08-PCA-Fin.ipynb 622 KB
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis\n",
    "\n",
    "In this lesson we will investigate Principal Component Analysis (PCA), which is a powerful technique for manipulating data. So far we have only considered supervised learning algorithms, where labels are predicted based on training data. For unsupervised learning algorithms we do not use labels, but rather investigate relationships within the data features. Cluster analysis is another class of unsupervised learning algorithms, which is particularly useful for  classification problems. This will be considered next week.\n",
    "\n",
    "PCA can be used for unsupervised learning, but it can also be used for visualization, dimensionality reduction and noise filtering. These will be briefly discussed below.\n",
    "\n",
    "PCA treats the $n$ samples and $m$ features of the data as an $n\\times m$ matrix or table, and uses a linear algebra technique known as Singular Value Decomposition to split this into $m$ matrices which are ordered by the amount of variation they account for in the original matrix. As PCA deals with the variance of a matrix, the data should first be normalized so that each column has zero mean. However, the `sklearn` function `PCA` takes this into account, so this normalization does not need to occur.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first introduct the standard libraries."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 34,
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   "metadata": {},
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   "outputs": [],
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A simple two-dimensional dataset\n",
    "\n",
    "To introduce PCA we create a simple two-dimensional data set that approximately lies on a straight line."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 35,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1) # initializes a random number generator\n",
    "# rand(n,m) creates a (n,m) matrix with random numbers uniformly distributed in [0,1)\n",
    "# randn(n,m,mu,var) creates a (n,m) matrix with random numbers with mean mu and variance var\n",
    "# default values are mu=0 and var=1\n",
    "# dot multiplies a (p,q) and (q,r) matrix to produce a (p,r) matrix and T is the transpose\n",
    "# mean slope of the resultant line is dependent on the random seed\n",
    "X = np.dot(rng.rand(2,2), rng.randn(2,200)).T\n",
    "plt.scatter(X[:,0], X[:,1]) # scatter plot of dataset\n",
    "plt.axis('equal'); # keep the scale of the axes equal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA has the same calling structure as other `sklearn` routines, so we first import the library, then instantatiate it with the chosen hyperparameters and finally fit the data to the model.\n",
    "\n",
    "Since this is unsupervised learning, there are two things we should note about fitting the data: \n",
    "1. We don't split the data into training and testing sets.\n",
    "2. We don't have target values.\n",
    "\n",
    "The argument for `PCA` in this case is the number of components to calculate. This must be an integer less than or equal to the number of features or a floating point number between 0 and 1. We will consider the floating point option later. If `n_components` is not specified, it is set equal to the number of features. Here we specify the `n_components=2`, which is equal to the number of features."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 36,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
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     "execution_count": 36,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=2) #instantatiate PCA to calculate two PCs\n",
    "pca.fit(X) # fit our data to the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now investigate the output of `PCA`. The first output of interest are the principal components. These are vectors in the feature space which are chosen to account for the primary variation in the data. The first principal component has a slope of approximately 1/3, which is the approximate slope of the scatter plot above. This is consistent with the observation that most of the variation in the data points occurs along the line $y \\approx x/3$. The second principal component is chosen as a vector which is orthogonal (at right-angles) to the first principal component. Since we are working in two-dimensions, there is only one direction (to within a plus or minus) which satisfies this. `PCA` normalizes the principal components so that their length is one, which can be seen by calculating their norm (without any other arguments this is the length of the vector)."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 37,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First PC is: [-0.94446029 -0.32862557]\n",
      "Length of vector is: 1.0\n",
      "Second PC is: [-0.32862557  0.94446029]\n",
      "Length of vector is: 1.0\n"
     ]
    }
   ],
   "source": [
    "for ord, vector in zip(['First','Second'], pca.components_): #loop through the array of strings and the PCs\n",
    "    print('{0} PC is: {1}'.format(ord,vector)) # print the PC\n",
    "    print('Length of vector is: {0}'.format(np.linalg.norm(vector))) # print the length of the PC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second output is the explained variance or the explained variance ratio. The explained variance is the contribution of that principal component to the variance of the data matrix. Recall that the principal components are ordered based on their contribution to the variance of the data matrix, therefore the explained variance decreases with each principal component. An alternative version of this is the explained variance ratio, which is a rescaling of the explained variance such that the contributions sum to one. Hence for this example 97.6% of the variance can be explained by the first principal component, and the remaining 2.4% by the second principal component."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 38,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First PC variance and variance ratio is: 0.763 0.976\n",
      "Second PC variance and variance ratio is: 0.018 0.024\n"
     ]
    }
   ],
   "source": [
    "#loop through the array of strings and the explained variance and explained variance ratio for the PCs\n",
    "for ord, var, ratio in zip(['First','Second'], pca.explained_variance_, pca.explained_variance_ratio_):\n",
    "    # print the explained variance and explained variance ratio for each PC\n",
    "    print('{0} PC variance and variance ratio is: {1} {2}'.format(ord, np.round(var,3), np.round(ratio,3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The explained variance can also be considered geometrically. If we scale the principal component vectors so that they have length proportional to the standard deviation (the square root of the variance), then we can expect a particular percentage of the data points to lie within the limits of that vector. If the vector is three times the standard deviation then, assuming points are normally distributed, 99.8% of the data points should lie within an ellipse whose major and minor axes are the scaled principal components. This is shown in the figure below. In higher dimensions this will be an ellipsoid."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 39,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "def draw_vector(v0, v1, ax=None):\n",
    "    '''Function to draw a vector from v0 to v1 with an arrow head'''\n",
    "    ax = ax or plt.gca() # if ax is specified use these axes, otherwise get the current axes\n",
    "    # define a dictionary with the properties of the arrow, '->' is a one-sided arrow\n",
    "    arrowprops = dict(arrowstyle='->', linewidth=2) \n",
    "    # draw a line from v0 to v1 with the arrow properties, string to annotate figure is empty\n",
