{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

CSCI-UA 9473 - Introduction to Machine Learning

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Summer 2022

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Unsupervised Learning

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Partial Solutions

" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part I Market Basket Analysis\n", "\n", "#### Market Basket analysis and the A priori algorithm\n", "\n", "Market basket analysis works by grouping together items that are frequently purchased together. Download the following two grocery datasets from \n", "\n", "- The [github of Jose Zuniga](https://github.com/jzuniga123/SPS/blob/master/DATA%20624/GroceryDataSet.csv). \n", "- [Kaggle's Basketballoptimisation page](https://www.kaggle.com/shwetabh123/basketballoptimisation)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"\n", "\n", "image credit: [www.hybridexcellence.com](http://www.hybridexcellence.com/super-market-rack.aspx) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Association rule analysis is powerful approach that is used to mine commercial databases. The idea is to find product that are often purchased simultaneously. If the customers are represented by a vector $\\boldsymbol X\\in \\mathbb{N}^D$ (for ex. dummy encoding), where $D$ is the number of products that can be purchased, we then look for those entries in $X$ that often take the value $1$ simultaneously. \n", "\n", "For the two dataset above, we can represent the basket of each customer through a one hot encoding where we set the $(i,j)$ entry to $1$ is customer $i$ purchased any quantity of item $j$ (note that we could be more accurate and use additional binary variables to encode the exact quantity of each item that is being purchased). From this, the whole idea of Market Basket Analysis is to find subsets $\\mathcal{K}$ of the indices $1, \\ldots, num_items$ that maximize the probability\n", "\n", "$$P\\left[\\bigcap_{k\\in \\mathcal{K}} (X_k = 1)\\right] = P\\left[\\prod_{k\\in \\mathcal{K}} X_k = 1\\right]$$\n", "\n", "Given our encoding, we can replace the probability by its empirical version and try to find a subset $\\mathcal{K}$ that maximizes the quantity\n", "\n", "$$P_{emp} = \\frac{1}{N_{cust}} \\sum_{i\\in cust} \\prod_{k\\in \\mathcal{K}} X_{i,k}$$\n", "\n", "where $X_{i,k}$ is the binary variable associated to customer $i$ and item $k$.\n", "\n", "__Exercise II.1.1__ Represent each of the datasets above using an appropriate one hot encoding. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.1.1 The A priori algorithm__\n", "\n", "Running through all possible item sets ($2^{\\text{num items}}$) can be intractable on large datasets. It is however possible to use efficient algorithms that lead to a substantial reduction reagrding the number of passes over the data they require. This is the case of the A priori algorithm. The algorithm proceeds as follows\n", "\n", "- The first pass over the data computes the supports of all size 1 itemsets\n", "- The second step computes the support of all size 2 itemsets that can be formed from pairs of the single itemsets that survived the first step.\n", "- At the $k$ step (size $k$ itemsets), we only consider those size $k$ itemsets that are formed by an item set which appeared at the previous step together with a single item that as retained by step 1. \n", "- The itemsets with support less than the threshold are discarded. \n", "\n", "The key idea here is that we can focus our attention only on those itemsets of size $K$ for which all of the size $K-1$ subitemsets appeared at the previous step. That reduces the number of itemsets we need to consider and leads to a significant reduction in the computational cost.\n", "\n", "In pseudo code, we have \n", "\n", "- Build all size one itemsets and store them in $S_1$\n", "\n", "- for k=1,...desired size\n", "\n", " Go over all possible size K-1 itemsets $S_{k-1}$ and build the size K sets $S_k$ from $S_{k-1}$ and any elements from the size $S_1$ that are not alread in $S_{k-1}$ and such that all size $k-1$ subitemsets $S\\subset S_k$ are in $S_{k-1}$\n", "\n", "- Count the support and discard the itemset if the prevalence (i.e the empirical probability defined above) is lower than some threshold $t$. \n", "\n", "__Code the 'A priori algorithm' and apply it to the grocery datasets that you loaded above__. You can downsample those datasets if it makes it easier. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# put the code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once all the itemsets have been computed, they can be used to define association rules. For any two subsets, $A$ and $B$ of the item set $\\mathcal{K}$, $A\\cup B = \\mathcal{K}$, one can define the total $T(A\\Rightarrow B)$ to be the probability of observing the item set. and use $C(A\\Rightarrow B)$ to encode an estimate of the posterior \n", "\n", "$$C(A\\Rightarrow B) = P(A\\Rightarrow B) = \\frac{T(A\\Rightarrow B)}{T(A)}$$\n", "\n", "where $T(A)$ is the empirical probability of observing the item set $A$.\n", "\n", "Together those two quantitities can be used to predict the items $B$ that a customer might want to purchase given that he bought the items in $A$. Or conversely, the items $A$ that are usually bought by customer that buy the items B. I.e. If we set thresholds $t$ on both $C(A\\Rightarrow B)>t$ and $T(A\\Rightarrow B)$ we could look for all transactions that have some proudct as consequent and for which the probability estimates $C(A\\Rightarrow B)$ and $T(A\\Rightarrow B)$ are sufficiently large. \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "### Part II: Clustering\n", "\n", "\n", "##### Exercise 1.1. General K means\n", "\n", "Consider the dataset given below. Implement the K means algorithm and run it on top of this dataset. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "import matplotlib.pyplot as plt\n", "\n", "n_samples = 200\n", "random_state = 170\n", "X, y = make_blobs(n_samples=n_samples, centers = 4,random_state=random_state)\n", "\n", "plt.scatter(X[:,0], X[:,1], alpha=.4)\n", "plt.show()\n", "\n", "\n", "def Kmeans(data, K):\n", " \n", " '''function should implement a simple K means clustering with random \n", " initilization of the centroids. K is the number of clusters'''\n", "\n", "\n", " return " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "num_clusters = 4\n", "import numpy as np\n", "\n", "x1min = np.min(X[:,0])\n", "x1max = np.max(X[:,0])\n", "x2min = np.min(X[:,0])\n", "x2max = np.max(X[:,0])\n", "\n", "centers_x1 = np.random.uniform(x1min, x1max, num_clusters)\n", "centers_x2 = np.random.uniform(x2min, x2max, num_clusters)\n", "\n", "centers = np.vstack((centers_x1, centers_x2)).T\n", "\n", "plt.scatter(X[:,0], X[:,1], alpha =.3)\n", "plt.scatter(centers[:,0], centers[:,1], c='r', marker = 'x', \n", " s = 90, linewidth = 2.5)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import copy \n", "\n", "\n", "def Kmeans(X, num_clusters, delta):\n", "\n", " \n", " centers = np.zeros((num_clusters, np.shape(X)[1]))\n", " for d in np.arange(np.shape(X)[1]):\n", " \n", " xdmin = np.min(X[:,d])\n", " xdmax = np.max(X[:,d])\n", " \n", " centers[:,d] = np.random.uniform(xdmin, xdmax, (num_clusters,))\n", " clustering = np.zeros((np.shape(X)[0], ))\n", " \n", " previous_centers = copy.deepcopy(centers) + 10\n", "\n", " while np.linalg.norm(centers-previous_centers)>delta:\n", "\n", " previous_centers = copy.deepcopy(centers)\n", "\n", " # assignment step \n", "\n", " for i in np.arange(np.shape(X)[0]):\n", "\n", " distance2centers = np.zeros((num_clusters,))\n", "\n", " for k in np.arange(np.shape(centers)[0]):\n", "\n", " distance2centers[k] = np.linalg.norm(X[i,:] - centers[k,:])**2\n", "\n", " clustering[i] = np.argmin(distance2centers)\n", " \n", " # re-compute positions of the centers\n", "\n", " centers = np.zeros((num_clusters, np.shape(X)[1]))\n", " \n", " for k in np.arange(num_clusters):\n", "\n", " indices_k = np.argwhere(clustering == k)\n", " \n", " if len(indices_k) >0:\n", " \n", " centers[k,:] = np.mean(X[indices_k,:], axis=0)\n", " \n", " else:\n", " \n", " new_center = np.zeros((np.shape(X)[1],))\n", " for d in np.arange(np.shape(X)[1]):\n", " \n", " xdmin = np.min(X[:,d])\n", " xdmax = np.max(X[:,d])\n", " new_center[d] = np.random.uniform(xdmin, xdmax, 1)\n", " centers[k,:] = new_center\n", " \n", " return centers, clustering\n", "\n" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "centers, clusters = Kmeans(X, 10, delta=.01)\n", "\n", "plt.scatter(X[:,0], X[:,1], c=clusters, alpha =.3)\n", "plt.scatter(centers[:,0], centers[:,1], c='r', marker = 'x', \n", " s = 90, linewidth = 2.5)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(10, 2)\n" ] } ], "source": [ "print(np.shape(centers))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise 1.2. The Elbow method\n", "\n", "Run your algorithm with a number of clusters $K=1,2,3,4,5,6,7,8,9$ and $10$. For each of those values, Compute the Within-Cluster-Sum of Squared Error (i.e. $E = \\sum_{\\mathcal{C}_k}\\sum_{i\\in \\mathcal{C}_k} (c_k - x_i)^2$) then plot this error as a function of $K$. What do you notice?\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "MaxClusterNum = 20\n", "\n", "error = np.zeros((MaxClusterNum,))\n", "\n", "for k in np.arange(MaxClusterNum-1)+1:\n", " \n", " centers, clusters = Kmeans(X, num_clusters=k, delta=.01)\n", " \n", " clusters = clusters.astype(int)\n", " # computing the error \n", "\n", " for i in np.arange(np.shape(X)[0]):\n", " \n", " error[k]+= np.sum((X[i,:] - centers[clusters[i],:])**2)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cluster_numbers = np.arange(MaxClusterNum-1)+1\n", "error_values= error[1:]\n", "plt.semilogy(cluster_numbers[:20],error_values[:20], 'x-')\n", "plt.title('Evolution of squared error')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise 1.3. The importance of initialization\n", "\n", "Extend your implementation of K means from the previous exercise so that it takes an additional argument specifying the initialization. You should contain implementations of each of the following approaches\n", "\n", "- Random partitioning (the method starts from a random assignment of the points)\n", "- Forgy (The method picks $K$ feature vectors at random and assign the remaining points to the nearest centroid)\n", "- K means++ (see below)\n", "- MacQueen (see below)\n", "- Kauffman (see below)\n", "\n", "In the Macqueen Approach proposed by MacQueen (1967), one chooses K instances of the database (seeds) at random. We then assign, following the instance order, the rest of the instances to the cluster with nearest centroid. After each assignment a recalculation of the centroids has to be carried out\n", "\n", "In the Kauffman approach, we first select the most centrally located instance. Then for every non selected instance $x_i$ repeat the following steps:\n", " - For every non selected instance $x_j$ calculate $C_{ji} = \\max(D_j -d_{ji},0)$ where $d_{ji} = \\|x_i - x_j\\|$ and $D_j = \\min_{s} d_{sj}$. $s$ being one of the selected seeds\n", " - Calculate the gain of selecting $x_i$ as $\\sum_{j} C_{ji}$\n", "Select the not yet selected instance $x_i$ which maximizes $\\sum_{j} C_{ji}$. If there are $K$ selected seeds then stop. Otherwise go to step 2. \n", "\n", "In K means++, we choose a center uniformly at random among the points. For each point $x_i$ from $\\mathcal{D}$, compute the distance $D(x_i)$ between $x_i$ and the nearest centroid that has already been chosen. Choose a new point at random as the next center using a weighted probability distribution where a new point is chosen with probability proportional to $D^2(x_i)$. Repeat the steps until $K$ centers have been chosen.