test)\n",
    "\n",
    "for ev in svd_vects:\n",
    "    np.testing.assert_array_almost_equal(1.0, np.linalg.norm(ev))\n",
    "print('Everything ok!')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "y5JS154SaaQq"
   },
   "source": [
    "### 3.2-3.3 - Selecting Principal Components, Projection Onto the New Feature Space\n",
    "\n",
    "The typical goal of a PCA is to reduce the dimensionality of the original feature space by projecting it onto a smaller subspace, where the eigenvectors will form the axes. \n",
    "\n",
    "In order to decide which eigenvector(s) can be dropped without losing too much information for the construction of lower-dimensional subspace, we need to inspect the corresponding eigenvalues: the eigenvectors with the lowest eigenvalues bear the least information about the distribution of the data - those are the ones can be dropped.\n",
    "\n",
    "So now we need to implement following steps:\n",
    "1. Compute eigenvectors $(e_1,e_2,...,e_d)$ and corresponding eigenvalues $(λ_1,λ_2,...,λ_d)$.\n",
    "In order to do so, the common approach is to rank the eigenvalues from highest to lowest in order choose the top $k$ eigenvectors.\n",
    "2. Sort the eigenvectors by decreasing eigenvalues and choose $k$ eigenvectors with the largest eigenvalues to form a $n_{features}×k$ dimensional matrix $W$ (where every row represents an eigenvector)\n",
    "3. Use this $n_{features}×k$ eigenvector matrix to transform the samples onto the new subspace. This can be summarized by the mathematical equation: $$Y=X_{normalized}×W\\tag{9}$$ (where $X_{normalized}$ is an normalized input matrix with shape $n_{samples}×n_{features}$, and $Y$ is the transformed $n_{samples}×k$-dimensional matrix of samples in the new subspace.)\n",
    "\n",
    "4. To restore input matrix $X$ we should do next operation: $$X_{restored} = Y×W^T.\\tag{10}$$ But don't forget that we worked with normalized data, so we also have to put it to the initial form back (use `norm_parameters` from `normalization` function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "04kV_rK3aaQs"
   },
   "outputs": [],
   "source": [
    "# GRADED CLASS: PCA\n",
    "\n",
    "class PCA():\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "    -----------\n",
    "    X -- matrix of input features of shape (n_examples, n_features) \n",
    "    n -- number of principal components\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, X, n, eigendecomposition):\n",
    "        self.X = X\n",
    "        self.n = n\n",
    "        self.eigendecomposition = eigendecomposition\n",
    "        self.X_norm = None\n",
    "        self.norm_params = None\n",
    "        \n",
    "        \n",
    "    def transform(self):\n",
    "        \"\"\"\n",
    "        Transforms the samples into the new subspace\n",
    "        \n",
    "        Returns:\n",
    "        transformed -- reduced matrix of input features with shape (n_samples, n)\n",
    "        matrix_w -- matrix of n eigenvectors with largest eigenvalues with shape (n_features, n)\n",
    "        \"\"\"\n",
    "        \n",
    "        ### START CODE HERE ###\n",
    "\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        return transformed, matrix_w\n",
    "\n",
    "        \n",
    "    def restore(self):\n",
    "        \"\"\"\n",
    "        Restores \"original\" values\n",
    "\n",
    "        Returns:\n",
    "        matrix with shape (n_features, n_examples), \n",
    "            containing restored values depending on reduced input matrix of features   \n",
    "        \"\"\"\n",
    "        \n",
    "        ### START CODE HERE ###\n",
    "\n",
    "        ### END CODE HERE ###"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WRMghyQ8aaQ0"
   },
   "source": [
    "After completing all steps, the next question is “how many principal components are we going to choose for our new feature subspace?” A useful measure is the so-called “explained variance,” which can be calculated from the eigenvalues. The explained variance tells us how much information (variance) can be attributed to each of the principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "mDyCNuCXaaQ2"
   },
   "outputs": [],
   "source": [
    "tot = sum(cov_vals)\n",
    "var_exp = [(i / tot)*100 for i in sorted(cov_vals, reverse=True)]\n",
    "cum_var_exp = np.cumsum(var_exp)\n",
    "\n",
    "with plt.style.context('seaborn-whitegrid'):\n",
    "    plt.figure(figsize=(6, 4))\n",
    "\n",
    "    plt.bar(range(3), var_exp, alpha=0.5, align='center',\n",
    "            label='individual explained variance')\n",
    "    plt.step(range(3), cum_var_exp, where='mid',\n",
    "             label='cumulative explained variance')\n",
    "    plt.ylabel('Explained variance ratio')\n",
    "    plt.xlabel('Principal components')\n",
    "    plt.legend(loc='best')\n",
    "    plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "vS_uUQMGaaQ9"
   },
   "source": [
    "The plot above clearly shows that most of the variance (~77% of the variance to be precise) can be explained by the first principal component alone. The second principal component still bears some information (~19%) while the third and fourth principal components can safely be dropped without losing to much information. Together, the first two principal components contain ~96% of the information.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ynEAoZ5waaRD"
