{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem Sheet 9 - Dimension Reduction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this exercise, we focus on the two dimension reduction techniques considered in the lecture:\n",
    "- Principal component regression (PCR) and principal component analysis (PCA) \n",
    "- Partial least squares (PLS)\n",
    "\n",
    "Both techniques are used to construct a low-dimensional set of features from a large set of variables, i.e., instead of solving a learning problem in terms of the original variables $X_1, \\ldots, X_p$, we replace these by a smaller number of new variables $Z_1,\\ldots, Z_M$ with $M < p$.\n",
    "The $Z_m$ are chosen as linear combinations of the original predictor variables, i.e.,\n",
    "\n",
    "$$ Z_m = \\sum_{j=1}^p \\phi_{j,m} X_j $$\n",
    "\n",
    "with coefficients $\\phi_{1,m}, \\ldots, \\phi_{p,m}$ for $m = 1,\\ldots,M$.\n",
    "\n",
    "After this step, we can use one of the already known learning methods.\n",
    "Denote by $\\boldsymbol y \\in \\mathbb R^n$ and $\\boldsymbol Z \\in \\mathbb R^{n \\times (M+1)}$ the observation vector and the data matrix (now with the $M$ data columns obtained as linear combinations of the columns of the original data matrix $\\boldsymbol X$ with coefficients $\\phi_{j,m}$). \n",
    "\n",
    "In the case of (standard) linear regression, our new problem reads\n",
    "\n",
    "$$ \\min_{{\\boldsymbol \\theta} \\in \\mathbb{R}^{M+1}} \\|{\\boldsymbol Z} {\\boldsymbol \\theta} - {\\boldsymbol y}\\|_2^2.$$\n",
    "\n",
    "One important application of this approach is given in situations where $p$ is large relative to $n$.\n",
    "In this case choosing $M << p$ can significantly reduce the variance in the model, while a regression applied to the original data might lead to a a highly overfitted model with a training error of zero.\n",
    "Another advantage lies in the reduced computational cost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 9.1 - Principle Component Analysis and LDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by loading the iris data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris()\n",
    "X = iris.data\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Scale the data matrix `X` to have mean 0 and variance 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import scale\n",
    "Xscaled = scale(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Import the function `PCA` provided by `sklearn.decomposition`.\n",
    "Take a short look into the documentation and perform a principal component analysis on your scaled data using 2 components.\n",
    "Store the 2 principal components as a variable `pc`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 2)\n",
    "pc = pca.fit_transform(Xscaled)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Find out, what fraction of the variance in the data is explained by these 2 principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9581320720000165"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now you should be able to plot the principal components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (15,9)\n",
    "\n",
    "for i in range(3):\n",
    "    idx = (y == i)\n",
    "    plt.scatter(pc[idx,0], pc[idx,1], label=iris.target_names[i])\n",
    "    \n",
    "plt.title('2 component PCA')\n",
    "plt.xlabel('1st principal component')\n",
    "plt.ylabel('2nd principal component')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe, that the data is quite well seperated.\n",
    "But if we plot all variables against each other, we see that there are also pairs of variables that are similar, or even better separated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (15,9)\n",