    "    ax.annotate('', v1, v0, arrowprops=arrowprops) \n",
    "\n",
    "plt.scatter(X[:,0], X[:,1], alpha=0.5) # scatter plot of data and specify transperancy\n",
    "# loop over the explained variance and the PCs\n",
    "for length, vector in zip(pca.explained_variance_, pca.components_): \n",
    "    v = vector * 3 *np.sqrt(length) # define a vector which is 3 times the standard deviation\n",
    "    draw_vector(pca.mean_, pca.mean_ + v) # draw the vector with an arrowhead\n",
    "theta = np.linspace(0,2*np.pi) # define an array from 0 to 2*pi\n",
    "# create a zero array of size (length of theta, 2) which will have \n",
    "# the ellipse coordinates\n",
    "Y = np.zeros((len(theta),2)) \n",
    "# first component of Y is the x coordinate which is proportional to the\n",
    "# standard deviation of the first PC\n",
    "Y[:,0] = 3*np.sqrt(pca.explained_variance_[0])*np.cos(theta)\n",
    "# first component of Y is the y coordinate which is proportional to the\n",
    "# standard deviation of the first PC\n",
    "Y[:,1] = 3*np.sqrt(pca.explained_variance_[1])*np.sin(theta)\n",
    "Z = pca.inverse_transform(Y) # transform Y from component space to feature space\n",
    "plt.plot(Z[:,0],Z[:,1],'--') # plot Z in component space as a dotted line\n",
    "plt.axis('equal'); # make the axis scales equals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The datapoints can also be viewed transformed into component space. If we denote each of the principal components as $P_1$ and $P_2$, then the values in component space for the $j^{th}$ sample, $X_j$, are $Y_{1,j}$, $Y_{2,j}$, where\n",
    "\n",
    "$$\n",
    "X_j = Y_{1,j}P_1 + Y_{2,j}P_2.\n",
    "$$\n",
    "\n",
    "We refer to $Y_{1,j}$ as *Component 1* and $Y_{2,j}$ as *Component 2*. These are the amplitudes of the principal components. This component space is just a translated, rotated and rescaled version of the original feature space. Now the ellipse which bounds the data points has the x-axis as the major axis and the y-axis as the minor axis."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 40,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = pca.transform(X) # transform X to component space\n",
    "plt.scatter(Z[:,0], Z[:,1], alpha=0.5) # scatter plot of data and specify transperancy\n",
    "plt.xlabel('Component 1') # add x label\n",
    "plt.ylabel('Component 2') # add y label\n",
    "# plot the ellipse defined in the previous cell\n",
    "plt.plot(Y[:,0],Y[:,1],'--');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we only calculate one principal component then the dimension of the data is reduced. Storage is therefore reduced or compressed and any machine learning algorithm that is applied to the data is then significantly more efficient, as there is now only one feature. "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 41,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original shape:  (200, 2)\n",
      "Transformed shape:  (200, 1)\n"
     ]
    }
   ],
   "source": [
    "pca = PCA(n_components=1) # instantatiate PCA to calculate the first PC\n",
    "pca.fit(X) # fit the data\n",
    "Y = pca.transform(X) # transform the data to component space\n",
    "print('Original shape: ',X.shape) # print the size of the feature matrix\n",
    "print('Transformed shape: ', Y.shape) # print the size of the component space matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we transform the reduced data back to the original feature space, we obtain an approximation to the original data where there is now only variation in the direction of the first principal component. Now\n",
    "\n",
    "$$\n",
    "X_j \\approx Y_{1,j}P_1.\n",
    "$$\n",
    "\n",
    "However, as the first principal component accounts for 97.6% of the variance of the data, we are only losing a small amount of information. In the figure below the blue dots are the original data points and the orange dots are the approximation using only the first principal component. The other way to consider this is that the data is being projected onto the first principal component, i.e., each data point is moved to the closest point on the first principal component."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 42,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "Z = pca.inverse_transform(Y) # transform the component space matrix back to feature space\n",
    "plt.scatter(X[:,0], X[:,1], alpha=0.5, label='Original data') # scatter plot of the original data\n",
    "plt.scatter(Z[:,0], Z[:,1], alpha=0.5, label='Compressed data') # scatter plot of the data using 1 PC\n",
    "plt.legend() # add legend based on labels in scatter plots\n",
    "plt.axis('equal'); # make the axis scales equal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The iris dataset\n",
    "\n",
    "To investigate PCA further, it is helpful to have more than two features. Therefore we will load the iris data set which was investigated in previous notebooks. Here it is loaded from the `sklearn` datasets, so we first view the keys for each component of the dataset."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 43,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename'])"
      ]
     },
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     "execution_count": 43,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "\n",
    "iris = load_iris() # load the iris data set\n",
    "iris.keys() # display the labels for the components of the data set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that the features are the dimensions of the sepal and petal, and the targets are the three types of iris. These can be displayed by printing `feature_names` and `target_names`."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 44,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature names: ['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "Target names:  ['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "print('Feature names:',iris.feature_names) # print the feature names\n",
    "print('Target names: ',iris.target_names) # print the target names"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can investigate how the three types of iris are separated in terms of the first two principal components. Recall that as there are four features, there will be four principal components. Fitting the data to the first two principal components, we see that these are vectors in four-dimensional space and both have length one. Each of the principal components can be thought of as a three-dimensional space embedded in four-dimensional space. The first principal component accounts for 92% of the variance in the data, while the second component accounts for 5% of the variance of the data."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 45,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First PC: [ 0.36138659 -0.08452251  0.85667061  0.3582892 ]\n",
      "Length:  1.0\n",
      "Explained variance ratio:  0.925\n",
      "Second PC: [ 0.65658877  0.73016143 -0.17337266 -0.07548102]\n",
      "Length:  1.0\n",
      "Explained variance ratio:  0.053\n"
     ]
    }
   ],
   "source": [
    "X = iris.data # copy the iris features to an array \n",
    "y = iris.target # copy the iris target values to an array\n",
    "\n",
    "pca = PCA(n_components=2)  # instantatiate PCA to calculate the first two PCs\n",
    "X_pca = pca.fit_transform(X) # transform the data to component space\n",
    "# loop over the string array, the principal components and the explained variance ratio\n",
    "for ord, vector, ratio in zip(['First','Second'], pca.components_, pca.explained_variance_ratio_):\n",
    "    print('{0} PC: {1}'.format(ord,vector)) # print the PC\n",
    "    print('Length: ', np.round(np.linalg.norm(vector),3)) # print the length PC rounded to 3 figures\n",
    "    # print the contribution to the variance rounded to 3 figures\n",