   },
   "source": [
    "Initialize model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "5lQqOjCaaaRE"
   },
   "outputs": [],
   "source": [
    "pca = PCA(X, 2, Eigendecomposition().correlation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4qxSCzoqaaRJ"
   },
   "source": [
    "Reducing of input matrix dimencion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "iyoR8Iz3aaRK"
   },
   "outputs": [],
   "source": [
    "reduced_x, reduced_eigenvects = pca.transform()\n",
    "print('Reduced input matrix:')\n",
    "print(reduced_x[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PuptB9EfaaRT"
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\">\n",
    "    <tr>\n",
    "       <td style=\"width:15%\">\n",
    "           <b>Reduced input matrix:</b>\n",
    "       </td>\n",
    "       <td> [[-1.49086967 -0.15159675]<br>\n",
    " [-1.3199115  -0.10840709]<br>\n",
    " [-1.50049321  0.29895991]<br>\n",
    " [ 0.87097958 -0.90026658]<br>\n",
    " [ 0.7886636  -0.71439948]]\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "-ueVCiI3aaRV"
   },
   "source": [
    "Let's plot our reduced data and compare it with original:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "G4yIZtwmaaRY"
   },
   "outputs": [],
   "source": [
    "plt.plot(reduced_x.T[0,:], reduced_x.T[1,:], 'o', markersize=7, color='blue', alpha=0.5, label='Reduced')\n",
    "\n",
    "plt.xlabel('x_values')\n",
    "plt.ylabel('y_values')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "iPbOaVunaaRf"
   },
   "source": [
    "Now let's restore \"original\" values by the reduced:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "eYUZ_E_caaRi"
   },
   "outputs": [],
   "source": [
    "new_x = pca.restore()\n",
    "print('Restored:')\n",
    "print(new_x[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "zb1bvdpSaaRp"
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:60%\">\n",
    "    <tr>\n",
    "       <td style=\"width:10%\">\n",
    "           <b>Restored:</b>\n",
    "       </td>\n",
    "       <td> [[11.51573657 41.48068378 39.47263947]<br>\n",
    " [14.1995759  43.36459173 40.86399609]<br>\n",
    " [19.41116905 38.09599585 36.27911059]<br>\n",
    " [24.69623033 77.24494687 67.94674095]<br>\n",
    " [27.07495924 74.84206341 65.85558128]]\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "hvtfeBnZaaRq"
   },
   "source": [
    "Visualising of restored values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "g6kZU-PYaaRr"
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from mpl_toolkits.mplot3d import proj3d\n",
    "\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(X.T[0, :], X.T[1, :], X.T[2, :], 'o', markersize=8, color='blue', alpha=0.5, label='Initial')\n",
    "ax.plot(new_x.T[0, :], new_x.T[1, :], new_x.T[2, :], '^', markersize=8, alpha=0.5, color='red', label='Restored')\n",
    "\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1-NEa2ipaaRx"
   },
   "source": [
    "## 4 - Trying the Algorithm on Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "J8rLkRUAaaRy"
   },
   "source": [
    "Initializing the model for processing our data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "AutIQu6waaRz"
   },
   "outputs": [],
   "source": [
    "pca_img = PCA(img, 50, Eigendecomposition().covariance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "8-pIiKWpaaR4"
   },
   "outputs": [],
   "source": [
    "reduced_img, reduced_eigenvects_img = pca_img.transform()\n",
    "print('Reduced array:')\n",
    "print(reduced_img.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "AcVkXBWxaaR8"
   },
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:25%\">\n",
    "    <tr>\n",
    "       <td>\n",
    "        <b>Reduced array:</b>\n",
    "       </td>\n",
    "       <td> (1280, 50)\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "NIvpWjTkaaR9"
   },
   "source": [
    "Now let's restore the image and compare it with original:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9hlAvHa3aaR_"
   },
   "outputs": [],
   "source": [
    "restored_img = pca_img.restore()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zZ1qd0bgaaSE"
   },
   "outputs": [],
   "source": [
    "imgplot = plt.imshow(img, cmap='gray')\n",
    "print('Initial:')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "1Hb6O3dCaaSJ"
   },
   "outputs": [],
   "source": [
    "imgplot = plt.imshow(restored_img, cmap='gray')\n",
    "print('Restored:')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "bKI29Qy-aaSN"
   },
   "source": [
    "## 5 - Conclusion\n",
    "\n",
    "As we can see, our algorithm solves problem of reducing dimension of data well.\n",
    "\n",
    "**What's next:**\n",
    "1. Try to experiment with different ways of eigendecomposition and values of k.\n",
    "2. Compare the results you have obtained with the `sklearn.decomposition.PCA`.\n",
    "3. Try this model in the wild! Select your favorite dataset [here](https://www.kaggle.com/datasets?sortBy=hottest&group=public&page=1&pageSize=20&size=small&filetype=all&license=all&tagids=13303) and play with it."
   ]
  }
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