    "fig, ax = plt.subplots(3,3)\n",
    "\n",
    "for i in range(4):\n",
    "    for j in range(4):\n",
    "        if i < j:\n",
    "            for k in range(3):\n",
    "                idx = (y == k)\n",
    "                ax[i][j-1].scatter(X[idx,i], X[idx,j], label=iris.target_names[k])\n",
    "                ax[i][j-1].set_xlabel(iris.feature_names[i])\n",
    "                ax[i][j-1].set_ylabel(iris.feature_names[j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Fit a linear discriminant analysis using the 2 principal components from above.\n",
    "What proportion of the *training data* is classified correctly?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "clf = LDA()\n",
    "clf.fit(pc, y)\n",
    "clf.score(pc,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Compare the optained score to the classification error of models incorporating exactly two of the original variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LDA on variables 0 and 1\n",
      "\t\tscore = 0.8000\n",
      "LDA on variables 0 and 2\n",
      "\t\tscore = 0.9667\n",
      "LDA on variables 0 and 3\n",
      "\t\tscore = 0.9600\n",
      "LDA on variables 1 and 2\n",
      "\t\tscore = 0.9533\n",
      "LDA on variables 1 and 3\n",
      "\t\tscore = 0.9667\n",
      "LDA on variables 2 and 3\n",
      "\t\tscore = 0.9600\n"
     ]
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "\n",
    "for i in range(4):\n",
    "    for j in range(4):\n",
    "        if i < j:\n",
    "            print('LDA on variables %d and %d' % (i, j))\n",
    "            clf = LDA()\n",
    "            clf.fit(X[:,[i,j]], y)\n",
    "            print('\\t\\tscore = %6.4f' % clf.score(X[:,[i,j]],y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation**:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation**:\n",
    "Altough principal component analysis has explained more than 95\\% of the variance in the data, this doesn't, by any means, guarantee that a regression applied to the principle components `is better` than any other fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PCA for dimension reduction\n",
    "\n",
    "As we have already mentioned, principal component analysis can be used to decrease the computational cost of different learning procedures by reducing the number of variables in our model.\n",
    "Therefore, we now use a slightly larger data set.\n",
    "The **MNIST** data set is widely used for testing.\n",
    "It contains 70,000 grey-valued images of size 28x28, each assigned with a digit from 0 to 9.\n",
    "\n",
    "**Task**: Download the `mnist_784.csv` from the class web page.\n",
    "Adapt the following code and read the `csv` file into a `pandas DataFrame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "df = pd.read_csv('./datasets/mnist_784.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell splits the data into training and test data.\n",
    "It should be executable once you read the `csv` file correctly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "ntrain = 60000\n",
    "X = df.iloc[:ntrain,:-1].values.astype(float)\n",
    "y = df.iloc[:ntrain,-1].values\n",
    "Xtest = df.iloc[ntrain:,:-1].values.astype(float)\n",
    "ytest = df.iloc[ntrain:,-1].values\n",
    "\n",
    "# Number of pixels along on axis\n",
    "npxl = np.sqrt(X.shape[1]).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following cell plots the first numbers in the data set.\n",
    "Images can be plottet using the function `plt.imshow()`.\n",
    "\n",
    "**Task**: Execute the code from below and try to explain the term `ax[i//npix][i%npix]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "npix = 4\n",