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def Kmeans(data, initialization):\n", " \n", " '''function should implement K means clustering for each of the \n", " initializations listed above'''\n", "\n", "\n", "\n", "\n", "\n", " return " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise 1.4. Semisupervised: Constrained K means. \n", "\n", "Clustering is traditionally viewed as an unsupervised method for data analysis. In some cases however, information about the problem domain might be available in addition to the the data instances themselves. Within such a framework, one approach is to define so-called 'Must Link' and 'Cannot link'. The former referring to points that must be placed in the same cluster. The latter referring to points that cannot be placed in the same cluster. One can then extend K-means as follows\n", "\n", "1. Let $C_1, \\ldots C_K$ denote the initial cluster centers\n", "2. For each point $x_i$ in the dataset $\\mathcal{D}$, assign the point to the closest cluster $C_j$ such that the point does not violate any of the constraint. If no such cluster exist, return Failure\n", "3. For each cluster $C_j$, update its center by averaging al the points $d_j$ that have been assigned to it\n", "4. Iterate between (2) and (3) until convergence \n", "5. Return ${C_1, \\ldots C_K}$\n", "\n", "The constraint check can be carried out as follows. For every point $d_i$ in the dataset with closest cluster $C_j$, you need to check that for every $(d_i,d_k)$ in the set of all constraints, the constraint is satisfied. \n", "\n", "Apply this extension to the dataset below. setting as the 'Must link' a unique cluster for all the samples in consi and as 'Cannot link' a different cluster for the points in distinct consi, consj." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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yeRQhWiop23nafqS47dn2XlEBuJDkoIv6snv9vqm3KVIZ56IIHVN28yyfRxGi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\nA7arTfyg767SAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.io\n", "import matplotlib.pyplot as plt\n", "\n", "cluster1 = scipy.io.loadmat('cluster1.mat')['cluster1']\n", "cluster2 = scipy.io.loadmat('cluster2.mat')['cluster2']\n", "cluster3 = scipy.io.loadmat('cluster3.mat')['cluster3']\n", "\n", "cons1 = scipy.io.loadmat('cons1.mat')['cons1']\n", "cons2 = scipy.io.loadmat('cons2.mat')['cons2']\n", "cons3 = scipy.io.loadmat('cons3.mat')['cons3']\n", "\n", "\n", "plt.scatter(cons1[:,0], cons1[:,1])\n", "plt.scatter(cons2[:,0], cons2[:,1])\n", "plt.scatter(cons3[:,0], cons3[:,1])\n", "\n", "plt.scatter(cluster1[:,0], cluster1[:,1], c='m')\n", "plt.scatter(cluster2[:,0], cluster2[:,1], c='m')\n", "plt.scatter(cluster3[:,0], cluster3[:,1], c='m')\n", "\n", "plt.show()\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Exercise 1.5. Image segmentation\n", "\n", "K-means is commonly used in computer vision as a form of image segmentation. To each pixel of an image is associated its color described in RGB. The image to be segmented can then be represented as a set of points in a 3D data space. Consider the image below. By carefully initializing K means with the right number of clusters (and possibly merging subclusters), try to separate the parrot from the background. You might want to downsample the image" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "import matplotlib.pyplot as plt\n", "import matplotlib.image as mpimg\n", "img = mpimg.imread('KmeansParrot.jpeg')\n", "imgplot = plt.imshow(img)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "img_ds = img[1::4,1::4,:]\n", "imgplot = plt.imshow(img_ds)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [], "source": [ "pixels_list = np.reshape(img_ds, \\\n", "[np.shape(img_ds)[0]*np.shape(img_ds)[1], np.shape(img_ds)[2]])\n", "\n", "\n", "centers, clusters = Kmeans(pixels_list, num_clusters=5, delta=.01)\n" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[2 3 3 ... 0 0 0]\n" ] } ], "source": [ "clusters = clusters.astype(int)\n", "centers = centers.astype(int)\n", "print(clusters)" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "num_clusters = 5\n", "\n", "segmented_image_pixelsList = np.zeros(np.shape(pixels_list))\n", "\n", "\n", "for i in np.arange(np.shape(pixels_list)[0]):\n", " \n", " \n", " segmented_image_pixelsList[i, :] = centers[clusters[i],:]\n", " \n", "segmented_image = np.reshape(segmented_image_pixelsList, \\\n", " [np.shape(img_ds)[0], np.shape(img_ds)[1], np.shape(img_ds)[2]])\n", "\n", "plt.imshow(segmented_image.astype(int))\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dTf369SMAtGHDBsrKyuJcUmVlZemUTExMND5n9+7dtGjRIhKJRDRp0qRiv+PYsWNJIpGQRCKhWbNmFbu99wXoaA9UIj4RGGN9AKwkos6MsVUAUolog671K6tPhNOnT+cb8UAJYwwxMTGwsrICEaFz5864deuWTs9gjBXKP8Lu3bsRFBQEmUyG9evX61yvqqGrT4SSWgONBKB6lD2DMTYeCs+j84hI92PyKkhqaiqMjY0BAM2bN9d5x65GjRp4+fJlgb6v87J69erCdlFAC8XehWOM6QMYDECpLekFoD6AVgAiAGzUUm8yY8yXMeartJWpzDg4OEAqlUIqlaqd7xSVyMhIWFpaFroeY0yIeVpS6DLPyy9B4Uz+vJZ7dQE8LaiNyrgGOnDgAM9vgYODA3cvJyeHty4xMDCguLg4ql+/Ps8XQkmk58+fU4sWLejs2bOUkZFBUqm0HL+VigPKwrVvLqOgMn1TuvXNvRwGhbfSKodcLtfotyAjIwP29va8vKysLDg5OSElJaXE/b21b98eaWlp0NfXr3o7ZGVAsQSIMWYMoDeAKSrZ6xljraD4BQzOc6/KEhERgVq1agFQaFLnpbRc6hbHpzYRoXbt2pxQP3/+nNNkEFBQXOfy6QCs8uSNK1aPKgH79u1TU7mRyWQaXeY+efIEbdq0KbF1UUnz7t077nNJj46VAUEToRRISEjQ2b/0pEmTdPKTXRh8fHzQp08fZGRkFLst1e10XZxCVjUEASpnSsNNr4eHR4kIJWOsSmlWFwVBmbSUadCgAWdIV5owxuDt7Q1A4etNNWyKh4cHmjRpUup9qIoIAlTCnDlzBn/99Rd3bW1tjUGDBnHXEokEGzdqPBorFkTExU7dsGEDz4H9gAEDUKNGjRJ/poAwhStxbt26hWvXrgEA6tevjwkTJsDa2hpLly5FZmYmtm7dirS0tGI/x8LCAl9++SWysrKwefNmLFy4EGvWrMHSpUsxe/ZspKWlYd26dZgwYQJOnjwJc3PzAs0fBAqPIEAliI+PD/z8/LjrRo0aYcqUKUhISECdOnWQnp4OqVSKFStWFPkZtWrVwoABA2Bra4slS5bg119/xZQpU+Dh4YG4uDh4eHiAMQYHBweIRCLY29tj586dSEhIwMyZMwXniSWMEGCrBJk2bRq8vLwAALVr18bUqVMxZcoUeHt7Y86cORrrDBs2DCKRCCdOnNB48NqiRQvIZDKkp6fjgw8+QPPmzfHVV1/h0qVLSExMxLx58zSeK5mZmeHDDz+EgYEBl+fm5oYhQ4YIQqQDuiqTlntoE6pEqjxffvklp0IzZswYIiK6efNmvqo2OTk5RERkaWmpdq9x48Z05MgR8vb2pk2bNhGRIkSKl5cXASB9fX0aMGCAxr589NFHFB8fz8v7+uuvaePGjXT58mUKCAgoxW+i4oMyVOURKASMMbRo0QKPHj1Cy5YtNSp1NmjQACYmJvDw8MDAgQMRGRnJjU4BAQH48ccfoa+vjy5duuDUqVNq9R89eoTVq1fj7du3nMec+vXr4/PPP8fcuXMxb948jB8/XuOoqKenh+bNm5fwW1didJGy0k5VYQTS09MjJycnatSoEQUEBBAAksvlXF3lCFSrVi3y9fXltevh4UFTp06llJQUCg8Pp8ePH9OHH35IOTk5FBQURK9fvya5XE5BQUEUFBREzs7OakqpBw4coL59+3LX1atXJ2tra7VRz8LCgmtHmVT7WVWAMAKVPaampjA2NgYRoVq1asjKyuIcF9rb2yMwMJALtGVtba2xjYMHD6r5OTA2Noaenh4OHTqEQ4cO4Z9//sEff/yBgIAAdOnSBcnJyQgNDUX9+vUBKNRvOnbsiPT0dMTHx0Mul2PMmDG8NseOHYuGDRti1qxZvPyEhASuHSWRkZEQiRQnHpaWlpzfBgEII1BJs3z5cpo1axbl5OTQ0aNHSSQSkZGREdWqVYtCQ0O5kI2pqancL3tqaipZWFgQADIyMqJbt27x2szKyqLNmzeTnp4e9evXjzMTt7Ozo/DwcDI2NlYbSZKTkyk1NZXq1q1bouYRAQEBlJqaWunNIqDjCFTuwkOVTIBWrFhBc+fOpd9++4309PSoffv29OjRI41/jHK5nLKzs8nQ0JDLe/LkCa89qVRKHh4eJBKJaMSIEXTx4kUSi8Wkp6dHAMjS0pIyMzN57YrFYkpOTiYbG5sSFR7VdPv27XL6hssGXQVImMKVIER8n9fm5uYYOHAgWrZsqVZW6cvAyMiIp3aTd1Nh3rx5MDExwfbt23H16lX06NED2dnZCAwMRNeuXREeHq6m95aamsrTRBAoPQRVnhJk+vTpEIlEmDNnDg4cOKDRoYiRkRHkcjlkMhn09PR4wvP27Vs0bdo032dcunQJIpEIDRs2RGRkpEZ/CIaGhhCJRKgKpvLlji7DVGmnyjCF++yzz7idL8aYRtNsCwsLkkqllJOTQyKRSO2+0q2VEnd3d2KM0dKlS8nT05MAUK9evejOnTtcnWrVqqlN4coiiUQiOnfuXDl926UPhClc2dC5c2f4+fkhOztbsagEuH9VqVWrFgIDA5GdnQ1LS0vI5fIC25bL5Vxb//vf/2BmZgZ3d3d06dKlZF+iCKj2rSpT4BSOMbaXMRbNGHuqkmfJGLvAGAvI/ddC5d4SxlggY8yfMda3tDr+vpCVlYXMzEw1gfj0008RFxeHs2fPAlCsbTIyMlCzZk1kZmaqtRMYGMiZfGti//79mDp1KuRyeYkb4AkUHV3WQL8C6JcnbzGAS0TkDOBS7jUYY02h8BHnklvHkzFWaQ8NunXrphZ+EVBYmXp5eeHhw4cYP348l09EWgNade3aVaOb3hUrVmDBggXIysrSqMWdkpKSb9RvgdKlQAEiomsA8sYjHAJgX+7nfQCGquQfIqIsInoDIBBAu5Lp6vvFhx9+iNu3b/MUQJcvX44nT57gu+++w82bN/H5558jOjpap/bCw8N5GwpffvklTpw4AQsLC26joG/fvmphSIgIYWFhxX8hgSJR1F04O8p1XZX7r21ufi0AoSrlwnLzKhV9+/bFzZs3uanUpk2b4OPjg2nTpqFZs2awt7dHUlISQkJCdGrv4sWLMDMz4+WFhISoaVn7+vri+vXr8PHx4cU0FYvFnA2SkvPnzxfaY6lA4SnpTQRN7i41rjQZY5MBTAaAOnXqlHA3So/hw4fj8uXLkEql8PLyQs2aNdGxY0fY2NiolXV1dcVnn32GhQsXIjY2FqNHj9bY5qZNm7Bnzx6N6j0///wzLl++jODgYMTFxeH06dOwtLTkxUPV5Of6xx9/RHp6ejHfVqBAdNmqQx4PowD8AdjnfrYH4J/7eQmAJSrlzgHoWFD7FWUb+/PPP+dtP/v7+2st6+3tTQ4ODjRgwACdtoVjY2N59fv376+1rJWVFX388cdlvnWdN509e7a0v/JyAzpuYxd1CncCgHvuZ3cAf6vkj2SMGTDGnAA4Ayh5tzPlRNOmTTlNga+//lqrQqiPjw/8/f3Rp08fnD59mss3MjLC999/n+8zNmzYwIvno4m4uDj8+eefhet8KfDzzz/jwYMH5d2NckWXbeyDAG4BaMQYC2OMTQKwFkBvxlgAFJ5J1wIAET0D8AeA5wDOAphORDLNLVc8ZDIZFixYgEWLFmHBggVaHbvfv38fb968wccff8zLNzQ0xOzZs3l5CxcuhFismEn/9NNP+OGHH7Bu3Tp88MEHcHFxKZX3KCmOHj2Kly9flnc3ypUC10BENErLrZ5ayn8PIP+f2QoGEWHPnj0ICAiAl5cXJBJJkdrJysrCb7/9hokTJ2Lv3r0AFIZuylFt7dq1iI6Oxo4dO/DVV1+pbSwIvH8Imgg6cvr0aRw7doyzi9HG8+fP8eTJE4SFhakFyUpPT8fs2bORnJzMCdCUKVMwaNAgNeXPrVu3luwLCJQKggDpAGOM5+stPw4ePIi9e/fC1tYWsbGxavdlMhl8fHx4eTNnztQaOaFevXqQy+UFros00aFDB0gkEvj5+ZWIKy0BdQRt7FKid+/eWLdunVp+dnY2evTowcvr06cP71C2fv363PRt5syZ+OKLL4rUhzVr1mD79u3o3r07TExMACh08lS33KtVq4Z69eoVqf26detW+WgNggCVIHFxcUhKSoKZmZnWHbq81KlTB4wxdO3aFVFRUbC3t8eWLVvQpk0bWFlZ6bwOqlOnDneepvzs7u6OQYMGYe3atRg4cCDq1KmDDRs2YN68eVyZgQMHYs2aNUV63x07dqB///5Fqltp0GWvu7RTRTkHKgilU5EpU6ZQcnIynTp1qsCzlJycHKpVqxZn/nD9+nVq27YtAaCffvqJ0tPTycPDI982JBIJxcbGUmxsLDHGKCsri9evhIQEio2NpczMTCJSmJAry3t7ewvnQBqAYM5QPojFYuzduxdJSUn49NNP1e4bGRmphR159eoVHBwckJCQgF69eiE7Oxv6+vqYP3++VrMHxhgMDAyQmZmJnJwc1K5dG4C6KUVGRga6desGf39/7N+/HwMHDsTKlSuxZcsWiEQiQbO7mAhTuBJCJpOBiLBixQqsX78ehw4dwvDhw3llLCwsNG4s2NnZISEhAXp6evD19UX79u1x9OhRpKamYtq0aRqFqF69eggICAAA6OvrIzk5GWlpaWCMQSaTcQGNXVxc8PjxY5w6dQqHDx+GqakpNm7ciK+++gqenp6l82VUJXQZpko7VYYp3IgRIwgAffvtt/Tjjz9qnPJYWFhQWlqa2hROLpeTpaUlhYSEkFwup44dOxIA2rdvH82aNUun6RRjjORyeb5Bio8dO0aTJk0SVHl0AIJXnrJFKUAAaNasWbR///4C/wDlcjnnXQdQmHS7uLiUq36bIEAKdBUgYQ1UAvTr1w/nz5/nrrdu3arRZW9pUK1aNYSHhwvhF8sJQYBKAOX6R4ny16mwNGzYsNDBhpOTkzWaUgiUDcImQhlRs2ZNbtGvdDllY2PDWaEGBATA0tKySIJXlGDC06dPF9SFSgBhBCojoqKi0L17dwAKjzaurq6Ii4vj7nfv3h1RUVFq9b7++mtkZGRgw4YNJdofb2/vIivFCqigy0KptFNF3kT47LPPyNTUVOtCu0WLFvTXX3/x8kQiET169IgePXqk0T+cMnl4eFBMTAxFRUXRsmXLyn3TIG8SNhGKblAnkEtgYCBSU1MBAHPmzOF54enQoQMWLFgADw8PXh3GGJo3b46ZM2fyzniOHDnCxTFVmjZcuXIFtra2+bq8Eig/hClcCXLp0iXeJoClpSXq16+P+/fvc3n6+vo4fPgwAPAcgezfvx/9+/eHhYUFpk+fjuPHj+Pdu3e8cIydOnXC/PnzERQUhAULFhSpj9OmTUNkZCRkMhlq166N7du3F6kdAQXCCFSCPH78GP7+/tz1kydP1BQ19fT0MHToULW658+fR2ZmJv79918kJCSgXbt2WLFiBeLi4vDFF18gLCwM3333HRo1aoTQ0FDs3r0bu3fvxtatW6Gnp4ddu3Zp7NPq1auxe/duNGrUCADQunVrODs74/Xr13j06JHWdxGJRFrbBIClS5e+9xazZYEwAhWDDRs24N27dwCAUaNG4c2bN7h9+zYAoFWrVmjZsiX27dvHlTcyMsK3334LuVyOpUuXAgC+//57zkhvw4YN2L17N2JjYxEeHg53d3c8ffoUr1+/xqeffooePXrg4sWL+OOPP2BkZAQzMzPMmDEDc+bMQWBgoMY+vn37FklJSdxO3bFjx5CYmIgnT57k+25EhKCgIK33Bw8eDAcHBx2/qUpMQYskAHsBRIPvlecHAC8BPAbwFwDz3Py6ADIAPMxNO3RZiFXUTQRnZ2duQT127Fjq1KkTdz1mzBg1bWwLCwsiIsrJyeHylEGGt2/fTtWrVycANHLkSHJycqKRI0dSly5dqGfPnvTDDz/QiRMn6MKFC2RnZ0cTJ04kMzOzAjW1SyLNmTOHpzEBCPGBlEkXAeoK4IM8AtQHgDj38zoA6+g/AXqqy4NVU2UQoLypY8eONGfOHJ0FSDVK97Jly6hFixbk5uZGTZo04fLbtm1LmzZtopUrV9KrV6+0Pnvs2LEkFot5eX369CF3d/d8+6yaGGPk7u5O7u7uJJPJyMDAgEaNGkVGRkY0dOhQCgoKKs+vvtQpMQGiAgQDwDAABwoql1+qiAJ0/vx5qlmzpsY/PicnJ2rVqhUvz9DQkEaOHElSqZSOHz9OAGjAgAEklUrp9OnTNHz4cBowYABvS3zOnDm0ZMkSatSoEZfXs2dPIqJ8Beivv/6ioUOHkr6+Ppd3+fJlIiKNyqSWlpbUtWtXAhS2Rf369SORSEQnT57kwlAOGzaMjh49SpaWlvTy5cty+97LirIUoJMAxqqUSwPwAMC/ALrk0+ZkAL4AfOvUqVMW30mJUqNGDa1/wLNmzVIzVLO1taXbt2/ztLHlcjnduHGDDAwMOMeKSmXSJk2akI2NDX311Vc0efJksrOzo4YNG1KbNm3o4cOH+QoQoIiR2r9/fzIwMCAAtG3bNoqNjeUJkI2NDTVu3Ji6dOlCAQEB1LFjR+rVqxdduXKF0whXjdCtnGIePHiQbty4QQkJCeX07Zc+ZSJAAJZBsQZiudcGAKxyP7tC4Se7WkHtV8QRKD8BGjduHK1Zs0YtX9WcwcXFhdPGbtKkCd26dYuys7Np8ODBZGRkRJ6enjRo0CACQNbW1jR79mzasGEDASBXV1cKDg6mhg0b5itAL168oO7du5OLiwsZGxvTsWPH6Ouvv+bC2w8dOpS2bt1KXbp04d4rPj6ePvjgA3r48KFWAWrQoAEZGRkJB6nFESAoPJLeAmCcT72rANoU1H5lE6C8SSwWk729PVWvXp38/f1JT0+Pa0dPT4/S0tKoefPm9O7dOyIi7tdfmZQR6oyMjMjBwYH69+9P2dnZ5Ovrq/F5Dg4OlJqaSi1btqTg4GAiUphbnDlzhoiIFi1aRGZmZlxk8C5dulBWVhb3/LS0NHJwcKDatWtzAhQSEkLVqlUjAPTy5Utq166