    "    print('Explained variance ratio: ', np.round(ratio,3)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the dataset in terms of the first two components, it is apparent that the data can largely be classified in terms of these two components. "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 46,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# loop over (0,2) and the iris target names\n",
    "for i, target_name in zip(range(3), iris.target_names):\n",
    "    # scatter plot of the component values which match the particular species\n",
    "    # label this with the current target name\n",
    "    plt.scatter(X_pca[y == i, 0], X_pca[y == i, 1], label=target_name)\n",
    "plt.legend() # add a legend\n",
    "plt.xlabel('Component 1') # add a x label\n",
    "plt.ylabel('Component 2') # add a y label\n",
    "plt.axis('equal'); # make the axis scales equal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As well as choosing the number of principal components we can choose the explained variance which we want to include in the model. `PCA` will then choose the number of principal components which account for that explained variance.\n",
    "\n",
    "To understand this consider the explained variance for all the principal components for the iris data set. We can plot the effect of including up to the $n^{th}$ principal component, by calculating the sum of the explained variance ratios up to that component. This is known as the cumulative sum, and gives the proportion of the variance which is accounted for by including $n$ principal components. This is shown in the figure below, and for the iris model if we want to account for 95% of the variance, we need to include two principal components. "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 47,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA().fit(X) # fit the X data using PCA and calculate all PCs\n",
    "# np.cumsum calculates the cumulative sum of an array\n",
    "# plot the cumulative sum of the explained variance ratio against the number of components\n",
    "plt.plot(range(1,5),np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components') # add x label\n",
    "plt.ylabel('cumulative explained variance'); # add y label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To specify the proportion of variance that is accounted for, we can set `n_components` to a floating number between 0 and 1. Then `PCA` will calculate the number of principal components required to account for this variance. If we set this equal to 0.95, i.e., account for 95% of the variance, then from the shape of the transformed array it can be seen that two principal components are calculated, as expected."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 48,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original shape:  (150, 4)\n",
      "transformed shape: (150, 2)\n"
     ]
    }
   ],
   "source": [
    "# instantatiate PCA and calculate sufficient PCs such that 95% of the variance is accounted for \n",
    "pca = PCA(n_components=0.95) \n",
    "X_pca = pca.fit_transform(X) # transform the data to component space\n",
    "print(\"original shape: \",X.shape) # print the size of the feature matrix\n",
    "# print the size of the component matrix to show the number of components calculated\n",
    "print(\"transformed shape:\", X_pca.shape) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This data set can be transformed back into feature space and compared against the first two features of the iris data. As is apparent, some information is lost by only using two principal components, however the approximation is reasonably accurate."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 49,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1]) # scatter plot of the original data\n",
    "Z = pca.inverse_transform(X_pca) # transform from component space back to feature space\n",
    "plt.scatter(Z[:, 0], Z[:, 1]) # plot the projection of the data using 2 PCs\n",
    "plt.xlabel('Sepal length (cm)') # add a x label\n",
    "plt.ylabel('Sepal width (cm)'); # add a y label "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Image processing\n",
    "\n",
    "Finally, we investigate how PCA can be used for processing images. The `sklearn` digits dataset consists of a collection of 1,797 handwritten numbers from 0 to 9 each digitised onto an 8x8 grid of pixels. Hence we have 1,797 samples and 64 features. The targets are the number each image corresponds to. These can be used for training machine learning algorithms in image recognition. By printing the keys we can see the labels for each component of the dataset."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 50,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'images', 'DESCR'])"
      ]
     },
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     "execution_count": 50,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "\n",
    "digits = load_digits() # load the digits data set\n",
    "digits.keys() # display the labels for the components of the data set"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 51,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
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     "execution_count": 51,
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data.shape # display the size of feature matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand the format of the images we can plot the first 40 together with the target values shown in the lower left side of the image."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 52,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 720x360 with 40 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,5)) # set up a figure of size 10 x 5\n",
    "\n",
    "for i in range(40): # loop over the first 40 images\n",
    "    # on a 4 x 10 grid add the next plot with no xticks or yticks\n",
    "    ax = fig.add_subplot(4,10,i+1,xticks=[],yticks=[]) \n",
    "    ax.imshow(digits.images[i], cmap=plt.cm.binary) # plot the image i of the digits and use binary colourmap\n",
    "    ax.text(0,7,str(digits.target[i])) # add the target value in the lower left corner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will first use `PCA` to undertake some simple unsupervised learning by plotting the classifications of the digits against the first three components. This reveals that each of the classes occupies a distinct region in the component space. This could then be used in conjunction with a regression algorithm to obtain an approximate classification of the images."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 53,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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Simon Clarke committed
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      "image/png": 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\n",
650
>>>>>>> master
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Simon Clarke committed
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      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits import mplot3d # import function to enable 3-dimensional plotting in matplotlib\n",
    "\n",
    "pca = PCA(n_components=3) # instantatiate PCA with 3 PCs\n",
    "projected = pca.fit_transform(digits.data) # fit the data and transform to component space\n",
    "\n",
    "fig = plt.figure(figsize=(8,6)) # set up a figure of size 8 x 6\n",
    "ax = plt.subplot(projection='3d') # initialize the 3d axes\n",
    "# 3d scatter plot with points coloured by their targets values\n",
    "p = ax.scatter3D(projected[:,0], projected[:,1], projected[:,2], c=digits.target)\n",
    "ax.set_xlabel('Component 1') # add x label\n",
    "ax.set_ylabel('Component 2') # add y label\n",
    "ax.set_zlabel('Component 3') # add z label\n",