    "fig, ax = plt.subplots(npix,npix)\n",
    "\n",
    "for i in range(npix**2):\n",
    "    x = X[i,:]\n",
    "    ax[i//npix][i%npix].imshow(x.reshape((npxl,npxl)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: *Train/Fit* a `StandardScaler` using your training data, and *transform* both, your training and test set.\n",
    "Store the scaled versions under their names, i.e., `X` and `Xtest`.\n",
    "You can import it by\n",
    "\n",
    "    from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "stdScaler = StandardScaler()\n",
    "\n",
    "# Fit on training set, as discussed in previous exercise\n",
    "stdScaler.fit(X)\n",
    "X = stdScaler.transform(X)\n",
    "Xtest = stdScaler.transform(Xtest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Now plot the scaled numbers again. Copy and paste the code from above. Try to explain, why some numbers appear lighter and some darker."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(npix,npix)\n",
    "\n",
    "for i in range(npix**2):\n",
    "    x = X[i,:]\n",
    "    ax[i//npix][i%npix].imshow(x.reshape((npxl,npxl)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Perform a linear discriminant analysis on your full data set `X`.\n",
    "Measure the time your computer needs to perform this task.\n",
    "You can do this easily by using the *magic command* `% time` in front of your `*.fit(X,y)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 33 s, sys: 1.47 s, total: 34.5 s\n",
      "Wall time: 14.9 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/miniconda3/lib/python3.7/site-packages/sklearn/discriminant_analysis.py:388: UserWarning: Variables are collinear.\n",
      "  warnings.warn(\"Variables are collinear.\")\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis(n_components=None, priors=None, shrinkage=None,\n",
       "              solver='svd', store_covariance=False, tol=0.0001)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "lda = LDA()\n",
    "%time lda.fit(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: What is the proportion of correct classications on your test set?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.873"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.score(Xtest,ytest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Perform a truncated principal component analysis of your scaled data `X`.\n",
    "Depending wheather the optional parameter `n_components` is an integer larger or equal to 1, or a float betwean 0 and 1, the behaviour is different.\n",
    "Setting the option `n_components = 0.9` lets the algorithm choose the number of components, such that these principal components declare 90\\% of the variability in the data.\n",
    "Store the principal components as a `numpy.ndarray` named `pc`.\n",
    "\n",
    "**Caution**: You can find out the number of principal components in the model using the attribute `*.n_components_`.\n",
    "There is also the attribute `*.n_components` which is the value of the option that you specified."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "236\n"
     ]
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 0.9)\n",
    "pca.fit(X)\n",
    "pc = pca.transform(X)\n",
    "print(pca.n_components_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Perform now an LDA using these principal components. Measure the time that is necessary for this operation, and compare the score on your test set with the score obtained by using the full model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.27 s, sys: 548 ms, total: 7.82 s\n",