dIEBURE0Exlg/AIsADCaidJV8G2U8IMZYPShc+74uyjPeZxISErSaWhsaGsLIyIiXV79+fVy4cAGMMe48RomFhQUYY3j8+DFq1qyp1p6RkREYY0hPT0ffvn3x/PlznD59GsHBwWjTpo3GPgQFBcHExARXr16FmZkZ4uPj4eXlhZ49//OFOWXKFGzcuJG7DggI4ByEGBsbIzQ0FCEhIZxZRrt27aCnp8ddm5mZCbp00OEcKNe174cArBljYQBWQuFE3gDAhdwv9DYRTYVix+5bxpgUgAzAVCLKG1uowlO3bl0kJydrvLdw4UKYmppi4cKFXJ6/vz/69euHoKAgWFlZ8XzAaQsErK+vD5lMhm+++QZZWVlYsmQJcnJyMGzYMFy8eDHf/mVmZkIikaBFixYICwtTzgZw7NgxfPzxx5BIJJDL5bzYRi4uLnj48CGIiIugp/pD8Pq14newadOmyM7OxsmTJ4VI4IBuU7jSThVtCqecyuRN2oILi0QicnBwoJiYGDIyMsq3balUSp07d6aTJ0/S2LFjiTFGy5cvJy8vLxKJRNS7d28iIgoICCCRSKRRGVUkElFycjJJpVJycnLi8o8cOUIymYyIiNavX8/lq66BYmJiuGmnKsbGxgQorGYbN25MgKBMSrqugUo7VSQBksvlWgXop59+ouXLl/PyOnToQE+fPuWuCxIgFxcXunHjBhfe5Mcff1R7vmpKTExU64fSrZWNjY3avd27dxNR4QWI6L9NBGENVMw1UFXGyMhI6/RNE7dv30azZs0K/ZxTp05h3LhxavmXLl2CSCRCw4YNERkZqTEKnYGBAVJSUtTqyeVyTJo0CQAwf/587Nmzp9D9CgsLQ8OGDQtdr7IiCFAhodz1RFGwsLBQC9uYl4cPH6JDhw4YMmQIfvvtNy5/586dGD16NHr06MGtQZSeSPX19ZGdnY3s7GwwxpCamqrmI6FPnz44fvw4twnAGOM+X79+HRKJBM7Ozlx5qVQKfX197n1NTU25vjdr1gx3797FgAEDcOjQoSJ/H5UBQYBKiH379uH58+c8f9h9+/bFpUuXeOUK2rnq2LEj7t69q+ZnQS6XQyaTQSQSQSKRoGHDhlxsnuzsbFhYWHACamxsrObURCaTYdSoUfj111+5vLFjx+LQoUPo1KkTEhIScOLECTg6OnL3VTcZIiMjOT/YUqmUa7M4PyiVAl3meaWdKsoayM7Ojls3PHnyhOrVq8ddHzp0iHPtq0z6+vpkbm7OO0gtiLi4OMrOzqaEhASKioqitLQ0IiJKT0+nxMREXtnw8HC1NY6NjQ3Z2NhQSkoKZ82q6irLzMyMtmzZQkREv//+O40YMYLi4+OJiOjNmzdq7SnPgRwcHCgwMJCkUinvAPf3338vya/4vQHCGqjkUQ1ZP2DAgAKjcGdnZyMxMREAYG9vDz8/vwKfYWlpCYlEAnNzc9ja2sLY2BiAYu2VXyQExhgCAwMRGxuLmJgYEBGsra1ha2vLRcADgCVLlnBWs5mZmTh16hQvYLE2YmJiYGVlBT09vQLLViUEASoiISEh3FTG09MTly5dwpEjR7j7/fv3x5YtW7hrPT09zly7tFANU+Lm5ob4ePUjOC8vL/z111/Yt28fVq1ahfT0dISHhyMgIAADBgxQK+/q6qr10FhAMKgrEXbu3Inw8HCe3+v79+8jNDQUAODo6Ijff/+duyeTydCrVy8AwMWLF7X+qq9ZswbOzs745JNPCuwDEXEGd8r1j6mpKcaMGcMzjAsNDUVUVBT09PR4I6i9vT2WL1+O0aNH89p98OABiAjnzp3jNib279+PCRMmVPn4qIAgQDpBRPj00081LpjXrVuHevXqYdOmTTytgqioKM5NlbGxMTp16sRr7+rVqzhy5IhGD6bLli2Dv78/7t27hzlz5uDYsWM4ePAgAKB58+ZYuXIlIiIisGDBAuzfvx8TJ07k7nfv3p3X5u3btzmnJ6oMGTIEwcHBnIP5uLg47N+/X+P7jxgxAowxtGnTBmKxGO3bt0e1atWwfPlyuLm5Ffj9VWYEAdIBIsKxY8c03rt9+zaCgoJ4Pt169OgBR0dH/PLLL3BycsKqVas01h0+fLhGAWrbti3q1KmD3r17o2PHjjh58iT3/Nu3b0MikWD69Ono0KEDLl++DLlcjosXL2LHjh0FvsvYsWORnp6OJ0+e8HTpTE1N0aVLF5w9e1atzp9//olt27ZBLBZj0aJFSExMxJs3b+Dm5saFVamqCGugYjB79mzcuXMHu3bt4nTFACAlJQVxcXFo2LAhVqxYgREjRhSq3aioKISEhKBdu3Zo0aIF7967d+/w559/onr16hg+fDh+/fVXyOVyjQ5AVq9eza2DJk6cCA8PD9SrVw8ikUjtANbKygrTpk3DkiVLNPbpiy++wPr16+Hp6Yldu3YhJiYG+/bty9cxSVVAEKACkMlkvM0AVb788kvY29ur5d+7dw+vXr3CvHnzMGHCBN49qVTKudTdvHmz2gJ9//79WLt2LVavXl2g4w8TExO1HbTNmzdj8+bNyM7OxubNm7ldQENDQ5iYmEAul8PNzY2nmQ0AsbGx+PPPPzF37lytz9u4cSNSU1Ph7u6OWbNm4caNG3j+/Hm+fazsCFO4ApDJZFr/qE6cOIH27dvj3bt3iIyMBAC0bNkSYrEYBgYGaNCggVoduVwOPz8/jBkzBnPnzsXMmTM5rzwAsH79ep0jckskErRr1w7JyckQiUQgIsydOxdEBFNTU06rGlBEwTt58iRWrFgBKysr3pZ6dHQ0du3ahV27duHTTz/FyJEjeRoGY8aMweHDh7mD1SVLlnAjbmnvLL7vCCNQMViwYAEaNWrEG4VatGiB4cOHo1q1avj333/V6ujr68Pb21ttt6uwpKWl4fTp0zh16hR+++03bgOgX79+6NevH44dO8Zz8tizZ0/Url2b81WnOsJFR0fDx8cH7du3x507d/Dzzz+DMYZ+/foBUGhZTJkyBZ06dYKBgQEAYNWqVfjoo4/QsWPHYr1HhUeX09bSTu+rJoJUKiUfHx+dLU+VadasWRQTE0MvXrzQ2m779u0J+M8rjxIXFxdq2rQptW/fnk6fPk1ExLmusrS0pMaNG5OrqyuFhIRQ//791dq+desWZ7Kg1MZu1qwZtW/fnrNAzZuU2thv3rwhKysrSk9Pp06dOpFcLicAdOPGDZJIJHThwgWytramw4cP06effkq//PILxcTElORX/t4AwZyh+KSkpOQrKE5OTpzTDgBkZ2dHjRo1otWrV5O3t7fGP3AihUnCixcvNArQgAEDyM/Pj7uOjIzkwjyOGDGCbt68ScOHD9fabuPGjSk7O5uIFKbhEomE/vrrL0pNTaVhw4YRoPCx0KhRI84svU2bNvTixQu6ePEiWVlZ8dpT9Qjk7OxMYrGYnJyc6MSJE9S5c+cqr8pT7sJDFViAfHx8qEWLFtz16tWrKTk5mVJSUmjr1q1aBUgqlXIusfIKUF5WrFhBZmZmBIAGDRpEYWFhFBYWRpGRkbxycrmcuxcWFsaNQkp9vcuXL9OwYcOoevXqtG3bNiIi2rt3LxkaGpKVlRX3DnkFKCwsjDPaS0hIoJo1a3L2QBB04QpeAzHG9jLGohljT1XyVjHG3jHGHuam/ir3ljDGAhlj/oyxvgXOISswXbp0wePHj7nrb7/9Fl5eXvj555/x1VdfcfkymYxnQ6Snp4ewsDBUr14dSUlJGg9olSxevBgLFy6EoaEhTp48CQcHBzg6OuKjjz7iyhAREhMT4eLiAgcHBzg4OCAtLU1je9999x2++OILZGVlISMjAz169MDvv//OaRko20pMTERSUhIcHBy4ncLk5GTI5XKkpKRwakxVHV124X4FsB1A3mPqH4mIF/WJMdYUwEgALgBqArjIGGtIRLIS6GuZQkSFCrcoFouxYcMGfPHFF/D09IS+vj5nuvDq1SsMGjSI57+aMYbExESYmJggNjZWzRGJkq+//homJibYtGkTZsyYAT09PTRv3hy3bt3iymRnZ8PKygoymQx6enogImRnZ3OCKZFIuJ2+uXPncrtzSr8NycnJuHLlCtq2bYv4+HhYWFgAUGx4KP0eZGdnc6YObdu21fl7qewUOAIR0TUAujoGGQLgEBFlEdEbAIEA2hWjf+VGTEwMrK2ttd7Pq0Hw22+/4dmzZzA0NERwcDAyMjJw/PhxAEDjxo3x6tUrje2kpaVpFR5A4XD+m2++AWMMn376Kf755x88fPgQzZs355XLq09nbW2NqKgoEBFu376Nrl27QiQSwdPTE/PmzVMzqMsrFGKxGOnp6cjKykJWVha3+6bt/assuszzkMcvHIBVAIKhcC6/F4BFbv525Hopzb3eA+ATLW2+155Jo6Ki8l3/hIeH8/xM57UHGjNmDOe34NmzZ+Tg4MC1reqsUFeUbWnKV/2syakJwHftu2bNGpLL5bR3794CdxSV7atulgAK5/J9+vQR1kBFlDsvAPUBtAIQAUDpYEzTz5LGCT4R7SKiNkTUpiJGma5VqxYXNFjJTz/9hGXLlnHXZ86cQefOnXll0tPTi+QOaufOnRg5ciQvLyIigptuaSMgIAAymQwffvghAGD37t1ITEzEokWLtNYxNjaGTCaDTCbTOtJ06NAB58+fL9xLVEKKJEBEFEVEMiKSA9iN/6ZpYQBUtQsdAIQXr4vvJ5Rn4T9mzBjs3LlT7Q8ubzkjIyO1BX716tURHx+PevXqQV9fn7e+UW3nyJEj3OEmANSoUYMz8pPL5TAwMFB7HmMMIpGI5wvh+++/Vwv8pUp6ejpMTU15GhJ5uX79OmeSUaXRZZiC+hTOXuXzHCjWPYBi8+ARFE4XnaDwSqpXUPvv2zb2mzdvyMTEROu0JiwsjGxtbbnr48ePU3JyMmVlZXFurcRiMRkZGVGHDh3UpnB5SU5OJrlcTg4ODnTnzh2SSqW8++vXr+emUD179iQ/Pz9q2bIlr4xMJiMAlJiYSBKJhOtbYGAgderUif79919e+c2bN5OhoaHau1laWlJycjLFx8eTqakpmZqaklQqVZvCGRsb08mTJ7kzp8oGSjA+0EEopmk5UIwwkwB4A3gCxRroRB6BWgYgCIA/gI906cT7JkBBQUH5rgtsbGx4Dg3Pnz/P1dXkFy4nJ4eio6M1PqtmzZpkZ2dH8fHxFB0dTTk5OTRgwAC6cOECVyYlJYUiIiIoIiKC85lw9+5dat68OVdGKUAymYwnQNbW1iQWi7k1kJLU1FTavHmz2rtZWVlRWloa9wMRERFB9vb2auXOnDlDmZmZJfzNvz+UmACVRapoApQ3aROgbt260YkTJ6hfv35an6WM/KYMb0JEFBoaSqmpqbxyBw4coK+++oqIiB4/fkyOjo5Uo0YN7r5cLqdXr16RXC7nCZAy5RUgIqKkpCTy8vLiytSqVYuCgoIoNTWVy2vQoAEBoKdPn9KrV684wbp9+zZNmDCBTpw4UeTv+X1GVwESlEnz4O/vjyFDhuhcfv/+/Wjfvr3GeyYmJrC2tsbbt295+TKZDG3atAER4c6dO2pbxA4ODjAxMeHl9erVizucrVevHo4ePYoDBw6gW7duABRrG2dnZzDGcOvWLbWt8alTp+Ly5cvctbe3N3r06IENG/47youJicHkyZN59Q4ePAjGGOrXrw9nZ2eeg5Lw8HCN1q5VCUGA8pCRkYGnT59qvX/69GnOUw4ANGnSBNWqVYOHhwdOnDih0zOICPfv3wegcNpx+vRpVKtWLd86tra2CAsLw8KFC2FiYoI2bdqgc+fOGq1dXV1dcerUKZ4Xn1evXnG2QYBCi2LNmjXw8vLihMjCwgLLly8HoDhXOnfuHJYsWaK2MSHwH