    "fig.colorbar(p); # add colourbar to p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For images the principal components can be interpreted as individual images. Each of these contribute to the variance of the collection of images. To illustrate this we can plot the 64 principal components in order of their contribution the variance. This is shown below where decreasing variance corresponds to left to right and then top to bottom. For the first few principal components there is information on almost every pixel, apart from the sides, but then as the importance decreases the amount of information decreases until the last row, where only one or two pixels are of importance for each principal component.\n",
    "\n",
    "Each individual sample can then be reconstructed from these principal components given their values in component space. If we denote each of the principal components as $P_1$, $P_2$, $\\dots$, $P_{64}$ and the values in component space for the $j^{th}$ sample as $Y_{1,j}$, $Y_{2,j}$, $\\dots$, $Y_{64,j}$, then\n",
    "\n",
    "$$\n",
    "X_j = Y_{1,j}P_1 + Y_{2,j}P_2 + \\cdots + Y_{64,j}P_{64}.\n",
    "$$\n",
    "\n",
    "If we only have $n$ principal components and we are projecting the data onto these components, then\n",
    "\n",
    "$$\n",
    "X_j \\approx Y_{1,j}P_1 + Y_{2,j}P_2 + \\cdots + Y_{n,j}P_{n}.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 54,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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b9WumZ5mamfXo0UPGVUVAbOZ3KtTn3HzzzTJXlZbFSn8uv/xyGf/yyy/dmNcrQvWQSNKuXTs3FivV3Hfffd2YKmsyM3vmmWdkXJWqemWcsbXaK+vXr58bmzJlisz94osv3NgZZ5whc3v37l3tfatZ+an2aNhzzz3dWKxUVa3RfsQRR8jcOXPmyLh6b3iVTKlUK5jp99q5554rc1Wp7eeffy5zr7/+ehn/5JNP3Jh3jqmeu1qTP1aquWzZMjf2y1/+UuZWLqOuTFWhqXs7KZaRkeG+C9XzF6uUmz9/vhu76KKLZO5HH30k448//rgb8ypMYteevxgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAI0ipXnDFjhhubMGGCzPW6/JnpJjVmZt99952Mq45aseZGqejcubMb69q1q8yt3NGtPK8bWpkBAwbIuGrmsqNKl1TJWqxZkbo3YqWav//972VcNe9SXSdTsd9++7mxqVOnylzV1CRW7vbxxx/LuDo/9b00bNhQ7rcydQ7vvfeezD3wwAPd2FVXXSVzf/azn8l4p06d3JjX/S7VMl1VTqvK5szMxowZ48Zizbdi78Ru3bqlnKvKzZOo5m2qOZiZbde9s7zYPRNrUNSsWTM3pkosk5p2lZaWug3i1LWPPfeq+2KsAdXBBx8s4+p99O9//ztxe6xEm78YAACAgIEBAAAIGBgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAIK11DNJZE6CoqMiNxVpYTp48WcbVce2zzz5uLNWaZq/e1czs5Zdflrmq9jbWhlTVE5vpmmivdjnVc1d1y7E2vtOnT3djI0aMkLlJtcflqfUjdtQaDoWFhW7s6KOPlrnt27d3Y6NHj5a5b775ZrX3rergU61nV+tknH/++TJX3Ru33HKLzB08eLCM5+bmujHvnku15bZaf0W1vTYz23///d1YrB38Aw88IOOqda/3nlLvryTqnRVrC92xY0c3FrsGsTr/gw46yI2p35JUn/vPPvvMjX3zzTcyV7VUP/LII2VubA0L1c7b+50tLi6W++QvBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAIK0yhVVm9dDDjlE5ubk5Lixww8/XOaOGjVKxmPtaXeU1atXu7FYq9DTTjvNjal2zmZmmzZtkvF9993Xja1fv17mVpVqfR0rvVJte1etWiVzY+WMquVzrJysqpYsWeLG1q5dK3OvueYaNxYrxVy2bJmMq3IyVY6aaqmqOv8rr7xS5qqSvYkTJ8rchx9+WMZj7cp3hI0bN7qxtm3bylzVAjj2zKhSTDOzrKwsNxZ7X1SVarUec+qpp7qxo446Sub26dNHxnv06OHG5syZow8sBerd8sEHH8jcI444wo3df//9MrdXr176wHYC/mIAAAACBgYAACBgYAAAAAIGBgAAIGBgAAAAAgYGAAAgYGAAAACCtNYxaNy4sRuL1by+9tprbizWtvfGG2+UcdXWV7UaTbU9qWo/26RJEzdmZjZ//nw3NmzYMJm71157ybiqh99R6xio1sPqezHT7XVvuOEGmTtu3DgZP+6449yYV6+fah2/anOq1rYw0/d2rN14bG0QVbPdunVrN7Zt27bttpWWlrr3/dSpU919DRo0yD9AMzv33HPdWOydMXv2bBlXrcBTbbHrnfvixYvdnNh9dM8997ix448/XuZ26NBBxtUaCamsY5CRkeGeh2r/u3TpUrlf1Xb42muvlbk33XSTjKs1YVJtN16jRg23DXmLFi3cff3+97/3D9D0+h7vvfeezJ01a5aMq7U1vGcq1nKbvxgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAIAgrXUM1q1b58bmzp0rc1UdvFofwUyvU2Bmlp+f78ZUXWtSPbeiakHVd2Nm1rlzZze2atUqmRv7bn8I6juO9UBX9fixWv3ly5fL+IQJE9zY5s2bE7cXFRVtt03V8c+YMcP9jFjN8dNPP+3GbrvtNpnbtGlTGc/JyXFjSedYlViSLl26uDF1X5iZ1atXz40ddthhMlfVq5uZjR8/3o1560ukur6BWodi0qRJMvfII490Y61atZK5W7dulfGRI0e6sQMPPDBxe0lJidxnZQsWLHBjsTU49ttvPzc2bdo0mRuLX3DBBW5Mremi7sVUxdaWuffee93Y5ZdfLnPz8vJkfPjw4W7M+y2NrbnBXwwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAAEaZUreuVfZmZZWVkyt2/fvm4sVo73yiuvyPjKlSvdWMOGDd2YVxLklXaoUphY6WPLli3d2H/+8x+ZO3PmTBlXGjVqlLg91dbDubm5bqxTp04y94orrnBjsRaxseMcM2aMG/PKk5JK0FT7WVWyFitbOuigg9xYv379ZG6sHXlmZqYbKygocGNJJXvq/Nu1a+fuS5XkmZl99913bizWrnvDhg0yrkqRvbJE7zv1zl2VN/7v//6vODpddhcrwz322GNlXN0b3nstabsq01X30P777y+Pz3vvxPZrZnbffffJuHqXLlmyxI0l/UaVlJS4ZZzqd+WDDz4QR2i29957u7GzzjpL5sbKmJs1a+bGvPep+u024y8GAACgHAYGAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIIiWK6qyNNVRK1auqDoT1qihxyuqPCOWrzrUJZXUqDKbBg0auLFYuWLdunXdmPrOzeLnr3gd+FI9d3V+GzdulMegzj1WRhP7blQ5qve5SfeE2o+yZcsWGVdd9FT5q5kuxzPT5YrqmUjKU50aVWmcOgYzfU/F3hmxa1JcXOzGvPs16TOzs7Pd/ajr2759e3F0Wuzatm7dutr53jOTdJ7q+ijqOzPT90WsBDn2TKn3sDqfpGNW9716hlq0aOHGzOIdg5XYO6958+ZuzLsusePJKFW/0AAA4CeF/5UAAAACBgYAACBgYAAAAILo5MP77rvP1q1blxhTE15ik2nURCu1JrWZ2ffffy/j3lrXZmZ77rmnG2vcuLHdfffdFba99957VlhYmPjv1SS6tm3bymP89ttv3VhsEtOaNWtkXE0EWr9+feL2+vXr23HHHVdh24svvmj5+fmJ/16de1FRkTw+NXHxkUcekbmvv/66jKsJQlOmTEncnpmZaWeffXaFbUOGDHHvezVZKjZlp02bNm5s9erVMjfWI+TJJ590Y6q/RnZ2tl188cUVtj3//PPutY/1s1CuvvpqN/bxxx/L3NjkTDXRbMaMGYnbGzZsaKeffnqFbf/+97/dc1T3bq9eveTxed+nmdk333wjc/v37y/js2fPdmPe+6J+/frb9WAYPXq0e+5qUnHsna1648R6THg9TsoMGjTIjU2YMMGN1a1b1w488MAK29555x33PNWEPfU+NNP3Zqw3TqyHyAknnODGli5dmrg96X1fXnRgsG7dOvfGUj/+sYYvaiZp7AW5bNkyGVcPr5p1mqSwsNBt8uE1JzGL/ziqxiGxmfmxWf+q0Usst7z8/Hy3cY16WGPHr67PggULZG7se1UDg7y8PJlbnrrv1cBADUrN9OzstWvXytzYd+MNYM38AaFHXXv1OTFq4BS7N2ODLvVOUT/KlW3atMk9R/XMq5iZrpqINRKKVTmpZy6VZ16du9pPrMGVOvfYtYl9r0rsXVTZxo0b3WuhBqaxezOd84+9F9Q7MZVrXx7/KwEAAAQMDAAAQMDAAAAABAwMAABAEJ18qKiJXosWLZK5X3zxhRtr166dzB0wYICMv/fee25MTRJJimVkZLiTzVTlQWyZz86dO7sxtdS0WXz5UTXhxpscl7RdnfsBBxzgfsaIESPk8aklnWOTeLzKgjJHHHGEG/MmACUtuarOXR3/O++8I49v3LhxbuyNN96QubHlhgcOHOjGpk6d6sZSXfxUTeI87LDDZK6qnPjuu+9kbmwi2RVXXOHGvGV1kya2lZaWus/J/fff737GwQcfLI9PxTt27Chz1ex6M7NVq1a5MW9SZmxCY2XLly93YyeffLLMveOOO9zYm2++KXMHDx4s47NmzXJjqVbQqOf+yCOPdPP69esn9/viiy+6MVUpZxZfKly9F7xrHLv2/MUAAAAEDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAkFa5olp/PTc3V+Zec801buzzzz+Xua1bt652XJUCJvUYKC0tdcu5vAYVZmZHHXWUOEJd8vbPf/5T5sYaVKky0lTKV9S5q54AsbX0Vb+K0aNHy9xYqearr77qxryyLa9kzTv3WK8ORTW7iZ27Kkkz0+vtx9ZbT4V6hmIlh/vvv78bu/XWW2XuLbfcIuOqR4i3nrxXwuqVrKmGP6okzUyX2sae6fnz58u4uid79Oghc6tKNW+L3V/qnaaeCbN4+foLL7zgxlRjq1TLdNVvWqwscq+99nJjf/rTn2RurFxTlf5793H0N0RGAQDATwoDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAEFa6xisWLHCjR1zzDEy16spNzMbM2aMzG3fvr0+MCHVdQyUefPmubFYTXqLFi3c2IIFC2Ru7969ZbxevXpuzKtfTbWmV517nz59ZK6qx2/YsKHMvffee2VctSDt2rVr4vZYTW8q/37GjBkyV7Udfvfdd2XuxIkTZfyEE05wY2ptifr168v9VnbIIYe4sa+//lrmfvzxx24sVqsfu0fV+h1Ja1Wo7R61VsG+++4rc6+//no3dumll8rc2LooI0eOdGPee61WrdRe/2oNh1jbZXVffPjhhzI31tL4nHPOcWOq1XXS+av1S1auXOnuK9YO/swzz3Rjl19+ucz11uAoo9YEGjZsWOJ29ayY8RcDAABQDgMDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEKRVrqj87ne/k/FTTjnFjR166KEyd8OGDTKuSiF3pEaNGrmxWGteVVo2a9YsmbvnnnvKuCrJVCVHqfDaN5vp1rpmuqTvqquukrmxkrDbb7/djb322msyt6pUy+xYaZUqRVUto83Mfv/738v4V1995cZUqV+qpaqqDW7Hjh1lrirXVMdvFi+xUq19VRlrZRkZGW67WtX2+80335T7VSWJ3bp1k7lz5syR8YMOOsiNrVu3LnG7d44e1VpZtRU20+24r732Wpm7fv16GY+Vxu8ozz77rBvr1KmTzFXXZ/PmzTI3Vq6YasltVfAXAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEKS1jkHLli3dWN++fWWuqjl+8MEHZW6sre8rr7zixjZt2uTGUq3nbtKkiRu7+uqrZW5eXp4bU9+rmdmoUaNkfNCgQW7MqwVPtaZZ1RZ7ddNl1DoH6vqYmY0dO1bGO3fu7Ma8dslJ34mqZVfrGOTn58vjGzBggBsrKSmRuerczMwuuugiN/bAAw+4sVSv/dy5c93YkiVLZO7AgQOrnRtb30S1tv3lL3+ZuD3pO1etd6dNm+Z+xsKFC+Xx3X333W5s+PDhMvett96ScbV+RyrUuat277E1JtS7dePGjTJ3xYoVMq6OK9X1O9T5f//99+6+evXqJY5Qr/Nw5513ytwnnnhCxlXbZu+dEnvX8BcDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQpLWOgapdVb27zcxuvPFGN/bUU0/J3Pvuu0/Gly1b5sbq16/vxoqLi+V+KysoKHBjTz/9tMx95JFH3Nijjz4qcydMmCDj/fr1c2PeOdapU2e7baqmV9Wyx+puf/Ob37ixm266Seaef/75Mj5r1iw35p1LqutXqHv7r3/9q8x96aWX3NgNN9xQ7c81q/4aCanWc0+ePNnd17vvviuO0OzKK690Y+qdYGb25ptvyriqZ2/YsGHi9gYNGsh9VtajRw83dvTRR8tcde1jdfCqVt1MvxN79uyZuD3V637IIYe4n6HWjjEzKywsdGP77ruvzL3nnntkvH///m5MXV/1W5BErb+yePFimeutoWJmdt5558ncoUOHyri6d4qKihK3J73vy+MvBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAIK0yhVVuccxxxwjc1Xb3iOOOELmfvTRRzI+ffp0N7bffvu5sVgJR2WqBOXUU0+VuT/72c/cWLdu3WRu27ZtZXzp0qVuzGsLnNR6V7Ue7tixo/sZl1xyiTy+7t27u7HnnntO5o4bN07GVWtUr2yrcePG221TZVuqHHbYsGHy+Nq0aePGYuWKr776qowPHjzYjTVv3tyNJbW6Vte+bt267r7OPvtscYT6ucjMzJS5e+65p4yrVudeqWdSOZs6961bt7qf0a5dO3l8qtW6eh+YmX377bcyrkqnvVbmtWpt//qvUaNGtVqzx45P3Ztr1qyRuaeffrqMqxLS+fPnu7Gk+1hd+z322MPdl4qZ6d+W2O9do0aNZDzpOpbxykTVfWzGXwwAAEA5DAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAEC1XVKUSqnwl1rVMlTxt2bJF5qqujma6JEyVbTVt2nS7beo8VJmIOj8z3dFPlUHGjslMXxev21ZSqVhWVpa7H3WMsXOvV6+eG4uVrDVp0kTGVdlWUlmimVlubu5222IlQp7Yuefk5LgxrwNgGXXvmulzT7q3yzRr1my7bera165du1oxM/3MxK59bN/qvvKemaSSa1WGre772HObaje/8mLnrp4L71om3W/qGNU7y3u2yqjrHutuGvveqvsuSiohVM+geu/Gnnt1/dR3Y6afxVi+F4s9axmlqfacBQAA/7X4XwkAACBgYAAAAAIGBgAAIIhOPvzwww/d9ZbV+s+xyRjeJDgzswEDBsjcN954Q8ZbtWrlxrw1083+b5LL0UcfXWHbK6+84k7qKikpcfcVm1AyZ84cN/byyy/L3L///e8yvnz5cje2YsWKxO1ZWVl23nnnVdj24osvur0V1Frb//u//yuP7+c//7kb27x5s8xVk/fMzGbPnu3GvMlpmZmZdtZZZ1XYdt9999m6desS/7267moCYMzKlStl/MILL5TxyZMnuzG1Tn/jxo3trrvuqrDt2WefdXPUtKTYpM3nn3/eje29994yt0OHDjL+7rvvurGBAwcmbs/Jydmux8ITTzxhGzZsSPz3SRM1y8R6mDz99NNu7KKLLpK5o0aNknE14dqbzJ2bm2s33nhjhW2PP/64e+7qunfu3Fken+ovElu3/5133pFx1WdCvYdzcnLsqquuqrDt5Zdfdt95avLvkiVL5DGqe3fVqlUyN/Zbqr6/4uLixO2ZmZl2zjnnuHnRgUFhYaFt3Lgx5QNSL0+z+A+A4h1PVfbtDXI8BQUF7gsynYGBGqAsWLBA5sa+O/X9qB+IyvLz892XhLr2sR84dXxew5cysdnZ3vGa+Q9JknXr1rnNXbZt2+bmeS+VqlADOrP4fa+a0aimZUny8vLcnHQqatQLNKk6pLzYoHDx4sVuzBvkJdmwYYP779VLOvZuUT+OsWsb+/FQs+lTue/Vuav3XaxiRt1/sSo0dV3N9LWNvYcry8/Pd9+R6jtW7x2z9N7JqtrGTL+L1X+AK/yvBAAAEDAwAAAAAQMDAAAQMDAAAABBdGZGaWmpO9lITXqITfpQs1jVJCozs8cee0zGb7jhhmodV6qLQKrJUr1795a5/fv3d2NDhw6VuY8//riMq8l/3kSW2MzXyg499FA3dsghh8jc5557zo2pag0zs5YtW8p4ly5d3Jh37WOTnypbtGiRG1PLUZuZ/fvf/3Zjp512mswdN26cjI8ePdqNqfsxdsyVqaqfytUdle23335u7K9//avMffjhh2U8NjkxSWwZ6spWr17txmIVGUOGDHFjjz76qMydNGmSjKuZ+dOnT0/cnrS0fEZGhns/qPfjp59+Ko9PTZ7s27evzH3ppZdkXE1onTZtmhtLOv8aNWq4S+6feuqp7r5UzMzst7/9rRu74IILZG6s2kVNWu7atWvidjWB2oy/GAAAgHIYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAIAgWq6oylcmTJjg5p1wwglyv19//bUb++Mf/yhzY3G1trYquUm1bG2fffZxY5Ubs1TWrVs3N6a+VzNdmmRmNn78+JRzUy3VVGvif/bZZzL31ltvdWM9evSQub/+9a9lXJWjeuW1sdKdynr27OnGRo4cKXOPOuooN3bQQQfJ3JkzZ8q4uoaqHFU1Q0uimpipRk5mZg0aNHBj7dq1k7mqFNXM7KmnnnJj3jPhlaZ5VPlbrMnTiy++6MZi1/7999+XcVUO5137pOuuytOPPfZY9zNiZcadOnVyY5dddpnMjZUrnnHGGW4s1etbUlLi9oQYMWKEm6caw5mZDRo0yI1Vbl5XWazXheqd4/12x0qU+YsBAAAIGBgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIousYKFlZWW5s7ty5MlfVZr7yyisyNz8/X8ZVrbFq25tq+1nVHjpWl6xaJ6u20WZmZ555poxv3LjRjWVmZiZuT7X97MSJE93YrFmzZK6qN3/77bdl7pgxY2RcrSNQWFgoc6tK1dPH1kT4/PPP3ViLFi1kbqzOv0+fPm5MPY+p3vebNm1yY+3bt5e5XttvM7M99thD5sZqxdV3771vUl27pGPHjm5s2LBhMvfEE090Y6qds5nZYYcdJuPLli1zY6effrrMraqPPvrIjU2ZMkXm5uXlubHY+hy/+MUvZLyoqMiNqfVWYusDVHbddde5MbUuj5nZ+vXr3dh3330nc2fPni3jl19+uRvz3pexdWv4iwEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAIAgrXLF3NxcNxYrrxk8eLAb69q1q8yNtXS+9tpr3ZgqV0yVKoVp2rSpzD366KPdWKxccdGiRTJ+8sknuzGvNCbVkrVRo0a5sQceeEDmPvvss27sz3/+s8xVpahmZq+//robGzBgQOL2VM/9iy++cGPqnjAzu+mmm9zYxRdfLHNVq24zs//5n/+R8R3lmGOOcWPnnnuuzFX3fSw31nb5+OOPd2O/+93vZG5V9e3b143FygJV2dnw4cNlrnfvllHlcF4bYW+759VXX3VjsbbQjzzyiBtTbZPNzPbdd18Zf/TRR93YjTfeKHNTccghh7gx9d4x0+WosdL2Vq1ayfjixYtlvDr4iwEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAICAgQEAAAjSWsegUaNGbqxx48Yy94ILLnBjsRbAb7zxhowfeOCBbmzs2LFurEaN7cdJNWrUSNxuZta5c2d3Xzk5OeIIdYvYo446SuYeccQRMq7WMcjOzpa55W3bts09zu+//97N+9vf/ib3O3/+fDcWq9W/7LLLZFy1pPZavyadY0ZGhru+gWo3Hmu9q87vn//8p8yN1TPHauF3lLVr17qxhx56SOaqttj33ntvtY/JTLfFTaWWv2bNmu56FE2aNHE/Q63vYKaf6wsvvFDmqjVjzPQ6BvPmzUvcnnTfl5aWut/VihUr3M9QawmY6XVd7rrrLpn72muvyfitt97qxurUqVOtWBLVNju21sLo0aPdmGpJbaa/dzOzNWvWuLFOnTolbo+t3cJfDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQBBdx6C0tNRKS0sTY5s2bXLzbr/9drlftQbCzJkzZe5VV10l47F671SUlJS4db2TJ0928z777DO53169ermxAw44QOY+9thjMv7//t//c2MDBw5M3J7qGg5nn322+xk333yzPD61zsGQIUNk7rnnnivjqt7b61vu1ax7mjdv7sa++eYbmduvXz831rJlS5kbWxvjlltucWOff/55tfdbmaq7Vn3nzcz+8Y9/uLFYX/opU6bI+BlnnOHGJk2alLg91TUsvHehmV6bxczsD3/4gxv77W9/K3Pfe+89GVfvkwYNGiRuT3p/Z2RkuM/8CSec4H6GWjvGzGzr1q1ubMCAATL3vPPOk/EXXnjBjZ1zzjlurLi4eLtt6tqr50Stj2Nm1qJFCze2cOFCmdulSxcZnzVrlhvz1jGI4S8GAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIGBgAAAAgmi5oirfUOVVv/zlL+V+P/74YzemyiDNzJ544gkZ98ptzHRL51TLtpYtW+bGVGteM7P+/fu7sbZt28rc3r17y7hXnmRmVrt27ZS2V+czLr30Upnbo0cPN9auXTuZq1r+mpldcsklbuz4449P3J5USqTKdJcsWeJ+RqyF7I033ujGNm/eLHNjJWsffPCBG1Mlhlu2bJH7raxNmzZuLFYeVVRU5Ma861NGfe9mZm+99ZYbq1+/fuL2pHeFKlH+7rvv3M847rjj5PGpkkJ17GZmN910k4wfffTRbswr31bXIknXrl3dWEFBgcx955133FistP3bb7+VcdVqvV69em6sbt26221Tz7367ejZs6c4QrMJEya4sf3220/mqlJPM7NDDz3UjWVnZyduz8zMlPvkLwYAACBgYAAAAAIGBgAAIGBgAAAAAgYGAAAgYGAAAACCaLmiKktLKvcoo8pEzHQXvFhurLROlSt6ZUtmySWGqqxDdVqLlQLVquV/9eoYzfT5mekyUq8kM+ncVcmlKnFr1qyZODp97b3S2DKx76Z9+/ZuzOtw1rRp0+22qe6fqhujeibMdEls7L6PdQ1t0qSJG6tTp44ba9y48XbbvDInM10+pT7HTD8XsedaXRMzfe94323SvaiukfpeVDmbmS5Djt03se9G7dvrBpq0PdWS7armqXdS7HtT7wsz/d2o90XStVTvPPVboN7nZsnPWFU+0yz+TlSf7R1z7DvPKFW/bgAA4CeF/5UAAAACBgYAACBgYAAAAILo5MO3337bNm7cmBhTExhiE4XUmvhDhw6VuQMHDpTxyZMnu7GkiWZlGjZsaIMGDaqw7dVXX3XXAVcTM+fMmSOP8cgjj3RjnTt3lrlXX321jKtJbCeddFLi9oYNG9opp5xSYduIESPcNfbVuU+fPl0en1pzPbYefmySz7HHHuvGvv7668TtWVlZdv7551fYNnz4cPfc05l0q/p8xHoFnH766TJ+1llnuTHVuyQnJ8euv/76CtueeOIJ27BhQ+K/V5Owli5dKo/xF7/4hRt79913Ze7f/vY3GVe9JEaNGpW4PTMz084444wK21566SXLz89P/Peqn0WsT4S678ePHy9zFy9eLOOqb0uXLl0St2dlZW13X7z++uvu+149e61bt5bHp+6/sWPHytxY75X333/fjX366adurF69etv1GXjxxRfda68m986dO1ce46RJk9zYySefLHOLi4tl/KuvvnJj3bt3T9yelZVlv/rVr9y86MBg48aN0QYZSWKzx9XM5jVr1sjcWLOZ9evXu7HY7N/KCgoK3B8Ir9GKmdm6devkftU5bNu2Teaql4CZ/tFO5Vrm5eW5Pw7q+q1evVru19unWfzax2Znq+9VfW5leXl57n2kfvxjD/GiRYvcWOzcY5UuCxYscGOx5lOVbdiwwb2H03l21fejnlsz/d2Z6efGe9l7/9Z75gsLC9087we1jKrkiR1f7H2yatUqN6YqAirbuHGjeyzq2Ys1vlP3ZqxJUGywqcSOq7L8/Hz3PaF+O2LXZ/ny5W5MNTgzi79T1LVP5Z1XHv8rAQAABAwMAABAwMAAAAAEDAwAAEDAwAAAAATRqoTS0lK3J8CUKVPcvEceeUTu9+GHH3ZjJ554osyN9QpQs5vbtGnjxmKlcJWp2emx2dkdOnRwY3/5y19k7nPPPSfjapbrzJkzE7cnzbjNyMhw1+n+zW9+437G3nvvLY/PKxs0M7vllltkrio3NdOlqt6M8tj6/pWpXgmxGcQ9e/Z0Y/vtt5/MffHFF2X82muvdWNqLfuktdpr1qzpnmfv3r3dfZ1zzjniCP+vDNSjrp2Z2bhx42T8hRdecGNexYJXWeS981RJZaxiRn1vr7/+uswdMmSIjKv32t///vfE7am+77755hs3FptZ/8wzz7ixe+65R+bGfkuefPJJN6be0Ullt+qdV7mcu7zbb7/dP0DTJebqezWL9zW45ppr3JhXyqgq18z4iwEAACiHgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIUqtXqcTr1GemyxHNzM4991w31qxZM5k7cuRIGVclU6p7X6zcqDLVUatfv34yV5UcNm7cWOYOHjxYxlW545dffpm4PalER5WqPvjgg+5nxMrOXn31VTcW67QWK4tSpZBeuZF3jh7V8CbWTKVyF8PyYk2Evv/+exl/+eWX3ZgqE0wq/1XX/o9//KO7r9j1ueqqq9xY7Dqo7oRmuqzr4osvTtzulaZ521XJqOryZ2Z21113ubFYKeqZZ54p4+edd54b85o3qaZOSVQzptzcXJmrnotYievEiRNl/IMPPnBjlTtnlpdUrllSUuKWsB5++OHuvm644QZxhGYffvihGzvttNNkbuy+mjBhghvz7uPYtecvBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIIiuY6DaUCa1rSxz8skny/1efvnlbixWz/3zn/9cxrt16+bG5s2b58ZiLXMrU3XTsVaZqh1orP2uqqM3MzvggAPc2E033ZS4fevWrXKfld18881u7I033pC5Rx55pBuLreGg6pLNzN555x035rWZVW2Uk4wePdqNPf744zL3mGOOcWN33nmnzFV18GZmV1xxhRtT7Z6TWhKreu699trL3dfZZ58tjlC30D3iiCNkbmx9DBX/7rvvEreneu0//vhjN6bWSDEzu+iii9zYgAEDZK5an8PMrHnz5m7sxhtvTNyeartxtZbCp59+KnPr16/vxry1Vcq0a9dOxp944gk39vnnn7sx73fN8+tf/9qNLV68WOYef/zxbuztt9+Wub/4xS9kXLV8PvHEExO3x9YM4S8GAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIGBgAAAAgrTaLk+ZMsWN9erVS+aqkkRVUmgWLwVUbYdVq+hUde/e3Y2pVqBmuuwu1oYz1n531apVMr4jzJw5040VFRXJXFXul9QCuLznn39exmP3xo7w7bffurFhw4bJ3H/9619uLHbPqBJRM7Orr77ajc2aNcuNpdp2WpUVeqVxZVRJ5qRJk2TuscceK+OqbGtHUc9ehw4dZK4qyxsyZIjMPfXUU2Vctf1NtSzPc8cdd7ix2LmrEmrVvt4sXlb5wgsvuLFOnTrJ3MpUeb4qBz7rrLPkflUZtiqvNzN77rnnZPzpp592Y175duye4C8GAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIGBgAAAAAgYGAAAgiK5jUFpa6tY5FxYWunmxVpGqPe2hhx4qc1u1aiXjbdu2dWOrV692Y0ltZlVda9euXd19/ec//xFHaDZq1Khq58baMu+5555uTLXMraxmzZpuW9rWrVu7eZ07d5b7vfLKK93Y/PnzZW7Hjh1l3Guva2bWsmVLmVtejRo13DUVRo4c6ebNmDFD7letNXD66afL3KuuukrGVRv0VKlrr9qTX3jhhXK/r7zyihtr0KCBzP3HP/4h4998840b895hSdvVtVfXL7YOhdfG2izeUnrfffeV8WuuucaNDR8+PHG714bc079/fze2//77y9y///3vbuyQQw6RuVOnTpVx1cI+qaW4im3dutVtQa/eH08++aQ4Qv2+79Gjh8w9+uijZfyxxx5zY+3bt0/crr4XM/5iAAAAymFgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIEitkLWSoqIiNxbrL37RRRe5scWLF8vc559/XsYHDRrkxtQ6Blu2bJH7rWzBggVuLCsrS+aqumXVXzv2uWa67vfTTz+VuVX11VdfubE777xT5no15WZmS5YskbmxtQi6d+/uxhYuXJi4PakOWtWy165d2/2Mt99+Wx7fX/7yFzf21FNPydx58+bJuFpXRH1vSfXsqp579uzZ7r5ix6jW0TjnnHNk7nnnnVftfdetWzdx++bNm7fbVlJS4tZ5q/t+2rRp8vjUWgSx9Ttitf7quznjjDMStzds2HC7bWr9ii5durif8cwzz8jjU2twxN7nsfU91Loa06dPd2NJ76Ft27a59/2KFSvcfa1cuVIcodlRRx3lxj755BOZG3vnqfs+Pz8/cbv6zsz4iwEAACiHgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIouWKqu2waq8baxU5adIkN5aTkyNzr7vuOhm///773ZhXimJm1qxZs+22qbbTqjQrVvp44oknurHLL79c5g4YMEDGVRvORo0aJW5v3Ljxdtu2bdvmlm2NHz/e/QzV/tZMt+Zt166dzP3jH/8o46q0ySszTNquyvVUC1VV0mVmdvDBB7uxv/71rzK3U6dOMq5KcTdu3OjGkp5v9dx7pX9mZqtWrRJHaPbtt9+6sVi78ZkzZ8r4AQcc4Ma8lsfe9+Kdu1fyambWr18/cXRmF198sRuLtRY+88wzZVyVwXrlbEnluOqZVy3NL7nkEnl8qkT55JNPlrkvvfSSjPfq1cuNZWdnu7GkNuV16tRx7+8HH3zQ3VespLCgoMCN9ezZU+bOmTNHxr3WymZm69evT9xO22UAAFBlDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAEC1XTOrAVaZBgwZurE6dOnK/qvug+kwz3d3OzKxp06ZuTJVpJJXsJZW0VCWmyiJjuar8xEyXi5kll12W8cp3cnNzq/xvY8egvn+z5G6GZVRZk1m8LEgds9ctMelaqP2o+z4dSfdfeeqYzPQ9p65XUnmwKhlWz3bs+qjjaNGihcyNadWqlRvzyhWbN2++3Tb1bvLKGM30M22mn+vYO22PPfaQcfW9evd90nb17lXXPfZOSurgWUa9D8zMmjRpIuPqeqljTnqO1b7UNYq9E9R7LfbO80rMy6j7Lum9bhZ/l2SUxo4KAAD8ZPC/EgAAQMDAAAAABAwMAABAEJ18+Nxzz1l+fn5iTE0aiU2W6datmxt76KGHZO4555wj49OnT3djGzZscGM5OTl25ZVXVtg2cuRIKywsTPz3s2fPdvd1+OGHy2OcOHGiG+vdu7fMja1HryarbN68OXF7/fr17Zhjjqmw7bXXXnPX+FZrf6tJYGZ6Tf/YRJuVK1fKuDfJzMyfWJWZmbndPfXYY4+594qa7BObRLZp0yY3VlRUJHNjk3Kff/55N6b6mjRr1syGDx9eYduwYcMsLy8v8d+rSXRnn322PMbBgwe7MW9N/zLr1q2TcTXp1psc17BhQzvllFMqbHvrrbfcHgrq/lyzZo08vvr167sx77suE7v2auKq17elfv36dtRRR1XYNnz4cPdYvEmMZmY33nijPL6HH37YjcUmqseeC/VMqWc1Ozt7u/4VX375pft5anJs7NqrXiWxd96CBQtk/NRTT3VjHTp0SNzepk0bGzt2rJsXHRjk5+e7L8ji4mI3L3ayagZ17IfP+3Erox6y2MulssLCQvdHUO0rdoxecwszfaOb6R9lMz1g8wY53ud436U3WDTTM3vN9PWJ/bCqgZ2ZHhjEGodU/py1a9cmxtS9G3vJqe8/ds/EGnMtWrTIjcV+WCrLy8tz79HYLHFFvUBjVQmxZ1fd9+pdVdnGjRvdZ0zNvlfPhJm+N2MDg9gccTXoSOXc1XVXA4MY9b6LVTTEngv1TMWqwyorKipyP089f+kMXmIVDWpQERMbVHj4XwkAACBgYAAAAAIGBgAAIGBgAAAAgujkw4yMDHcZUDVpIjZB6dZbb3Vjapalmdm4ceNkfO7cuW6sdevWbkwtd5pkxowZbkxVXZiZ7bnnnm4sNvM+NslJ8SYQJS1ZWlpa6k56ev/9993PqDzLuzK1HGds4mlsoo76XufNm5e4vWbNmtttU+e+ePFi9zNiS42qiVSxyXeq2sZMT84bNGiQG1Oz+ZNMnjzZjU2ZMkXmerOkzcyWLFkic73lXct88sknbqxyxU2Z2ITOytR9f8IJJ8hcNXE26R4sLzapdfTo0W7s4IMPTtyeymRcM/3uvPTSS2WuqorxJvlWlTouNakz1UV/1UQ+teSzmZ6QHZtQ3alTJxn/xz/+4cZ69OiRuF19Z2b8xQAAAJTDwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAAE0XJFZdSoUW5MlTSZmZ1xxhlubMyYMTJXlb6YmfXt29eNLVu2zI3F1uyu7N1333Vjjz32mMxVZVux8p1YKejy5cvdmFfylbSmuCpVrdx0p7yRI0fK41PlmG3btpW5se9m6tSpbsxrqJJUtqXOvU2bNu5nxEpJVbObWKlmly5dZFyV2/7qV79yYzk5OXK/le2zzz5ubMWKFTJXXfuWLVvK3FhZ18CBA92YVwqZ1L9AXXtVlvfRRx/J41ON5WK9LGLr5ffr18+NpdL7oKSkxO3pMGHCBPczVJmwmX5uVaOjqlDl6arENdU+CqofRazsVfVSiJU4q/e5mVn//v3dmNebJNbPhr8YAACAgIEBAAAIGBgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAIK11DFTt7N577y1z33jjDTd26KGHytzZs2fLeEFBgRtT7TG9lsQetZ7Cn//8Z5n72WefuTGvVWaZWK28Oi6vpjnW9rWyoUOHurHu3bvL3Pbt27ux8ePHy9zYdzN//nw35tXrp3ru6jM6duwocxcuXOjGYu2PV69eLePvvfeeG1NrjqRaR/7FF1+4MXVtzfQ6DrFa/dg6I6ode/Pmzau8T9Vy+9FHH3U/Q7W2NtPrMMRavntrC5RRLYG9VuVJtfc1atRw34OHH364+xmzZs2Sx6fq5lW7cLN4y+lWrVq5MbV+QKrv+8LCQjdWu3ZtmaveMbH7PvZeUO9Mr2VzvXr15D75iwEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAIAgWq6oSndUq8kHH3xQ7veuu+5yYyNGjJC5AwYMkHFV/uK1oayOsWPHurFnn31W5h5zzDFubPTo0TK3a9euMv7JJ5+4sQMOOCBxe6xcqrKkVsVlVPmQmW5Pe/bZZ8vcd955R8affPJJN/anP/1J5laVajv81VdfyVyvfMgs3na5RYsWMv6Xv/zFjcXaWafisssuc2OqZNLMrLi42I2pFrlm8Zbbqkw3VuJbVc8995wbU/eemW5vrZ4nM93y1yze9ndHUCXmhx12mMxV33+s7XesrFC9771SzepQ18D7jSyjrk+sHFOVXJpV7xxj3yl/MQAAAAEDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAEFabZf32msvN3bbbbfJ3N/+9rdu7LrrrpO5Y8aMkfFXXnnFjd1www0ytzK1jsPixYvdvJYtW8r9qrbLPXv2lLmqxaqZ2UknneTGvLa/Xp2tt76BarkdO76DDjrIjcXaVQ8cOFDG1XoMjz32WJVz1HVX91+fPn3k8S1fvtyNNWrUSObG2rOqtQpUnXWsBruyK664wo1dfPHFMlfVZMfWGIm1n1X5sVrxqlKtlc8//3yZu3LlSjem1rcwM5szZ46Mq3bXXp1/Ui17SUmJ2+L517/+tfsZsfUrVLvtWJ3+5s2bq73vWG4q1L5iLcHVugGxNSy2bt0q47HPThJrNc9fDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQBBdx6C69dzr16+X+x06dKgbu/3222XukUceKeOrV692Yy+88IIby8zM3G7bli1b3Br/gw8+2N3Xv/71L3GEuvY2tg5ArG/93Llz3ZhXT+vVLntUTXZxcbHMXbJkiRs744wzZK5a/8HMbNWqVW7sxRdfTNyedO4ZGRnud3Xuuee6nxFbY0PVHBcWFsrcWA/1hg0bujFVC127du3ttmVkZLhrQjzyyCPuvsaNGyeOUK+ZEOsrv3TpUhnv3LmzG2vevHni9qTvrGbNmm6dt3cPmZk9++yz8vjatGnjxmbNmiVze/ToIeOTJ092Y956K02aNLFzzjmnwraSkhK3rv7mm292P+PCCy+Ux6feF7F1NNT6HGZmX3/9tRtT933seatMrbdQnbUEqiq2b3WO3vodar0XM/5iAAAAymFgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAIJouaIqW2rVqpWbV1BQIPfbu3dvNxYrX1Gfa2Y2f/58N9a1a9eUPrd27dqJ5Vxmug1prMRElfRlZ2fLXO94yqhyzUMOOSRxe7169RK3e9dClTc2adJEHJ3/WWbxUs0DDjhAxu+++243Nn369MTtLVq0SGwX7J2717raLH7fq2sbaz8bK1fMz893Y6qUMWm/qkxZtX/+wx/+II7Q7J577nFj6ns1M+vSpYuMv/baa27srbfeStyeVJaoWg9795CZWVZWljw+r/2xWbztcqyt8ZNPPunGvPd3+/bt7b777quwrUaNGm6p5jHHHON+xuDBg+XxDRkyxI2pUkYzs9mzZ8v46aef7sauuuoqN6bKR5Oo346ZM2fK3JYtW7oxdV+YmdWvX1/GVenhpk2bZK6HvxgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIouWKqgTHK2sxi5estW/fPvbRrliZiepcqM4nqbui6vimPkeV5JmZ28GsKryOWWVycnLcmHdcSeWVSd9HGVVuqfK8zyoT+15U2Z2ZviYtWrRI3N60adPttqnvUMWS9lVeo0aN3FisK2WtWvpxVV3W1H2cdD6qrFLtK/Zcq+8u9s6IlfGqMmbvXZVUqqnuMfVcx8oVVYlvrLOkuq9jvGuS9B6tbjltOtdd3bdm8edClfOp34qkEkL1blJl4rHrp/YbK0dM57fEi8XK6TNKY4sGAACAnwz+VwIAAAgYGAAAgICBAQAACKKTD8ePH2+bN29OjF133XVu3gcffCD3q9aWVpMazeK9FNTkvHnz5rmxhg0b2qmnnlph27Rp09zJL2oyUWxdezX5I7a+dWwSmpqM4k0gqlu3rh188MEVtr300kty/X2PWrvbLH790tl3Xl6eG7v55pur/DnDhg1z93XLLbe4effff7/crzr+2PeSzveqcrOzs+2KK66osG3+/PnupDC1L/VMmOnnYmdOd/KeiVq1alnnzp0rbPvggw+ssLAw8d+nc+5Kus+M+l69d152drZdcsklFbatWbPGPQ81STD2zo6d386iJgzWqFFju8mWEydOdN+R6hzTmUy+M3n3Td26dd2+OWZVGBhs3rzZ/aFatGiRmxf7otSPX7oDA/WApvpDV1xc7N4o6QwM1IMSa6YT+25V3BvkJcnPz5c/tJ5dOTBYv359tfddXl5eXrX2FcvZHQcGSbZu3WpbtmxJjKl7O3Zv7m4DgySFhYVuo6gf48Aglfu4pKTE/a7S+fHbVQOD2G9JZUVFRe478r9pYBDD/0oAAAABAwMAABAwMAAAAAEDAwAAEEQnH2ZkZLgTR7766is379NPP5X77dSpkxtbu3atzI3NylcTG9VyvUnLWpaWlroTONTEjthEJLXMZ2ziYmzfaqKPt/xmbInMytQxxpY4TXVCUHmxST5qSWLve2nfvr3Nnz+/wjY1CUtV48SWbE5HOpMTVW5STD336v7bmRNP0+FVKsXeJZXtrONPd+KpN1HUzOzuu++u1jFVpmb478zrms49tXr1ajdWq1Yty83NrfJx7K4TDBXvPR37jeEvBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAIJorY4q15syZYqb17x5c7nfVatWubF69erJXFWaY2aWk5PjxlTJSVIpnyrbSmfdd1XylU45oln1ygFj5SuVqe8x9vnprCmfTgOt9u3bJ25v06bNdttq1KjhnkflxivlxUqadmZZV3V7JSTFSkpK3OuUzrr3O6vXgJm+h73171UJ3o78fLOde+29MmSz1Mp01b/fVdIp5dx777139OH84NI5f690PNrTJH5YAADgp4KBAQAACBgYAACAgIEBAAAIGBgAAICAgQEAAAgYGAAAgCC6joGqZ06nDafKjbXtVbXqZrpts2ovnGpNc6q14eWlum5AebHvVq3z4NXmp1pDvrPq0WNtcGNrWKiW25dcckni9qR1L9T6FbFjUNK5Z37IlsXq/NNR3bUWqkLdd959lWrb5XTu+3SufazuXH320KFDE7dnZWUlbq9Om/lduYaDMm3aNDdWu3Zt6969+w94NNWTznPhtYFXv4Nm/MUAAACUw8AAAAAEDAwAAEDAwAAAAAQMDAAAQMDAAAAABNFanRo1arilKC1btnTzFi5cKPerWivHSnOKiopkXLUgTbe1a3mqbC3WOrq4uNiNxUp/YufglaiY+e1nU5VOy2klVqqaTkmfV46aVLKm2o3vrFLTXdWSOdXPTafl9s4seVOlh94xp1oKpp69nVmCHPte1TXxyhLVeyLJzmrHvDPLdFu0aOHGqtOefnekvp/qvu/5iwEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIGBgAAICAgQEAAAjSWsdg9OjRbl6fPn3kftevX+8fVKQVaqxeWK0RkGrb1OrWs8da86rW0bF1HGL1t+q7nTNnTuL2zMxMO+igg+R+y1P1sam2r05FOvXcqbSTrVWrlnsfprMGRTq14OnUc6fa8re69/3OPL/Yc6HeG1573fbt29v8+fMrbNu6dav7/Kp7O522yzHpXHvvXZN0Lm+//bbl5eUl/vvzzz/f/YzYtdlZ657E8lP9zi+88EJbsGBBYuyjjz5y83bk+jipqk4779j3wl8MAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAEF3HoGbNmm598G9+8xs375VXXpH7bdq0qRuL9ZCO1cyqNQJUvWlSjXxGRoZb81m/fn13X6rW3WznrgPQoUMHN3bssccmbm/fvr2dd955Vf4Mde6x66OuQWwNi9j6EOq7877zrVu3Jn6Odw0zMzPdzygsLJTHt7PWIohR33mqx5TqWiBVzY2JrWGhnqlUzjE/P9+t5W/WrFmV97O7KCoqStye9Kzde++9bh3/ZZdd5n5GQUFB9Q7O4vdE7Nqp/FTv7cprWpQ3atSolPa1O0hl7Zby+IsBAAAIGBgAAICAgQEAAAgYGAAAgICBAQAACBgYAACAIFquqMq2VJnI22+/Lfe7bt06N1a3bl2Zq8oRzfzyHDOzTZs2ubGksjVFlSSqYzDTZXmxkq9Yyd6yZcvcWLotTstUp71xVcTOPdbWWOV791XsfqrsjjvucGO33XabzE3nu0knN9VWyapMN52Sw51JXcdJkya5Ofvvv3+Fbbm5uW7ZazotfnfUs5cq79onbR87dqz7bOfn56f8GVWxO7VdnjBhgvvuVr8PsTLrHxv+YgAAAAIGBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACCI1ljUq1fPjbVv396Nqe57ZrpTWqx8LBZX+1blK0nHnGopW1U+x6z6xxjLNUu/O2OZrKysHbKfynZkeVEqvH0nnWdOTo67H3Xf5+bmymPYVSVr6nvNzs7ebpsqv9qR3ex2JHVc3nOctL1BgwbV+ozdtVzRO66k81TvlnTeWbujpBJLVSqfamfe3VlsSYCM0l35JAMAgN0K/ysBAAAEDAwAAEDAwAAAAATRyYdqTfx01o7emROY0tl35UkkX331leyJUN3PSWeyzs7Yd506daxXr14Vts2bN8+9xrvrBDTFW8+9Vq1a200onDhxortm+o/x3JW6detanz59KmwrKChwzyWdc9yZk9SqM6k1IyPDMjMzd9Yh/ei89tprVlBQsKsP4weRmZlpZ555ZoVt/fr1s8WLFyf++/nz5/8AR7V7+O/q/LATFBcXRxsiJfmxDQySbN261W3Y9GP8cUyl0UtRUZFt3rw5MfZjPPdUlZaWuueiZmfvytnp/y3f/a5UUFBgeXl5u/owdpnFixfbggULdvVh7HL8rwQAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQRKsSOnfu7M7SVLOAVZljutJZkzzVWdOVy7jKGzNmzA77nFTsjIqGVGd0764zwNV3k0rpZUFBgRUWFib++6TeAj8lqVR3/JB+CtUi2Ll+SiWJyu75hAMAgF2CgQEAAAgYGAAAgICBAQAACBgYAACAgIEBAAAIouWKzzzzjFu2pZqp7EzplB6lmtuhQwe3XFOVK/5QjY5SpbrMVVZSUuJe4921ZE197zk5OYnbK3fUNDM78cQT3f2MGjUq9QP7kfkxlv6p40q6xma7tukTsLvaPd/uAABgl2BgAAAAAgYGAAAgYGAAAAACBgYAACBgYAAAAAIGBgAAIIiuY9C3b99q1S2n0xp5Z0q1bvmSSy6xdevW7aSj2b3VrFnTXcdgd61lV9q1a5e4vX379tu1W1XrV6h1DHbX70UdV1Js27Zt7rX31gTY1dSzPXXq1MTtdevWtYMOOmgnHRHw48RfDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEDAwAAAAAQZpZH6qm3btu2cD95N27pWLsWaOHGiFRUVJf5bdZzptHNNt2VzdY6rbt261qdPnwrbZs+ebVu2bJGf9d+gdu3attdee1XY9tlnn9nmzZt30RH9sOrVq2dHHHFEhW35+fm7benljpSRkWFZWVkVtqlS1R/jd1L5uS7TqlUre+utt6q8nz/96U875oB+QDfccIMbSypTxv/hLwYAACBgYAAAAAIGBgAAIGBgAAAAAgYGAAAgYGAAAAACBgYAACCItl3eWXbWGgCxfadah1xaWurmpHucu7uMjAz3HH+M9dyouuLiYrftcp06ddy8/4Zn4r+ttn3ixIlV/rcjRoywvLy8nXg0P6xHH33UjWVnZ/+AR/Ljwl8MAABAwMAAAAAEDAwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAEF3HQNUlp7MWwY5cayAVNWvW3Gn7Li92Dur7SbcWvDrXLGl748aN3Vr2lStXVu/gsEuker81adLE/ff/TXXuALbHXwwAAEDAwAAAAAQMDAAAQMDAAAAABAwMAABAwMAAAAAE0XJFVXZXo4Y/rvDK3MrsqvasseNKpZxxZ5VrppMby/diSdsbN27s7mf58uVuTN0XPxY1a9Z074Vt27b9wEeTvlTLgzt06GALFixI/PeqXJF23MCP34//DQ4AAHYYBgYAACBgYAAAAAIGBgAAIGBgAAAAAgYGAAAgiJYr/tTVrVu3Wnm7a7mip06dOin9+9q1a7uxH1u5Yq1a2z8G6rr/GMsVlaRzbdOmjfvvd1Wp8c7w33QuO0JmZuauPoQfzE/pXFOVUUrhMQAA+P/9uP7TDgAA7FQMDAAAQMDAAAAABAwMAABAwMAAAAAEDAwAAEDw/wHmreR6dOSd1gAAAABJRU5ErkJggg==\n",
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      "text/plain": [
       "<Figure size 504x504 with 64 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA() # instantatiate PCA and calculate all PCs\n",
    "pca.fit(digits.data) # fit the digits data to PCA\n",
    "fig = plt.figure(figsize=(7, 7)) # set up a 7 x 7 figure\n",
    "# create some horizontal space and whitespace between the subplots\n",
    "fig.subplots_adjust(left=0,right=1,bottom=0,top=1,hspace=0.05,wspace=0.05) \n",
    "\n",
    "for i in range(64): # loop over all the PCs\n",
    "    # on a 8 x 8 grid add the next plot with no xticks or yticks\n",
    "    ax = fig.add_subplot(8,8,i+1,xticks=[],yticks=[])\n",
    "    # reshape the current PC into an 8 x 8 grid, plot as an image and use binary colourmap\n",
    "    ax.imshow(np.reshape(pca.components_[i,:],(8,8)), cmap=plt.cm.binary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we view the cumulative explained variance, we see that 95% of the variance is accounted for by around 30 components."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 55,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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     "metadata": {},
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the cumulative sum of the explained variance ratio against the number of components\n",
    "plt.plot(range(1,65),np.cumsum(pca.explained_variance_ratio_))\n",
    "plt.xlabel('number of components') # add x label\n",
    "plt.ylabel('cumulative explained variance'); # add y label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test this we can set `n_components` to 0.95 and PCA returns 29 components."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 56,
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of transformed data:  (1797, 29)\n"
     ]
    }
   ],
   "source": [
    "# instantatiate PCA and calculate suffient PCs such that 95% of the variance is accounted for \n",
    "pca = PCA(n_components=0.95)\n",
    "digits_pca = pca.fit_transform(digits.data) # fit the digits data and transform to component space\n",
    "# print the shape of the component matrix to show number of components used\n",
    "print('Shape of transformed data: ',digits_pca.shape) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we reconstruct the digits with 29 modes and compare them with the original images, it is apparent that less than half of the components are reasonably able to model the digits."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 57,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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\n",
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      "text/plain": [
       "<Figure size 720x180 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rdigits = pca.inverse_transform(digits_pca) # transform the component matrix back to feature space\n",
    "\n",
    "# intialize a 2 x 10 grid of plots on 10 x 2.5 figure\n",
    "# pass keywords to subplots so that don't have xticks or yticks\n",
    "fig, ax = plt.subplots(2,10, figsize=(10, 2.5),\n",
    "                      subplot_kw={'xticks':[], 'yticks':[]})\n",
    "\n",
    "for i in range(10): # loop over (0,9)\n",
    "    # reshape the digits data to a 8 x 8 matrix, plot as an image on the first row and use binary colourmap\n",
    "    ax[0,i].imshow(digits.data[i].reshape(8,8), cmap='binary')\n",
    "    # reshape the reduced digits data to a 8 x 8 matrix, plot as an image on the second row \n",
    "    # and use binary colourmap\n",
    "    ax[1,i].imshow(rdigits[i].reshape(8,8), cmap='binary')\n",
    "    \n",
    "ax[0,0].set_ylabel('full-dim\\n input') # label for the first row\n",
    "ax[1,0].set_ylabel('95% var \\n input'); # label for the second row\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amongst other applications PCA can also be used to filter noisy data. Since noise is random the correlation across images will be very low, therefore the principal components associated with the noise signal will have minimal effect on the variance of the feature matrix. Hence if we choose a relatively low cutoff for the proportion of variance that we want the principal components to account for, this will remove much of the random noise. In the example below we choose a cutoff of 60%, which removes much of the noise which was added to the images."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 58,
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   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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      "text/plain": [
       "<Figure size 720x180 with 20 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42) # initialize a random number generator\n",
    "noisy = np.random.normal(digits.data, 4) # add normally distributed noise of amplitude 4 to the digits data\n",
    "# instantatiate PCA and calculate suffient PCs such that 60% of the variance is accounted for \n",
    "pca = PCA(0.6) \n",
    "digits_pca = pca.fit_transform(noisy) # fit the noisy data to the current model\n",
    "rdigits = pca.inverse_transform(digits_pca) # transform the component matrix back to feature space\n",
    "# intialize a 2 x 10 grid of plots on 10 x 2.5 figure\n",
    "# pass keywords to subplots so that don't have xticks or yticks\n",
    "fig, ax = plt.subplots(2,10, figsize=(10, 2.5),\n",
    "                      subplot_kw={'xticks':[], 'yticks':[]})\n",
    "for i in range(10): # loop over (0,9)\n",
    "    # reshape the noisy digits data to a 8 x 8 matrix, plot as an image on the first row and use binary colourmap\n",
    "    ax[0,i].imshow(noisy[i].reshape(8,8), cmap='binary') \n",
    "    # reshape the filtered noisy digits data to a 8 x 8 matrix, plot as an image on the second row \n",
    "    # and use binary colourmap\n",
    "    ax[1,i].imshow(rdigits[i].reshape(8,8), cmap='binary')\n",
    "    \n",
    "ax[0,0].set_ylabel('Noisy\\n data') # label for the first row\n",
    "ax[1,0].set_ylabel('80% var \\n input'); # label for the second row"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For these exercises we will use the Wisconsin Breast Cancer Dataset from `sklearn`. This is the analysis of 30 properties of breast cancer cells, which have the classification of 'malignant' (0) or 'benign' (1)."