      "Wall time: 3.1 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8717"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda_pc = LDA()\n",
    "%time lda_pc.fit(pc,y)\n",
    "lda_pc.score(pca.transform(Xtest),ytest)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You should observe that the computing time has been reduced by 3/4.\n",
    "The score of 87.2\\% is comparable to the previous reached 87.3\\% in the full model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A closer look at PCA, and its connection to SVD\n",
    "As you all know from the lecture, principal component anaylsis (PCA) is strongly connected to a (truncated) singular value decomposition (SVD).\n",
    "\n",
    "Assume, that the matrix $X \\in \\mathbb{R}^{n \\times p}$ is scaled, i.e. has column-mean zero and variance one.\n",
    "Then the covariance matrix $C$ is given by $C = X^T X$.\n",
    "This is a symmetric matrix, and thus can be diagonalized into\n",
    "\n",
    "$$ C = V \\Lambda V^T $$\n",
    "\n",
    "with $V \\in \\mathbb{R}^{p \\times p}$ the matrix of eigenvectors of $C$ and $\\Lambda = \\text{diag}(\\lambda_1, \\ldots, \\lambda_p)$ the matrix of eigenvalues on the diagonal.\n",
    "The columns of the matrix $V$ are called principal directions of the data, and projections of the data on the principal directions are called *principal components*.\n",
    "Thus, the $j$-th column of the matrix $XV$ is called the $j$-th principal component.\n",
    "\n",
    "#### Full SVD\n",
    "\n",
    "If we perform a full SVD of the matrix $X \\in \\mathbb{R}^{n \\times p}$, we obtain the decomposition\n",
    "\n",
    "$$ X = U \\Sigma V^T $$\n",
    "\n",
    "with a unitary matrix $U \\in \\mathbb{R}^{n \\times n}$ (left-singular vectors),\n",
    "a \"diagonal\" matrix $\\Sigma \\in \\mathbb{R}^{n \\times p}$ (singular values $\\Sigma_{i,i}$, rest zero),\n",
    "and a unitary matrix $V \\in \\mathbb{R}^{p \\times p}$ (right-singular vectors).\n",
    "\n",
    "Thus, we see that\n",
    "\n",
    "$$ C = X^T X = (U \\Sigma V^T)^T (U \\Sigma V^T) = V \\Sigma^2 V^T. $$\n",
    "\n",
    "In other words, this says that the right-singular vectors are principal directions, and the principal components are given by\n",
    "\n",
    "$$ XV = (U \\Sigma V^T) V = U \\Sigma. $$\n",
    "\n",
    "#### Truncated SVD\n",
    "\n",
    "In comparison to a full SVD, a truncated SVD **approximates** the matrix by restricting only on the $k$ largest singular values, i.e.,\n",
    "\n",
    "$$ X \\approx U_k \\Sigma_k V_k^T $$\n",
    "\n",
    "with matrices \n",
    "$U_k \\in \\mathbb{R}^{n \\times k}$,\n",
    "$\\Sigma_k \\in \\mathbb{R}^{k \\times k}$,\n",
    "$V_k \\in \\mathbb{R}^{p \\times k}$.\n",
    "\n",
    "Thus, we get the first $k$ principal components by\n",
    "\n",
    "$$ X V_k = U_k \\Sigma_k \\in \\mathbb{R}^{n \\times k}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Task**: Read the documentation of the sklearn function `PCA`.\n",
    "We see, that `pca.components_` is equivalent to the matrix $V_k^T$.\n",
    "Assign the matrix `V` by `pca.components_.T` and check the size of the matrix.\n",
    "\n",
    "The rest of this notebook is prepared for you.\n",
    "Please make sure, that you understand each step.\n",
    "Ask questions or have a look into the documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Solution**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784, 236)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = pca.components_.T\n",
    "V.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Can we resemble the principal components? Yes, we can! Remember, it's the matrix product of $X$ and $V_k$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.105427357601002e-15"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(X.dot(V)-pc).max()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can assign the matrix with the singular values.\n",