4IAFZKePXvyfoWV9OjRA02aNOGu3dzcsGjRIjg7O2POnDmYPn16vm0qtRbmz5+PkSNH4sGDB2rlnJyceCo8GRkZ2LlzJ8aOHauxP8rt8rVr16Jp06a8+0+ePEFgYCB69+7NHaIaGhriww8/hIGBAby9vbF3715eJIiJEyciPj4emzZt0mjrVBURBKiQzJ49m1OFWbFiBedet1OnTjzXuI6OjujatStSUlJw5coV7N+/HwsXLkR2djZmz56Nbdu2aWz/gw8+gJubm8bznTp16qB79+7ctUQigZubm9pZEwDMmzePm149ePBAzaXwy5cvcffuXV5efHw8Fi1aBLFYjE8++QSHDx/m3e/YsSMMDAxw//59Nd/bVRVBgFQIDg4u0DHHjh07kJ2dDUBx9mNra8vdO336NK5du4b27dujQYMGOHDgACIjI3Hw4EGIRCJYWVlBKpXC09OT5wJLldGjR2PGjBk6WXoqFTs1OUbctWsXpk+fDgsLCxw+fBjv3r3j3e/UqZPaWk/ZR014eHhg3LhxMDExgYWFhcZRuCoiCJAKwcHB2LlzJ8zMzDBx4kS1+9OmTcv3cDE1NRXp6eno0KED+vfvz9PArlatGvfrPnXqVHzzzTeF6tvTp0/VPOakpqZi7dq1amW9vLyQk5MDKysriEQifPbZZ6hVqxavjJGREczMzHh55ubmvMBgqsTFxXFa2TNmzMCtW7cK9MxaFRAESAOGhoZo105dB1bp2gkAhg4dqvYH+Nlnn3GaAu3atcOQIUNw4cIFAIrT/WPHjkFfXx/btm3DqFGjCtUnHx8f/PLLL9x1SkoKp6yal5s3b2LYsGFYtWoV4uLi0LJlS1SvXh0+Pj6ck0WlN1Jd+fHHH3mbJxs2bBAcKwLCOZCSyMhIXtApTUkmk5G+vj6nTJqXZ8+e0YoVK2jx4sX0+PFjOnXqFK++0rm8XC6ns2fP0tmzZ0kul9OFCxfyPdEPCgqidevWkYeHBxERJSYmcoqg1apV01ovvwBbqvz7778EKCxqledFOTk51Lt3b65eRkYGERGNGjWKQkNDBYM64RyIz82bN7VOX3Tl5MmT0NPTg7m5OXbs2KH1F14ul2P58uXo168f7ty5g4EDB+YbtOvq1auQy+WcompAQIDGKWZeWrVqpXbGlB8JCQlYvXo1AIU5w7lz57h79+/fh1QqxcKFC/M186hqCAKkI87OzggICAARoX79+hoX0YsWLUJOTg5evHgBJycnzJkzB4aGhnB0dIRYLEb9+vUBKM5YlDtgHTt2LNBwb+LEiVi8eDEAxVRQde0hl8s1CmpgYCC2b9/O2+TIS1JSEsLD/9P1tbe356acRMSzYXJzc0NqaioGDBiAf//9l+cyqyojbKXoAGMM/v7+nLXn/fv3NYYaSUpKQmpqKvbt28flubi4YOPGjRg7dizu3bvHK1+jRg3On5yu3Lx5E8OHD+eu09LS0LNnT9y9exc1atTg8lu3bg1jY2OIRCKIxWKNJtj//PMPzp49y41mMpkMUVFRsLOz45lA5GXs2LEFRtqrKggjEBTmyhkZGcVuZ8mSJfD09ORNm+7fv6/xD5ExhoiICJibm8PMzAyMMaSkpEAm41u/Z2Zmqv3ai0QimJmZwdTUFKampvDz80Pjxo15ZczMzPD06VNERETAxcVFY38//vhjeHp6Qk9PDyYmJggLC+PKisVi3uikytmzZ9GhQwchVhAEAQKg0GcbM2aM1vv6+vqcV06JRKLVyEwsFmP58uVYs2aN2h+XNiO6hIQEJCcnw9LSEq1ateLtbCnXHN999x2vTuvWrZGUlIRnz54hMzMTTk5OnJqO0hdCeHg4bGxseL4R8nLgwAGMGjUKnTt3xs2bN7l8IuLOupQoNSUkEgnatGmDH374Qc09cFVEEKACkEgkSEtL44zVUlJStOqtbd26FTk5OQgJCcGvv/7K+R1o0qQJL0aPNoKCgnijxaRJkziNhbxCEBAQgPbt2yM7O5vTCiAiGBkZITs7G3K5HHK5HE2bNuV5DlJF1S+C8lokEnEGdaplkpOTYW5ujuDgYDRs2FDV3KVqo8tWXWmn8t7G3r17t86mCwXZwKj6LpDL5XTz5k1q0qRJkfoll8s5p4pTp04lIqILFy5wfVE1Z1Ctk9egrmXLllq3sfP6VFDte948JUKMVGEbWydMTEx464+cnJx8/RlMnz4d33//PbZs2YLx48eDMYYOHTrgjz/+gEgkKvT2r6apYs+ePXHnzh0AisjZeXXmVOtERESgb9++ePToES5evIhhw4aptXfixAlujaY6Iqn+K3jgyQddpKy0U3mOQBs2bCCxWMwbZerWrUuhoaFkYmJCcrmc0tPTuYPU/MjOzqacnBz68ccfSSQS0ZAhQ4hIYS0aEBCgU5TuvOTk5NCqVau4EUjZ3tOnT7UepEokEoqNjSW5XM55JpVIJPTHH39w5uIbN24kfX19GjZsGGVlZRWqTw0bNiQfHx/q1atXlR+BCi6gcFsVDb5PhMMAHuamYAAPc/PrAshQubdDl06UpwCtXbtWbZrm5OREMpmMCysvl8spISFBZ3dUmZmZlJCQwLMqVW2vsHh4ePAESOkTISEhgUJDQ8nGxoZXPjExketrUlISNW/eXM1/gaY+EhHFxsZS9erVeS5+LSwsOE2ERo0akUgkIhMTExKLxYIAFVgA6ArgA1UBynN/I4AV9J8AaSyXX3ofBaiorFu3jr7++msiUqxXBg4cSP7+/lScd0xOTuYJX1ZWFkVFRVFUVBTZ2dmRvr5+vvWjo6N5azcPDw+yt7cne3t7mjBhAq9sTEwMIdcpihKRSMQJUM2aNcnHx4fevXtH3bp1EwRIp0JaBAMKP3ChAJzzK1dQKi8BWrduHVlbW/OEp3HjxhQUFERERGlpadS0adNCtRkTE0NRUVFERHTq1CkyNDSknj170vXr16lt27Ya67Ro0YISEhJ0av/GjRvUsGFD6t27N+Xk5NDLly/J39+/UH2Mjo6mBQsW0LBhwygsLIzLDw0Npfr162sVIFdXV7p58yZlZWXRJ598QgcPHqSkpKRCPbuiUFYC1FX1Qbnl0gA8APAvgC66tF9eAjR//nwCQIMHD6Z169YRAJ67KKlUSnfu3NG5vXXr1tGePXu4a6UyqaGhIbVs2VLrGsjIyIjnVCQ/lLtwDRo0yLdct27dKD4+XuO97du3U+3atcna2prmz59PREQBAQG83TpNAuTr68utl54+fVrkKWlFQFcBKu4u3Cgo3F4piQBQh4haA5gL4HfGmMZDE8bYZMaYL2PMVzU8fHlgY2PDsyZVoqenp9GsQRvBwcE8w7V27drhn3/+wZYtW/INxnv8+HGYmZlh3Lhxag5INOHs7Iw9e/YgPj4eH3/8scYyy5Yt45kfqNK7d2/06dMHrVu3xqhRo/DkyRO4u7tzfTQwMMCpU6fU6rm6uuLzzz9Hv379IBaLNaozVTWKLECMMTGAj6HYUAAAkMKpfFzu5/tQ+IdrqKk+vSeufQcOHIgGDRpg8+bNaNy4MaeNXBQ+//xzDB06lLu2sbFBv3798Nlnn2kNVAwAffr0gb6+Pj7++GOd/ijj4uJw/PhxGBkZqbn7VXLo0CFMnDiR81yqip+fH+zt7fHNN9/ggw8+gJ2dHaZNm4bffvsNXl5ekEqlOHDgAFfe29ub00S4evUqzp07x3NQUpUpjjJpLwAviShMmcEYswEQT0Qyxlg9AM5QeCd9b2natCmsra1x7do1dOvWDf379y+4kha0hf3IyMjA27dv83WnC0DjOY0qDx48gKenJ+Lj47F3716YmJhwaj5yuRxz5swBoIim7erqipycHI3mDLVr14aDgwMX39TW1hbdu3fHunXrkJGRAZlMht9++w0WFhbYvHmzWjzXpUuX4tixY/j9998xfvx4uLq65tvvyowuAbYOArgFoBFjLIwxNin31kjwp2+AYk30mDH2CMBRAFOJSNfQKGXKyZMnNfqgLgnu3LnDsxaNj4/Hzz//jOjoaDUT7O+//57TswMUPhdCQ0MBAH///Td3aAoodO2MjY1hb2+PMWPG4Oeff+a1tXXrVmzdupXzlfDFF1+ojWinTp3C5cuXceXKFXz33Xf4448/ACgUVOVyOXbv3g1AsTbeunUrAIU/BFVt7vHjx6N+/fqoVq0aNzJVVQocgYhIo+0xEU3QkHcMwLHid6v0OX78OG7cuMF5tKlbty4GDx5cIm3funULvr6+3HTOwsICo0ePxps3b3Do0CEsXrwYRIQdO3YgLCwMu3fv5k77X716hd69ewNQKJoqddIAoHnz5li+fDlcXFwwadIk3j1Vdu3ahZCQEOzduxfu7u483b3ExET8+eefICJYWFjA19cXI0aMQI0aNTBv3jxs375drb3w8HDlJhHGjRsHc3NzTJkyBadOnco3tlFVoErbAzVv3hz6+vrw9fVFq1atMHfu3FJ5jr29Pby8vJCamsoznrt8+TIOHTqE8ePHIzs7G6dPn8bdu3c5w7sJEyaotdW4cWMsWbIEALBu3ToACjueY8f++92aOXMm9u/fjxkzZqB///48AWrcuDEcHR0hl8vh4ODA2/QwNjbGoEGDcObMGQwbNowTak9PT66M6gj68OFDmJuba9yAqSpUaQEaN24c5HI59uzZgy+++KLE2q1du7ZG+yJTU1Nucc4Yw5EjRwCAyxs5cqTWUSU/pFIpPvvsM/To0QMAcOXKFYwfP15j2atXryIlJQVv377FvXv3eO9ta2uLvXv3wtHRketbfgwcOJBnxFcl0WWvu7RTeZwDrVq1in799Vdau3YtTZo0qcTbj4uLo8DAwBJvl0hxwPv06VPuOisriz744APuWqmN3axZMwoNDVWrHxYWRrNmzaJBgwZxh8ZKEhISqGPHjjr1Q4hQV4W1sVeuXAl3d3eYm5ujNLbRr127Vqwt8fx4/vw5b7tcX1+f87UNKFwA16tXD/v27eNinKqybds2bNmyBVeuXOGmgUrMzMzg7e2N1681b56+ffuWM7arUaMG0tLSqrZ5ty5SVtqpvO2BSpq0tLRCndJHRUUVqOmtyoMHD6h9+/YFtmllZUUA6MGDB7x73333Hdna2nLhUlRR6sLVrFlTY7s1a9akGzducIqpI0eOpG3btunc94oChBGo/Pjll18wb948ncu7uLjg3bt3nOfPgmjVqhVu3ryJlJQUpKamgojUfFXXr18fcXFxGusvX74cUVFR2LBhg8a1mrGxMV6+fKnR/7WJiQnc3Nzg5+cHQOGEskpvZesiZaWdKtsIVBRsbW0pJCREp7IymYyeP3/O2QNlZmbyNLKzs7PJ3NycJBIJSSQSevjwIXcvJyeHpFIpSaVS2rNnD3388ce8tpUjEHJtiDSZcDRt2rRQOoIVEeg4AlXpXbj3iaioKJ3L+vn58bQeDAwMeOscU1NTxMTEcK6HVS1Kp06digYNGkBPTw/Pnz/H0aNHuTMe1XISiQRZWVkarVGfPXsGABrrVTWEKVwFpUGDBlrdTmVmZqJWrVoQiURaNwPmz5+Prl27YujQofDx8UHLli25e8bGxkhLS4NIJOKERBP9+vXDoUOHivciFRxhBKqgBAYGwsHBQeO5UUEjwtKlSxEfH88FBOvSpQsX0MvKygoREREwNDQssA///PMPxo4di/j4+HwDiFVqdJnnlXYS1kB8PvzwQzpz5ozW+zKZjJ48eZKvc3lTU1MKCQlR293Lzs6mjIwMzn+DJn8IqkGGDQwMOD8KSpo3b053794lIsUZVE5OTmFf8b0Hwhqo4nLixIl8RwCRSKST03gDAwO1eEYSiYTbNTtw4ADOnDnDM12Ii4tDixYtEB0dDVtbW0RERKi14ePjwwVBzs9LUVVAWAOVMRkZGXB0dOSu69atq7aVPG7cOFy7di3fdpycnHiHp0Vh6NChanZK5ubmuHv3LszNzbnrvFPC6tWrCxHqchEEqBT5999/1WxpDAwM8M8//3DXZ86cURtNoqOjC4x+IBaLYW9vn2+ZLl26cKYRmjAxMVHzVaenp4datWpBLBZzu20C2hF+RkqR1NRUvHnzhpcnEol4EbPzRs8GgJ07d8LBwaHA9q2srHD+/HmN9y5cuAC5XF4kNaWMjAz07du3wFFwzpw56N+/P2d+USXRZaFU2qmybiJERkbS9evXy7sbhSYnJ4dOnTql8d748eM5BdXbt2/TrFmz6OTJk2XZvTIBgipP+WNnZ6cxBH1xefPmDRYsWFBguRkzZmj0iVAQYrEYAwYM0Hhv0KBBMDMzw6pVq/DTTz/h77//RnBwcKGfUVnQxaS7NmPsCmPsBWPsGWNsVm6+JWPsAmMsIPdfC5U6SxhjgYwxf8ZY39J8gaqI0qlIQTRr1kzrLtmVK1cKdQi6cOFCzJ07Fzdv3kRWVhYaNmyIO3fuwM3NDW5ubjq3U9nQZQSSAphHRE0AdAAwnTHWFMBiAJeIyBnApdxr5N4bCcAFQD8AnowxIRJTGbNhwwbO/FoTvr6+vBioBaH0j7B7924kJCRg9OjRqFu3LnJyctSCglUlChQgIoogIr/czykAXgCoBWAIAGUsw30AhuZ+HgLgEClcXL0BEAhAd+dqAiXCN998g7S0NK33W7RoAXt7e62bEJpYsWIFpk6dyjkq+eijj+Dr68v5gNi1axcuX75c7L5XJAq1BmKM1QXQGsAdAHZEFAEohAyAMpptLSjc/SoJy80TKCHMzc3Rp0+ffMsMGjQo38PWvn37wtnZGT/99FOhnv3DDz9wZtyzZ89G27Zt8ejRI6xfvx7r1q3TGsyrsqKzADHGTKHwuDObiLTHZFf4y86Lmkbi++SZtKLRoEGDAv/wf//99wKdNNaoUQPNmjXT6ZldunSBWCzGrVu3kJ6ezrt39epVREdHY9asWZg9e7ZO7VUadNmqAyABcA7AXJU8fwD2uZ/tAfjnfl4CYIlKuXMAOubXfmXdxq6M1KxZk16+fElEREFBQTRlyhQ6ePBgOfeq5EFJbWMzhR7HHgAviGiTyq0TANxzP7sD+FslfyRjzIAx5gSFd9K7RZZwgTJFJpPp5J8bAFatWoW2bdsWy5trRUeXKVxnAOMA9GCMPcxN/QGsBdCbMRYAoHfuNYjoGYA/ADwHcBbAdCKquts07ynp6ekaTbYTExPRpUsXrfUsLCy4COT79+/HnTt3dHKBVVlhlI/BVFnRpk0b8vX1Le9uVCk2b96MFy9eYOfOnQAUvrUzMjLAGNMa1QFQCJ6hoaGahnZlgzF2n4jaFFSucn8LAlqZPXs2JzyAwky7evXqqFOnTr71nJ2dERAQUNrdqzAIAiQAQOHmODAwsLy7UeF4L6ZwjLEYKCLbxZZ3X0oQa1Su9wEq3zvl9z6ORFSgKvt7IUAAwBjz1WXOWVGobO8DVL53Kon3EaZwAgLFQBAgAYFi8D4J0K7y7kAJU9neB6h871Ts93lv1kACAhWR92kEEhCocJS7ADHG+uVargYyxhaXd3+KCmMsmDH2JFfVyTc3T6vV7vsGY2wvYyyaMfZUJa9CWx1readVjLF3edTSlPcK/066aJyWVgKgByAIQD0A+gAeAWhann0qxrsEA7DOk7cewOLcz4sBrCvvfubT/64APgDwtKD+A2ia+39lAMAp9/9Qr7zfQcd3WgVgvoayRXqn8h6B2gEIJKLXRJQN4BAUFq2VBW1Wu+8dRHQNQHye7AptdazlnbRRpHcqbwGqTNarBOA8Y+w+Y2xybp42q92KQmW1Op7BGHucO8VTTkuL9E7lLUA6Wa9WEDoT0QcAPoLC8UrX8u5QKVKR/9+8ANQH0ApABICNuflFeqfyFqAwALVVrh0AaA56855DROG5/0YD+AuK4T+KMWYPALn/Ft5JW/mirf8V9v+NiKKISEZEcgC78d80rUjvVN4CdA+AM2PMiTGmD4U7rBPl3KdCwxgzYYyZKT8D6APgKbRb7VYUKp3VsfIHIZdhUPw/AUV9p/dgp6Q/gFdQ7HosK+/+FPEd6kGxg/MIwDPlewCwgsJnXkDuv5bl3dd83uEgFFOaHCh+jSfl138Ay3L/z/wBfFTe/S/EO3kDeALgca7Q2BfnnQRNBAGBYlDeUzgBgQqNIEACAsVAECABgWIgCJCAQDEQBEhAoBgIAiQgUAwEARIQKAaCAAkIFIP/A6iHinGtpoaqAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "segmented_image_pixelsList = np.ones(np.shape(pixels_list))*255\n", "\n", "\n", "for k in np.arange(num_clusters):\n", " \n", " if k==1 or k==2 or k==4:\n", " \n", " indices_clusterK = np.argwhere(clusters==k)\n", "\n", " segmented_image_pixelsList[indices_clusterK, :] = np.zeros((3,))\n", "\n", "segmented_image = np.reshape(segmented_image_pixelsList, \\\n", " [np.shape(img_ds)[0], np.shape(img_ds)[1], np.shape(img_ds)[2]])\n", "\n", "plt.imshow(segmented_image.astype(int))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2. hierarchical clustering\n", "\n", "##### Exercise 2.1. Agglomerative clustering\n", "\n", "On the dataset below, implement and apply each of the agglomerative clustering approaches covered during the lectures. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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TAO5S1acrTewPishXVPXbrnH/qqrvj1mWOU+YuOpmt5JJ5mSQzqWZJK4ohN11rFux2HNyHh0rGEvDO5VC2LJEf//1Y1h96aKWRPzEmZ8j2sb6xiLyZQCfUtWvOI69E8DvR1EEq1ev1gMHDrRewA7HHWLmhqWfSVIEPZvtxq+0e9hJPuw4rx1EEhV5ReSgqq52H2+bj0BElgIYAPB1w+l3iMgEgBMoK4XDhs9vArAJAPr7+2OUtHNxr9ZzfRZUyyajqA9ap1dTJOkiasx/3Pitf8MujRXlSf5ExWHshZdZbLJYqvr0ku5z0JYdgYi8CcC/APi4qj7iOvdjAGZV9Ucici2AP1fVy/2uxx1BvJhWb9xNkFaxbHh3pI58dmJZhCrRbSGfy1Y7n/30//oHoyM7a/Vg0YL5oZWf85px4LUjiD18VEQsALsAbHcrAQBQ1R+o6o8qr58AYInIBXHLRbyZC9UUSXqJ6qd683m9WNhnhVYC7Wj/bWWkJmLngZt+tm4y7akcj1IKI6k8nLijhgTA3wF4VlX/zGPMhQC+p6oqIlej/Pv7fpxyEX/mQjVFkg5MJsaoRd/CJE06cV4155Hk1SylGa2LCJrFG7uXvMGc6i6rYcqoTioPJ24fwVoAvwLgkIiMV459BEA/AKjqZwB8EMBvicg0gCKAW7WdHmxSR9RMZ0JMeNXHufmqfHuW7Sh32otLGXx+/zG8cPJHePrY6ep3nFGtaSZl44748TK/JpWH09aooVZBH0G80EdAWsHakT3GBYVXMbm4WNhn4fXSbFsjlhb2WYGJm0kEZCQeNUQ6B+YKkFYQtXFMEFmrB6+XZiM7jE9NlfDQxlWhq/a2glNTpcBeBGnq20FFQIyk6SElnUkzSWQ9KJcisMlaGZxn9XhWvQ1D37zehhRBn9WDqQbu24ry0+2CRecIIbEQtXGMk1mUdwB2Qbibr8o3tZq3d7eNMFWa9Zwo1162yPNznRRcQUVACImFwYF8TYVPu1VkWIqlWfTNy6AwWWy4zaqNbeJsFFsx2d8hI4Lb1/Rj+2++A7msZfxMJwVX0DRECIkNp4lx2fDuyJ8/cy6cg7dHgPN6vU04tp9r847xyDLYvF6axQsj19Ud33LDFamKAGoE7ggIIW0hzhXy/F5//8HUuWkAwO1rGi9P49coqpneBmmAOwJCSFswlTBvVdmI10uzvs7pU1MlDH1pAgvmlac8O4Q1bI6BwL8ftylPwN1FLc2KgTsCQkhbMK2cW5VNYE+2fs7p0oxWJ307hFUEsELMguXuaAWMjhUCx5q6l939yKFQn00KJpQRQhLDK+kMADI9gpkQZSiyVgY3X5XH3iMnUZgsxpqwFqYonNd3irugXBiYUEYIiURcma/O6+b6LFg9UlN3yM5iB+Dr3BWUdwLrViyuaUQfZ6XSMCGhnViri4qAEFKHV50goLl6+e7rnpoqwcoIclmr2jdj3YrFVUXhtbp3rq7XjuypKx+haJ3/wUkYh3cn1uqij4AQUkdcpci9mr4vmN+LF0auw9CG5dh1sFC1r5uUgDs002ul3awScGc9hA0JNfkqBGVlunZkTyp9BVQEhJA64jJvBF3XpCiA2kn5PJd312ulnW9iBW5lBLet6W8oJNTpFLdx9jtOo+OYioAQUofX5NqseSPoumFW96emSjWTqWkFbq/eF8xrrMRFaaZ8x33D6/HCyHXYN7w+cqP5oQ3LjdW209jkiYqAEFKH3+Qa53XP9yjX4MY5mXoldAHAuen6JLNMT7k8RFDpi+37jzW1ct/65HOe5qm0OY7pLCaE1BFXKfKg60YpR+ScTE3VcteO7DF2QXvz/F58bHBl9b1X6QtFfQXRKJFUfpN92hzHVASEECNxlSL3u+5khAqjQZOp10R82pVJfL5PdrHzGlEjqbyihwRIXR2idjSvf6+IPCciR0Vk2HBeROSTlfPPiMjb4paJEJJOwq6UTWYqu6zDsuHdWDuyx9PM5LzH6FgBZyp1iILGekVS3bVzonpPpynJK3rotjX9qSs3EasiEJEMgL8E8D4AbwXwIRF5q2vY+wBcXvnZBODTccpECEkvQxuWw8rU24d6UG7/6BXBYyrrcObcNKye2mu5wzi3Pvlc1THsJmyY6oyqsZSEyXfx4MZVNWaptBC3aehqAEdV9XkAEJEvArgRwLcdY24E8LlKw/r9IpITkYtU9ZWYZSOEJIzJ5r5gXm+dqWYWwA+K03hw4yrjatorP2Fhn4W+eb0oTBZrEszsSduvj7Fb2YTpuGY7se3PdUqnv7hNQ3kALzveH68cizoGIrJJRA6IyIGTJ0+2XFBCSHvxKs7mZa+fUfWMwfdarU9OlbBveL2xwF2xNOMZMZTPZesm8LAd19IWERSGuBWB6bfs/vcIMwaquk1VV6vq6sWLvcvBEkI6Ay+bu18nM68Y/EbzE2ZUQ4fJhu24lraIoDDErQiOA7jE8f5iACcaGEMImWNEmZyDPheUn+CXfRylqczgQL6aZPaJW66MJdciCeL2EXwTwOUisgxAAcCtAH7ZNeYxAB+u+A/eDuA0/QOEzH28bO75iq/grp0TxlpDpkk9KD/B1BTHnrQbtePHlWuRBLEqAlWdFpEPA3gSQAbAZ1X1sIjcUTn/GQBPALgWwFEAUwB+PU