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 59,
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   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean radius</th>\n",
       "      <th>mean texture</th>\n",
       "      <th>mean perimeter</th>\n",
       "      <th>mean area</th>\n",
       "      <th>mean smoothness</th>\n",
       "      <th>mean compactness</th>\n",
       "      <th>mean concavity</th>\n",
       "      <th>mean concave points</th>\n",
       "      <th>mean symmetry</th>\n",
       "      <th>mean fractal dimension</th>\n",
       "      <th>...</th>\n",
       "      <th>worst texture</th>\n",
       "      <th>worst perimeter</th>\n",
       "      <th>worst area</th>\n",
       "      <th>worst smoothness</th>\n",
       "      <th>worst compactness</th>\n",
       "      <th>worst concavity</th>\n",
       "      <th>worst concave points</th>\n",
       "      <th>worst symmetry</th>\n",
       "      <th>worst fractal dimension</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.99</td>\n",
       "      <td>10.38</td>\n",
       "      <td>122.80</td>\n",
       "      <td>1001.0</td>\n",
       "      <td>0.11840</td>\n",
       "      <td>0.27760</td>\n",
       "      <td>0.3001</td>\n",
       "      <td>0.14710</td>\n",
       "      <td>0.2419</td>\n",
       "      <td>0.07871</td>\n",
       "      <td>...</td>\n",
       "      <td>17.33</td>\n",
       "      <td>184.60</td>\n",
       "      <td>2019.0</td>\n",
       "      <td>0.1622</td>\n",
       "      <td>0.6656</td>\n",
       "      <td>0.7119</td>\n",
       "      <td>0.2654</td>\n",
       "      <td>0.4601</td>\n",
       "      <td>0.11890</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>20.57</td>\n",
       "      <td>17.77</td>\n",
       "      <td>132.90</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>0.08474</td>\n",
       "      <td>0.07864</td>\n",
       "      <td>0.0869</td>\n",
       "      <td>0.07017</td>\n",
       "      <td>0.1812</td>\n",
       "      <td>0.05667</td>\n",
       "      <td>...</td>\n",
       "      <td>23.41</td>\n",
       "      <td>158.80</td>\n",
       "      <td>1956.0</td>\n",
       "      <td>0.1238</td>\n",
       "      <td>0.1866</td>\n",
       "      <td>0.2416</td>\n",
       "      <td>0.1860</td>\n",
       "      <td>0.2750</td>\n",
       "      <td>0.08902</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.69</td>\n",
       "      <td>21.25</td>\n",
       "      <td>130.00</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>0.10960</td>\n",
       "      <td>0.15990</td>\n",
       "      <td>0.1974</td>\n",
       "      <td>0.12790</td>\n",
       "      <td>0.2069</td>\n",
       "      <td>0.05999</td>\n",
       "      <td>...</td>\n",
       "      <td>25.53</td>\n",
       "      <td>152.50</td>\n",
       "      <td>1709.0</td>\n",
       "      <td>0.1444</td>\n",
       "      <td>0.4245</td>\n",
       "      <td>0.4504</td>\n",
       "      <td>0.2430</td>\n",
       "      <td>0.3613</td>\n",
       "      <td>0.08758</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>11.42</td>\n",
       "      <td>20.38</td>\n",
       "      <td>77.58</td>\n",
       "      <td>386.1</td>\n",
       "      <td>0.14250</td>\n",
       "      <td>0.28390</td>\n",
       "      <td>0.2414</td>\n",
       "      <td>0.10520</td>\n",
       "      <td>0.2597</td>\n",
       "      <td>0.09744</td>\n",
       "      <td>...</td>\n",
       "      <td>26.50</td>\n",
       "      <td>98.87</td>\n",
       "      <td>567.7</td>\n",
       "      <td>0.2098</td>\n",
       "      <td>0.8663</td>\n",
       "      <td>0.6869</td>\n",
       "      <td>0.2575</td>\n",
       "      <td>0.6638</td>\n",
       "      <td>0.17300</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20.29</td>\n",
       "      <td>14.34</td>\n",
       "      <td>135.10</td>\n",
       "      <td>1297.0</td>\n",
       "      <td>0.10030</td>\n",
       "      <td>0.13280</td>\n",
       "      <td>0.1980</td>\n",
       "      <td>0.10430</td>\n",
       "      <td>0.1809</td>\n",
       "      <td>0.05883</td>\n",
       "      <td>...</td>\n",
       "      <td>16.67</td>\n",
       "      <td>152.20</td>\n",
       "      <td>1575.0</td>\n",
       "      <td>0.1374</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.1625</td>\n",
       "      <td>0.2364</td>\n",
       "      <td>0.07678</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
       "0        17.99         10.38          122.80     1001.0          0.11840   \n",
       "1        20.57         17.77          132.90     1326.0          0.08474   \n",
       "2        19.69         21.25          130.00     1203.0          0.10960   \n",
       "3        11.42         20.38           77.58      386.1          0.14250   \n",
       "4        20.29         14.34          135.10     1297.0          0.10030   \n",
       "\n",
       "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
       "0           0.27760          0.3001              0.14710         0.2419   \n",
       "1           0.07864          0.0869              0.07017         0.1812   \n",
       "2           0.15990          0.1974              0.12790         0.2069   \n",
       "3           0.28390          0.2414              0.10520         0.2597   \n",
       "4           0.13280          0.1980              0.10430         0.1809   \n",
       "\n",
       "   mean fractal dimension  ...  worst texture  worst perimeter  worst area  \\\n",
       "0                 0.07871  ...          17.33           184.60      2019.0   \n",
       "1                 0.05667  ...          23.41           158.80      1956.0   \n",
       "2                 0.05999  ...          25.53           152.50      1709.0   \n",
       "3                 0.09744  ...          26.50            98.87       567.7   \n",
       "4                 0.05883  ...          16.67           152.20      1575.0   \n",
       "\n",
       "   worst smoothness  worst compactness  worst concavity  worst concave points  \\\n",
       "0            0.1622             0.6656           0.7119                0.2654   \n",
       "1            0.1238             0.1866           0.2416                0.1860   \n",
       "2            0.1444             0.4245           0.4504                0.2430   \n",
       "3            0.2098             0.8663           0.6869                0.2575   \n",
       "4            0.1374             0.2050           0.4000                0.1625   \n",
       "\n",
       "   worst symmetry  worst fractal dimension  target  \n",
       "0          0.4601                  0.11890       0  \n",
       "1          0.2750                  0.08902       0  \n",
       "2          0.3613                  0.08758       0  \n",
       "3          0.6638                  0.17300       0  \n",
       "4          0.2364                  0.07678       0  \n",
       "\n",
       "[5 rows x 31 columns]"
      ]
     },
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     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "\n",
    "wdbc = load_breast_cancer(as_frame=True)\n",
    "wdbc.frame.head()"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [],
   "source": [
    "X = wdbc.data # numpy array of features of the dataset\n",
    "y = wdbc.target # numpy array of target values of the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "Calculate the first two principal components for this dataset and plot the data points in terms of these two components, coloured by the target values. Use the magic command `%timeit` to calculate the time taken to perform the PCA. Note that multiple commands can be put on the same line separated by semi-colons. (2 marks)"
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   ]
  },
  {
   "cell_type": "code",
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   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'PCA' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-40-7bd4986edf48>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mget_ipython\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'timeit'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'PCA = pca(n_components=2); projection = PCA.fit_transform(wdbc.data)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatterplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mprojection\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhue\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mwdbc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtarget\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mrun_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2312\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'local_ns'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msys\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getframe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstack_depth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf_locals\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2313\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2314\u001b[0;31m                 \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\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   2315\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2316\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m</opt/anaconda3/lib/python3.7/site-packages/decorator.py:decorator-gen-60>\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/IPython/core/magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(f, *a, **k)\u001b[0m\n\u001b[1;32m    185\u001b[0m     \u001b[0;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    186\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\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[0;32m--> 187\u001b[0;31m         \u001b[0mcall\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mk\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    188\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    189\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marg\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[0;32m/opt/anaconda3/lib/python3.7/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[1;32m   1156\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\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   1157\u001b[0m                 \u001b[0mnumber\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0mindex\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1158\u001b[0;31m                 \u001b[0mtime_number\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtimer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimeit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumber\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   1159\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mtime_number\u001b[0m \u001b[0;34m>=\u001b[0m \u001b[0;36m0.2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1160\u001b[0m                     \u001b[0;32mbreak\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/anaconda3/lib/python3.7/site-packages/IPython/core/magics/execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[0;34m(self, number)\u001b[0m\n\u001b[1;32m    167\u001b[0m         \u001b[0mgc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisable\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    168\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 169\u001b[0;31m             \u001b[0mtiming\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtimer\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    170\u001b[0m         \u001b[0;32mfinally\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mgcold\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<magic-timeit>\u001b[0m in \u001b[0;36minner\u001b[0;34m(_it, _timer)\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: 'PCA' object is not callable"
     ]
    }
   ],
   "source": [
    "%timeit PCA = pca(n_components=2); projection = PCA.fit_transform(wdbc.data)\n",
    "\n",
    "sns.scatterplot(x=projection[:,0], y=projection[:,1], hue=wdbc.target) "
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   "execution_count": 99,
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   "metadata": {},
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.22 ms ± 55.5 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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