    "The method `pca.singular_values_` returns a vector, but we can easily store it as a diagonal matrix $\\Sigma$.\n",
    "This is also true for $\\Sigma^{-1}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "Sigma = np.diag(pca.singular_values_)\n",
    "SigmaInv = np.diag(1./pca.singular_values_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Is the size correct?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(236, 236)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sigma.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And therefore, we can also compute the matrix $U_k$ by simple matrix multiplication.\n",
    "This can, as you know, done either by the `numpy.ndarray` method `.dot()`, or by the operator `@`.\n",
    "\n",
    "**Remember**: The operator `*` performs an element-wise multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "U = X @ V @ SigmaInv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 236)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is an interesting exercise to plot the first principal directions, i.e., the first columns of the matrix $V_k$.\n",
    "What do you observe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x648 with 16 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "npix = 4\n",
    "fig, ax = plt.subplots(npix,npix)\n",
    "\n",
    "for i in range(npix**2):\n",
    "    x = V[:,i]\n",
    "    ax[i//npix][i%npix].imshow(x.reshape((npxl,npxl)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we want to compare some numbers and their corresponding approximations using PCA.\n",
    "\n",
    "We can compute the approximations simply by setting \n",
    "\n",
    "$$ X_{\\text{approx}} = U_k \\Sigma_k V_k^T $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "Xapprox = U @ Sigma @ V.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, plotting is easy. You can play with $m$ to display different samples in the data set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, '%d principal components')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoTGfcA0BzETG6ZINErhjkcmVf1yjHmMg10vcryXYusJWMc+IYUSs5j5EYY2Z8kmKEh77S7xnWl8zindlmSorEMud+clubNJhoN47Jzker22ueq9tP5dIgOY+j3E5kal32ZbWztScRl5z79Hvdal5IBtO53fn+5snmuSZzhc793HrW2d9tHtTLvWexKbF8ZPeDlvr0q/rsAAAAAIDGaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFKYz7gFsZBGRCxwk4mKQy5UZY2Z8UnqM0U/EDZLz0Uoc2+j3c7mSWied2DgmOu1UrtgynYrzzbc1juk98D6pXLvvv6lxzKF7OJVr87dzy9Xx//frjWMieZjNzr02FCpTDka4DEQ7t6A6WR9bvRHWg0RYdHLzEa3cNtqZaUzOh7uJWtfOLYuDqdzua3/zRPOYqdGe0xhMNs+3/6Tc8nHoxObzH7lUmr49t05v+0bzhNPfOZjKldmetmZ6uVxLff5VfXYAAAAAQGM0agAAAABQGBo1AAAAACjMsj6jZvtGSXsl9SX1IuKslRgUAABrHTUSALAcK/FlIj8WETtX4HkAAFhvqJEAgBQufQQAAACAwiy3UQtJ/2D7c7bPn+8Bts+3vd329plB8usyAQBYe45aI4frY7e7fwzDAwCUbLmXPj4mIm6xfZKkS21/JSIuH35ARFwo6UJJOnbypOQf2AIAYM05ao0cro/HbD2V+ggAmGVZZ9Qi4pb6/x2SPiTp7JUYFAAAax01EgCwHOlGzfYW29uO/CzpJyRds1IDAwBgraJGAgCWazmXPp4s6UO2jzzPuyLi4ysyKgAA1jZqJABgWdKNWkTcIOlhKzgWAADWBWokAGC5+Hp+AAAAACjMSvzB6w0vIvllXYNkXAwSMblcnp5uHtTvp3JpUyKXJE1PNo9Jzv1g61TjGPdH+2VuiaVDUV2e1Zizy/697tk4pD/VTqXadHuvcczU7tx8bLlpXyoOyMqsg9HOHaN1N7Ftb+XWpXR9HCS2gK3cfPQ3N9+F6m3J7XZFbvMnZ8pxdruekaw9g04urrcpEZcc48Te3L5Qa6b5Mtw5lFuG2zOJ15ZcPCb35gIn9nYbx7iX2ROSNNl8RYvsNm6JOKMGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDCdcQ+gNBEx7iEsLjFGH7MtlWr/g05qHNM+PEjlah/qp+LcbR7nfm6M7ieWj+wylY2zm4ckc/lbO1Jxarcbh0zv2pvLlZGYQ0mKgwdHl2+QO84WiTAn5wOrL1qZZSe5vmc2f9lcyW10Zl3qbZ1IpTp8fPO47ubRrkvOlNXkECMR157JLR/t7gj31ZL1ceJALxXXub15HZnYM5XKNbW7eVxqP0jS1J2HU3Ht3c3nY7AlNx/RThTIVV4UOaMGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQmM64B7AuDCIXF4OVHcfRUu07kIqb2N9rHpR8We7nAjNx7iffswQfnMkFDnLzEVumE0G5+ejffkcqzu1285hOcnOVyTUxulyjZnvcQ8ACnFgPQ83fz1a33zhGkqLT/NhuJJe3bD3IGEzkjlkPEqu7c1OvVi+3jXYibNBJvmeJXJN7chMysbebihtMNn/T+lO55aO9PzfG1t79jWN8OLef0T6YGGNy38TZ7c5E4j3bMpHK1T7QfJ832qtbUzmjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwnXEPAAmDaB7TPZxKNXnjzsYxMT2VyuV9B1Jx/Xsd3zgm2k7lah3qNY4Z3HRzKpf6/VSYp5rPf+ukE1O5BqkorIhWbhlGucKJ9zSzGGTySIrEMudMvZLkXm7rEp3mx5/bh3Pb2qndzWPcy81Hq5+bj/5Uu3FMb1PuGH6r2/y1Te6eSeVq7zmUihtsmmgc0+o2j5GWsQxPJvJ1mr/PkqTEGB25ZTimcvPY3zLZPFeyPvpwt3HMYEtun3epOKMGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQmM64B4CyDXbe0TwoIpdrZiYV156abBzTO3FbKpfv2J2KS2m3U2Fx+HDjmN5NN6dyycljPdm4jNYaOB41yvnA+pLb3I7OIDnAfi7O0W8c096Xqz2d3c3H6G7z8UlSTCTrwXHTjWNaE07lavUS83E4Nx+a6abCWv1B45jsGN3tpeLUaf5ex+TodueTu3iKdm65cuI9ax9sHiNJMTXRPCb5upaKvQMAAAAAKAyNGgAAAAAUhkYNAAAAAAqzaKNm+yLbO2xfM3TbCbYvtf21+v/jV3eYAACUhxoJAFgtSzmjdrGkJ8657eWSLouIMyRdVv8OAMBGc7GokQCAVbBooxYRl0ua+9V/T5V0Sf3zJZKetsLjAgCgeNRIAMBqyX5G7eSIuFWS6v9PWuiBts+3vd329pnBwWQ6AADWjCXVyOH62O3uH+kAAQDlW/UvE4mICyPirIg4a7K1abXTAQCwJgzXx4mJLeMeDgCgMNlG7Tbbp0hS/f+OlRsSAABrGjUSALBs2UbtI5LOrX8+V9KHV2Y4AACsedRIAMCyLeXr+d8t6QpJ32v7Ztu/KOm1kp5g+2uSnlD/DgDAhkKNBACsls5iD4iIcxa46/ErPBYAANYUaiQAYLWs+peJAAAAAACaWfSMGja4iOYh3d4qDORoCRNj7OSOUQxOPqFxjO/clcoVide1rrU4rgTM5cz2z8lcg+a5nN2MZVf3QSLVoWTN6vWbx/QTMZKsyVRcRrRyC8ggs0fZzi6MuTjPdJvHHDiUypUVm6ebByXnI7P/lM6V5F5ipU7uPw2mJxrHuL+6+2rs+QAAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoTGfcA8BoRMS4h7BqBrfe1jimvW1TKld/61TjmM62balcceedubh+PxWX4uSxnpYTuRIxkpyJy76uEUq9Lqw7kVgORrl4Rzu5nE7mdk/cGzSOiUSMJI10DRzkxtiaaV4PPGincmUmpL9pIpeq27wWS5IOzjTP1UvW1LWw35XYfmTX6WiPbsPjSI4xEdbq59bNJT//qj47AAAAAKAxGjUAAAAAKAyNGgAAAAAUhkYNAAAAAApDowYAAAAAhaFRAwAAAIDC0KgBAAAAQGFo1AAAAACgMDRqAAAAAFAYGjUAAAAAKAyNGgAAAAAUhkYNAAAAAApDowYAAAAAhemMewBIiMHocg1GmCsp+s3H2LrxllSu1hmnNY6Jk++RytXePJ2Ki/0HGsf0d96eyiXnwrB8EZGKs3nT1pXM25lbdBSZZSe7uHWSx5ET64UjOchBYoz9fiqVD82k4jq7m48x2rm5721uN44ZTOZydY/flIprbZlsHNPeM5HK5UOHU3GpZbibW64itZ6NuIa0mueLQW4j1+o135/MzeHScUYNAAAAAApDowYAAAAAhaFRAwAAAIDC0KgBAAAAQGFo1AAAAACgMDRqAAAAAFAYGjUAAAAAKAyNGgAAAAAUhkYNAAAAAApDowYAAAAAhaFRAwAAAIDC0KgBAAAAQGE64x5AaWw3jglFLlkk49Yrj+64weDAgVRc64ZbGsfEqSencg2O3ZKKUyKu3W6nUsXuPbk4ln1gZSRWJfeT65+bx0U7t113b5CKUyYsuz1K7C+kYiSp10+Fef/BxjGd5Bjdm2ocM5jO1Z7u1uTuq5vHTSaX4c7uVJjcTbzXg9z64l7zmGgl1+nsLl5iexXt5DKcydVKrtNLxBk1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwnTGPQCsQy3n4gaxsuM4ikjm6t95Z+MYHziQytW+971ScYNjNjeOiVNOTOVqbd6Uiovbm89j9PupXCkxSAa2V3QYwGIczbdlg4ncMdpWt/l64W5uvXUvuQ4OEnHJVOHmtc4Tud2uSLzPkuRe8/lvHTiUy9XtNY6JTZOpXIrpVFh/uvk2urc5t12PdvNaLEmd/d3GMa0DM6lcSixXmW1OlSq5j5eIi06yvUm81V7lfVfOqAEAAABAYWjUAAAAAKAwNGoAAAAAUJhFGzXbF9neYfuaodsusP0t21fX/568usMEAKA81EgAwGpZyhm1iyU9cZ7b/zgizqz/fWxlhwUAwJpwsaiRAIBVsGijFhGXS7pjBGMBAGBNoUYCAFbLcj6j9kLbX6wv+zh+oQfZPt/2dtvbZwYHl5EOAIA1Y9EaOVwfu939ox4fAKBw2UbtLZLuL+lMSbdKev1CD4yICyPirIg4a7KV+5tLAACsIUuqkcP1cWJiyyjHBwBYA1KNWkTcFhH9iBhIequks1d2WAAArE3USADASkg1arZPGfr16ZKuWeixAABsJNRIAMBK6Cz2ANvvlvQ4SSfavlnSqyQ9zvaZkkLSjZKev4pjBACgSNRIAMBqWbRRi4hz5rn5baswFgAA1hRqJABgtSznWx8BAAAAAKtg0TNqG01EjHsIZWk17+U9GKRSRfawwaD5e+aWU6kimsfF4cOpXL0bv5GKa5+w4F/LWNDg9FMWf9A8+icek4rztsQ3wH79m6lcwLqW2P4NpnOl373m23b3kjU1WUeUCHOy7ocT9SBRUyXJU5OpuGj1mufqNo+RJO870DzmwKFUrsmDM6m4/vGbG8ccPmEqlevwCROpuMFk82VkMrkM+1Dz9zqz3FeB2W1BLiwj89qy24+l4owaAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMJ0xj2ADW0Q4x7B6mjl+n8PBqm4yKQbJMfYbh4T/X4qV1b/jjsbx/j0U1K5wqkwDbZONY6ZOGZbKlfsP9A8yBzDwtowmGy+UWodHuE2KbsqpTbsktS8jsQgtyHL1qxcsuTGttN8+Yjk63Ky9qdydXu5uH7z/a7+dO51Hd42uvno7M/tzrdnms+jI7fvGkouwwnuJ9fN1ujGuFTsjQAAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSmM+4BrAsxGG2+QYwul908JkY4PklOjDGyhyj6zUNaW7emUrWOPSYVF5unG8cMMu/zMrQO9hrHDPbsTeVyu52KA0bNmW1novx0dh9sHiSpd+ymxjHRyW1sW4ebbyMkydF8W+ZsDe8mxpitj9ntWCcRN5HbNYxEXCRfV0znxtjdNtk4pj+Rq49OvtXuNw90P7cMZ3Kl959aycARnlKKxL5QarvdAGfUAAAAAKAwNGoAAAAAUBgaNQAAAABN+SbeAAAVCUlEQVQoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACtMZ9wBQuIjmMYPByo/jKCIxxtbUVCqX73F845jBtk2pXP12OxWXknmfJTmci+v3mwe1kseVWrkxpniEubC+WBp0mi/j7YPdxjGDqYnGMZIU7ebLtwe5bYuyZSSxLYvkeuvMNimz7ZPS2+jMa4stufrY39R8uepvytW5wUTuPYtEPWh3c3PfOZxbiCd39xrHtA7MpHJll6tUqsT2I8v97PqSCUqlWjLOqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoTGfcA8CIDAYjSxURqTh3cotj+/jjGscMTtiWyjVotxvHODsfybiwG8e0DnZTuXT7rlRY7N3XOCa7fKS0ms8hsCwhud98nY+J5tukwydMNY6RpOnvHGoc424/lUu9XM3KbDejkztmHZ3JxjHp+UjWg8HmicYxM8fnlo/e5ubL4mAit63NrCuS1DnQfLma2ttL5Wodzr3X7UQ9zs5HtJov+5l9jGUZJF5bep+3vPNX5Y0IAAAAADY4GjUAAAAAKAyNGgAAAAAUZtFGzfZptj9h+zrb19p+cX37CbYvtf21+v/jV3+4AACUgxoJAFgtSzmj1pP00oh4kKQfkvQC2w+W9HJJl0XEGZIuq38HAGAjoUYCAFbFoo1aRNwaEVfVP++VdJ2kUyU9VdIl9cMukfS01RokAAAlokYCAFZLo8+o2T5d0sMlXSnp5Ii4VaoKlaSTFog53/Z229tnBgeXN1oAAArVtEYO18dud/8ohwoAWAOW3KjZ3irpA5JeEhF7lhoXERdGxFkRcdZka1NmjAAAFC1TI4fr48TEltUdIABgzVlSo2Z7QlUBemdEfLC++Tbbp9T3nyJpx+oMEQCAclEjAQCrYSnf+mhJb5N0XUS8Yeiuj0g6t/75XEkfXvnhAQBQLmokAGC1dJbwmMdIeo6kL9m+ur7tFZJeK+l9tn9R0jckPWN1hggAQLGokQCAVbFooxYRn5LkBe5+/MoOBwCAtYMaCQBYLY2+9REAAAAAsPqWcukjVktroYOwi4hEXOR68urjFw1jNue+3TPudc9UXH+i3TjGEalcHgxScalcB2dycbff2ThmsGdfLtdEchPSbv6epdeXTK7Ecl/FJY99JV5bZt1EwazUctCfTCzfSe3b9zaOiU5yfNm4xHoRrdx6O5hObP+2TKZyRXL7193afIz9Tbn5yOxmtA/naurE3n4yrnld9eFuKpeyuwuJeYzEfpAkRaaOtJO1Z5Db70pJrtNKDDE1hw1wRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYTrjHsC64GS/G/1c3NRU45DB/e6VShV2Ki6j1U3ORz9WdiBH4QOHmwftvDOVa7B3byouszx6IrkpaLdTYW4n1plkLmWW4ew63Rrd+gJI0uSO/c1jur1csoOHGof0Tj85lap77GQqrtUdNA9KlpD+VPPtRH9TbtvSnxjdtmXiQGIOJU3u6TaOae+ZSeVqHcrFqZ94bZl6JUmtXNygnajHnRGed4nR7XNJStXVQXLf1YnlI7LLxxJxRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwnXEPoDS2G8fs/pH7pXLd8cB2Km5qdyLmzkEq1/SufuOYzoHmMZKk5lMvSWp1m7+21o5dqVz9b+9oHjSIVC53kqtnu/ly5USMJKmVfNMy+RLrZhWXOB6VfV1Jme0O1plQalvRO2a6cUznjv2NYyRp79n3aRxz8xNyy7aPm0nF6TtTjUO23pQ7Zj21q/n7FdnNWK6MaGpP8/o4tfNwKldn597GMT6UfJ/bufcsNjVfPtRK5loD2/XM8ujkzlp2GR5k6nEyVySXq9VU3ogAAAAAYIOjUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQmM64B7AefPCNb0jFndTekop7yJU/3zjm0BeOS+Xy/2seM3X74VSu1qFeKs433do4ZjAzk8vVSawyrdzxENupOLUScU4es8nkkqTMaxv1GBPS7xkwQr0Tt6bibju73TjmtT/xrlSuZ27dnYp7867TGse8/rNPSOXqXzfdOGbTjkjlmto9SMVN39681rX35mp4Zrsem5vPoSTFVG73NdrNl2FH7j3TIPeejVSiPsYgNx9OTqN7iXlM1v0osIZzRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYWjUAAAAAKAwNGoAAAAAUBgaNQAAAAAoDI0aAAAAABSGRg0AAAAACkOjBgAAAACFoVEDAAAAgMLQqAEAAABAYTrjHsB68LxH/sxI850WO5sHDb6z8gNZSAyScZGLa7lxiCcnR5Zr5DzCMXqEx3pGOPce5RwCIzZxy52puNN/++rGMX/y+Welcv3Bcblty+ad/cYxD7j5QCpXa8/uVFyGe81flyRFYrsZ01OpXP0TtjTPNeqamtjNcD+3T+N+8rWNsv4MEhOSfM8G2deVCUvuTpaIM2oAAAAAUBgaNQAAAAAoDI0aAAAAABRm0UbN9mm2P2H7OtvX2n5xffsFtr9l++r635NXf7gAAJSB+ggAWE1L+TKRnqSXRsRVtrdJ+pztS+v7/jgi/mj1hgcAQLGojwCAVbNooxYRt0q6tf55r+3rJJ262gMDAKBk1EcAwGpq9Bk126dLerikK+ubXmj7i7Yvsn38AjHn295ue/vM4OCyBgsAQImWWx+73f0jGikAYK1YcqNme6ukD0h6SUTskfQWSfeXdKaqI4qvny8uIi6MiLMi4qzJ1qYVGDIAAOVYifo4MdH8b1ABANa3JTVqtidUFaF3RsQHJSkibouIfkQMJL1V0tmrN0wAAMpDfQQArJalfOujJb1N0nUR8Yah208ZetjTJV2z8sMDAKBM1EcAwGpayrc+PkbScyR9yfbV9W2vkHSO7TMlhaQbJT1/VUYIAECZqI8AgFWzlG99/JQkz3PXx1Z+OAAArA3URwDAamr0rY8AAAAAgNW3lEsfUZjqYxHNxChb8kEyWfOXlefBCHOtgeMhrVFOfk5muQdwd917HZcLvPe8f2XgqI65blcq1bH7c3/OJyaa79bElulUru4pxzTPldzWtg71c3Hd5nHRSdasQTQOae+bSaVyt5eKi6nE8jGZ21UeJOMy9dj93D6Ne83jmr/LtYnRLVfryRrYgwQAAACAjYVGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwnTGPQCMhu3RJWuPMFda7hhFRKzwOFbeSN9rABvHoPn2r3fcplyuZFwkNn9ObtZbB3vNcyXmUJKik6tZg4l24xj3B6lcmXkcbJ1M5Yr2dCouw91+Kq7Vy83jIPFeRytZ9zO5svsYa2D/qUScUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACgMjRoAAAAAFIZGDQAAAAAKQ6MGAAAAAIWhUQMAAACAwtCoAQAAAEBhaNQAAAAAoDA0agAAAABQGBo1AAAAACiMI2J0yezvSLppgbtPlLRzZIMpH/MxG/MxG/NxF+ZitlLm474Rcc9xD2KtoD42wnzMxnzMxnzMxnzMVsp8LKlGjrRROxrb2yPirHGPoxTMx2zMx2zMx12Yi9mYj/WH93Q25mM25mM25mM25mO2tTYfXPoIAAAAAIWhUQMAAACAwpTUqF047gEUhvmYjfmYjfm4C3MxG/Ox/vCezsZ8zMZ8zMZ8zMZ8zLam5qOYz6gBAAAAAColnVEDAAAAAIhGDQAAAACKM/ZGzfYTbX/V9vW2Xz7u8Yyb7Rttf8n21ba3j3s8o2b7Its7bF8zdNsJti+1/bX6/+PHOcZRWmA+LrD9rXoZudr2k8c5xlGyfZrtT9i+zva1tl9c374hl5GjzMeGXUbWG2rkbNRIauQwauRdqI+zrZf6ONbPqNluS/p/kp4g6WZJn5V0TkR8eWyDGjPbN0o6KyJK+GN8I2f7RyTtk/T2iPj++rY/kHRHRLy23lE5PiL+2zjHOSoLzMcFkvZFxB+Nc2zjYPsUSadExFW2t0n6nKSnSTpPG3AZOcp8PFMbdBlZT6iRd0eNpEYOo0behfo423qpj+M+o3a2pOsj4oaImJH0HklPHfOYMEYRcbmkO+bc/FRJl9Q/X6JqRdsQFpiPDSsibo2Iq+qf90q6TtKp2qDLyFHmA+sDNRKzUCNno0behfo423qpj+Nu1E6V9M2h32/WGpzEFRaS/sH252yfP+7BFOLkiLhVqlY8SSeNeTwleKHtL9aXfWyIyxjmsn26pIdLulIsI3PnQ2IZWQ+okXdHjby7Db/9m8eG3v5RH2dby/Vx3I2a57lto/+9gMdExCMkPUnSC+rT+sCwt0i6v6QzJd0q6fXjHc7o2d4q6QOSXhIRe8Y9nnGbZz42/DKyTlAj744aicVs6O0f9XG2tV4fx92o3SzptKHfv0vSLWMaSxEi4pb6/x2SPqTq0peN7rb6WuMj1xzvGPN4xioibouIfkQMJL1VG2wZsT2haqP7zoj4YH3zhl1G5puPjb6MrCPUyDmokfPasNu/+Wzk7R/1cbb1UB/H3ah9VtIZtu9ne1LSsyR9ZMxjGhvbW+oPPMr2Fkk/Iemao0dtCB+RdG7987mSPjzGsYzdkQ1u7enaQMuIbUt6m6TrIuINQ3dtyGVkofnYyMvIOkONHEKNXNCG3P4tZKNu/6iPs62X+jjWb32UpPprMd8oqS3pooh4zVgHNEa2v1vVEUJJ6kh610abD9vvlvQ4SSdKuk3SqyT9jaT3SbqPpG9IekZEbIgPDy8wH49Tdco+JN0o6flHrj9f72w/VtI/S/qSpEF98ytUXXe+4ZaRo8zHOdqgy8h6Q428CzWSGjkXNfIu1MfZ1kt9HHujBgAAAACYbdyXPgIAAAAA5qBRAwAAAIDC0KgBAAAAQGFo1AAAAACgMDRqAAAAAFAYGjUAAIAxsX1P25+yfY3tpw3d/mHb914g5nTby/r7T7b/t+0HJ2M/vYy8n7R9VjZ+rbD9tOz8AkfQqAEAAIzPOZIukfQoSS+TJNs/LemqiLhlNRLabkfEL0XElzPxEfHolR7TOvQ0STRqWBYaNQAAgPHpStokaUrSwHZH0ksk/eHwg2z/gO0v2L5C0gvmeyLbj7N9ue0P2f6y7T+33arv22f7v9u+UtKjhs9s1fe9pn7+z9g+ub795Pq5vlD/e/SRxy8h31tsb7d9re1XLzYJth9p+9N1nn+1vc32tO2/tP0l25+3/WP1Y8+z/Te2P2r732y/0PZ/rR/zGdsn1I/7pO031s97je2z69tPqOO/WD/+ofXtF9i+qI67wfaLhsb3C/W4rrb9F7bbC81dPU//UdIf1o+/v+0X1XP0RdvvWcJyAdCoAQAAjNG7JP2kpI9LukDSr0p6e0QcmPO4v5T0ooh41CLPd7akl0p6iKT7S/qZ+vYtkq6JiB+MiE/Nidki6TMR8TBJl0v65fr2P5H0T/Xtj5B0bYN8vx0RZ0l6qKQfPdIMzcf2pKT3Snpxnes/SDqouiGNiIeoPvNoe7oO+35JP1/nf42kAxHxcElXSHru8GurzwD+qqSL6tteLenzEfFQSa+Q9Pahxz9Q1ftxtqRX2Z6w/SBJPyfpMRFxpqS+pGcvNHcR8WlJH5H0sog4MyK+Lunlkh5e5/yVheYCGEajBgAAMCYRsTsifqpuaq6S9BRJH7D9Vtvvt/0o28dKOi4i/qkO+6ujPOW/RsQNEdGX9G5Jj61v70v6wAIxM5L+tv75c5JOr3/+cUlvqcfZj4jdDfI90/ZVkj4v6ft09MsAv1fSrRHx2TrXnojo1c/1V/VtX5F0k6QH1DGfiIi9EfEdSbslfbS+/UtD41c9JkXE5ZKOsX3cnOf9R0n3qOdYkv4uIg5HxE5JOySdLOnxkn5A0mdtX13//t2LzN1cX5T0Ttu/IKl3lLkA/l1n3AMAAACAJOl3VZ0dOkfVTv+7JH1Y0tMlxRKfY+7jjvx+qG6m5tONiCOP66vZ/uHd8tm+n6TfkPTIiLjT9sWSpu8WeRfP8zxHbl/I4aGfB0O/DzR7/PPNx3zPe+Rxw897ZC4s6ZKI+K154pY6dz8l6UdUXRL5StvfVzejwII4owYAADBmts+QdO/6rNlmVQ1HSJqOiF2Sdts+crbq2Qs8jSSdbft+9WfFfk7S3Mscm7hM0n+px9e2fcwS8x0jaX895pMlPWmRPF+RdG/bj6xzbas/q3e56tdq+wGS7iPpqw1fw8/V8Y+VtLs+Kzj8vI+TtDMi9hzlOS6T9LO2T6pjTrB930Xy7pW0rX58S9JpEfEJSb8p6ThJWxu+DmxANGoAAADj9xpJv1P//G5J50n6jKQ/qm97nqQ3118mcvAoz3OFpNdKukbSv0n60DLG9GJJP2b7S6rO8H3fUvJFxBdUXfJ4rarPhf3L0ZJExIyqhupNtr8g6VJVZ+D+TFK7zv9eSedFxOGFn2led7r6cwJ/LukX69sukHSW7S/WYz93kfF9WdV78w91zKWSTlkk73skvcz25yWdIekd9ev4vKQ/rptv4Kh819laAAAArFX12aHfiIinrMd8Tdn+pKrxbR/3WIAMzqgBAAAAQGE4owYAAAAAheGMGgAAAAAUhkYNAAAAAApDowYAAAAAhaFRAwAAAIDC0KgBAAAAQGH+P0qTDM5aqPD1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = 0\n",
    "fig, ax = plt.subplots(1,2)\n",
    "ax[0].imshow(X[m,:].reshape((npxl,npxl)))\n",
    "ax[0].set_title('Original (%d pixel)' %  (npxl**2))\n",
    "ax[1].imshow(Xapprox[m,:].reshape((npxl,npxl)))\n",
    "ax[1].set_title('Approximation')\n",
    "ax[1].set_xlabel('%d principal components')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}