6ZCCHpIGhyBhCpF7DfhB5nglwnTvxu2JiGEJIYQZm6cfVE6Fa8GtNQERBCSJfgpQhYdI4QQrocKgJCCOlyqAgIIaTLoSIghJAuh4qAEEK6HCoCQgjpcqgICCGky6EiIISQLoeKgBBCuhz2LCaEdC0sYVGGioAQ0pVEbUY/l6FpiBDSlXg1xjE1vpnrcEdACJlzhDH5eDXG6cRWk83CHQEhZE7h1QvZ3es4qL1lN0FFQAiZU4Q1+QS1t+wmaBoihCROK6N3wpp85lKryWaJTRGIyFYA1wM4B+C7AH5dVScN414E8EMAMwCmTU0TCCFzl7DRO2GVhVcv5DC9ju1dQ7cpgzhNQ18B8DOq+rMA/h3A3T5j16nqKioBQroPL1POXTsnqnb9sHZ/IJrJJ8p15zKxKQJVfUpVpytv9wO4OK57EUI6Fy9TzoxqdVKOEuo5OJDHAzetRD6XhQDI57J44KaVxlU+Q0jLtMtH8BsAdnicUwBPiYgC+GtV3WYaJCKbAGwCgP7+/liEJIS0Hy9TDlCelDfvGPf8rJcSGRzIhzLvMIS0TFM7AhH5qoh8y/Bzo2PMPQCmAWz3uMxaVX0bgPcB+B0R+S+mQaq6TVVXq+rqxYsXNyM2ISRFmEw5YWk21JMhpGWa2hGo6rv9zovIrwF4P4B3qap6XONE5f+visijAK4G8LVm5CKEtJ9GI3/sMXftnMCMeZow0opQz6ENy2sc1UB5dfzK6SKWDu9GRgQfevsl+Njgyqbuk3bijBp6L4A/APCLqjrlMWYBgB5V/WHl9TUA/jAumQgh8RC1bo9JaXzilivrJmUTAjQc6mnftzBZREYEM6pY2Gdhfm8PThdLOM/qQbE0WzZYo+yn+Pz+YwAwp5WBeCzUm7+wyFEA8wF8v3Jov6reISJLAPytql4rIj8B4NHK+V4Af6+qHw+69urVq/XAgQOxyE0ICYdzMu+pTKpu8rks9g2vr/uce8LPWhk8cFN5orUnahOm6wXJdn7WgghwaqoEQXWOr8G+v9euJCOC7z5wbeB9046IHDRFZ8a2I1DVn/Q4fgLAtZXXzwO4Mi4ZCCHx4J7MvUw6JqerV6TO5h3jyOeyWLdiMXZ882WUZmqvafVIjSnIvatYt2Ixdj/zCk5NlWo+N1l8473XsteOFPL6HlFMVmFJUwlsZhYTQiJjmsxNmJyufhE5hckitu8/Zpyw33Reb3WiNJmibBNOo5xwmIvcZESaurabtJXAZq0hQkhkwoRXejlzgyJyvNbek5WV/uhYAXftnAiliKKwJJfFh95+ifGc1/FGSVv+AhUBISQyXpN5RiQwiavRcNEluWx1Jd1qU42ttD42uBK3r+mv7gAyIrh9TX/LHcVpy1+gaYgQEhlT2KXtcA0ybTjr+3g5hd3YE3VYk1QYbDNQvmKfP/DSa1VncVwKwCZKPaR2wB0BISQyfmUcRscKWDuyB8uGd2PtyB5j3Z7BgTyGNiyH1RNse1/YZ1Wv3ciK2TLMclkrg0/cciUe2rgKALB5xzg+v/9Ydadhh43eO3oo8v3CkLYS2LGFj8YJw0cJaQ2tjlzxCw11X3ftyJ5QOwJ7xR5lB2Ejlf+YpjkRoFcEpVnvOTDOsNEkoobaHj5KCEk3cUSu+DlBw7aKdFOYLGLoSxN14aRh0Op/DOcUKAUshJ2+iFZP3GHrIbUDmoYI6VLiiFyJ4gSNYg9vRAm0AttpPNfLVXNHQEiX4jdpN7r69XOCmhLAdnzjZV/TTNLYYaNRdjqdCH0EhHQJ7on4zNnpmqxbm1zWwtnp2VB2ftPkvutgoe6zN1+Vrztu9QhmAcy0SBFYGcH0jHrmIUTBXWxu2fBuz+s2U/uo3dBHQEgXY/IHWBmB1VPrLM1aGYgg1OrXdM1dBwu4+ao89h45WbObMK2oW70T2PrBcrWaMIXrTCyYl8HHP2AOfz0/axmVJoAaUxHQmW0uqQgI6QKME/FMufJm37zemkn7To9GMG5Tkpe5ZO+Rk3WF4byu2SryuWx1Aj7w0mueZSr8OHOuXO/IboSTd6zyw1SY6GRTERUBIV2Alz9gcqqEsY9eU3PMK0zT7dyN6hiOGvoZFgFq4u/3HjnZEvOQc5U/OWXeDbjp1M5mjBoipAuI0okrbLJTs9dsFYpac0wrJ+NiaQZ37ZwIrVg6tbMZFQEhXUCUTNawzd8bvWarWdhnAUA1o7nV4S9h6xolmRncLIwaIqRLiCOT1RQ15HYUu+/hF4HTCLmshS03XNGwk7hVxFmbqFV4RQ1RERBCWkLY8hJhS0tEwauPQDvJZS2M33dN8MAE8VIEsZmGRGSLiBREZLzyYyzYISLvFZHnROSoiAzHJQ8hJJgwBeO8CJupHIe/IGklAMAzvLQTiDtq6EFV/VOvkyKSAfCXAN4D4DiAb4rIY6r67ZjlIoS4aLb2UNgoImcZapNJKddn4WxpBlOl2Wa+DolA0uGjVwM4WuldDBH5IoAbAVARENJmmi2jEKXGfpiCa0uHdwfeM03YTutOJO6ooQ+LyDMi8lkRWWg4nwfwsuP98cqxOkRkk4gcEJEDJ0+ejENWQrqaZrtmtarGvm2e6iSsjOC+669IWoyGaWpHICJfBXCh4dQ9AD4N4I9QDvP9IwCfAPAb7ksYPms09qnqNgDbgLKzuEGRCSEeRCkYZ4oGMpl8okYmjY4V8Hs7x9Gq6hMC7x7IYcl7/F4yIphV7Zg6Q340pQhU9d1hxonI3wD4P4ZTxwE4u0JfDOBEMzIRQhrDq/3kuhWLQ/sOmq2x/5FHnmmZEgCABzeuqiqmRi67sM8y/l4A4Meyvbjv+ivq6i+1u9lMK4gzaugix9sPAPiWYdg3AVwuIstEZB6AWwE8FpdMhBBvvBLJ9h452fK+BW5sc1AYB/HayxbhoY2rApPT7PpD+4bX44WR6yIns9nmHvv3ksvW+gBOTZVqehJ0cs+COH0EfyIih0TkGQDrANwJACKyRESeAABVnQbwYQBPAngWwE5VPRyjTIQQH5wT577h9b59gltVysE5gYbh6WOnAQD7htfjxZHr8NDGVaF8EyYfhm2bzueyuH1Nf43Dd8G8NwwmgwN5LJhfb0BxKsQ4Gv20i9iihlT1VzyOnwBwreP9EwCeiEsOQkhzRIkGagTTBOqHO5IprG8iaNzoWAG7Dr6xep8slmpMYEEKMW6FGSdJh48SQlKOl++gkWgg0yTcyERpyk0IY4v3GxcUPhukEONWmHHConOEEF/CFqHzw89+3shEGfSZRjKkg1b0QeGxrQqfTQLuCAghgTQbDeS12t7y2GFjwTi/sM+gyXV0rIChhyeqHdAKk0UMPTxR/R5eBK3og0xLrQifTQoWnSOExI5fxdGHNq4CUF9ywt3jGHij0ujgQL5qaipMFqtF5/K5LF47cxZFQ/RRUFG4sEXzOhn2LCYk5XRqDHoY/DqUbX3yuWqEkpPVly7ydew6J2276Jxf5FFQUbhOXtE3CxUBISmg2YJvaWdow/JqL2A3Xrb5qI7dVhDFBDaXFDedxYSkgE6OQQ/D4EDesyhbI87iRiKN+qz66a7RstudnDxmgoqAkBSQ9hj0ZvoU2Nx3/RUti6ppRHmUZrVG7mYm87mmuKkICEkBURrBt5tWrX5bEYZq00hzm9KM1kzUzUzmaVfcUaGPgJAU0KqkrThotk+Bk2bDUJ3XsWVzRg0F4Zyom5nMOzl5zAQVASEpIM0RK2ld/bqVSpheyM6JupnJPM2KuxGoCAhJCa1aLbeaTln9epWLtnFP1M1M5mlW3I1ARUAI8aVTVr/uyTnXZ0EVOF0sGSfqZifztCruRmBmMSEkkLkUM9/NMLOYENIwza5+qUjSDRUBISRW5nrW9FyAioB0PGlZbbZCjrR8l1bSyvBTEg+xKQIR2QHA9iblAEyq6irDuBcB/BDADIBpk/2KEC/SsNocHStgy2OHa4qaFSaL2LxjvFpmOYwsafgucZDW8FPyBrFlFqvqRlVdVZn8dwF4xGf4uspYKgESiaRT/e3J26uy5WSxhKEvTXRl2QKbNGdNkzKxm4ZERADcAmB93PcinU0jZpF2rjZN8oWpglmaUdz/+OFUfZd20inhp91MO2oN/QKA76nqdzzOK4CnROSgiGxqgzwkhTRaz8ZrValAw8XRosgXlMlqc2rKvxY+MHdXzq2sMUTioak8AhH5KoALDafuUdUvV8Z8GsBRVf2ExzWWqOoJEXkLgK8A+F1V/Zph3CYAmwCgv7//qpdeeqlhuUn68CoPkM9lsW/YezNp6irlxOoRvOm8XkxOmZOKmpUvbI0bAHhx5Drf893QIYskSyx5BKr67oCb9gK4CcBVPtc4Ufn/qyLyKICrAdQpAlXdBmAbUE4oa0JskkIaNYu4i4+5Kc1qdTUe5MD1M015yRFWCdjX95vQ51rZAtI5xG0aejeAI6p63HRSRBaIyJvt1wCuAfCtmGUiKaQZs8jgQB77htdDQt5rsliqMzuZTD937hjHvaOHQssRxF07g53G9nd5sNLH984d4y01cRFiIm5FcCuALzgPiMgSEXmi8vbHAfybiEwA+AaA3ar6jzHLRFKIqb6826EY1BwlymTtjsYxOX0VwPb9xzA6Vmio/r2bGdVQfo+51v2KpJ9Yo4ZU9b8ajp0AcG3l9fMAroxTBtIZBJlFwsTYr1uxGJ/ffyz0PZ3mHi+nr6K8kp9VxflZq+k+uWESqZiARdoNi86RjsDPWTuriiW5LKbOTYeKzrFZ2Gehb14vTlRW3mEQIHBspkcwM+s9SgC84OM4Xja823iPoM8REgSLzpGOJshZGzaM08mPXo+mOABvJbBgXgZT52aQ67Nw2iO5zGZJLmt0TAPl3YDXPTo9jJSkF/YsJh1BqyfBrNWDks+qPSqziqqD1++yWSuDdSsW1/kANu8Yx+Yd474K7czZafoJSCzQNEQSw29V7PYTBOULpIGgnIJc1oJIuOQyL5hXQJqBpiGSKkzO36EvTQCK6krd5BC2lUSPx6Sby1pYMD+a3b9VBOUUnJ2ebYuzeS5WMCXxQkVAEsEUGVOaqZ9Ii6UZ3P/44ZqJ7cGNq3Dgpdewff+xmsk+a2Ww5YYrAAD3P364qZV3qxFBy3Yzfkl2c7WCKYkXKgKSCFEKqZ2aKtVkBw89PAFIreNWANx8VXmiS5sJqQf+foOo+PlLGHpKGoGKgCTCkly2oUgfAEYnrwLYe+Qk9h452RYlECaM1OY8qwdnpzVSOQovgqp2ztUKpiReGDVEEsGUqWtlBFZP2EIR9ZyYLLZlwlt72aJI/oep0mygEshlLQCoK5NhZaTsZEa4qp1ztYIpiRfuCEgieGUSu4+dOTvt2fTFTdTxjbL/+VORPxMUUTR+3zUAmnf0svY/aQSGj5JUYwobtXoEkFrnctbK4Oar8tjxzZeNTuc0E1RqOyqMGiJeMHyUpIaoE9V5Vk9VEeSyVjUyyNQtrNOUgKBcI6mVDA7kOfGTSFARkLYSJbzRtBs4Oz1bHesev3nHeIyShyOXtSLlCyiAXQcLWH3pIk7eJDGoCEhbiRLeGGXs6FghUiRP2LEL5mWQ65vnm8TmvKZztxI2KqpYmsHmHeO4//HDuO/6cA1z7HvQ/ENaARUBaStRwhujjN3y2OFIkTw9ARVCbc6cm8HHP1CeZJcN7/Yd+5NvWVAzOeeyViTH9ampUjm7GvAtv/17O8dr8hKYNEaahYqAtBWv/AFTeGPYsaNjhciRQmGUgI09yZ4fMLEfffVMVRk1nCMxo9WGOV67CpPoTBojzcA8AtJWwnQiCzvW7lgWt2/AnmQlIMWhVW5qe4UfVZkwaYw0CncEpK1EadDuNzaOaqQigJcLoJ2TbEakoe/FpDHSKE0pAhH5JQBbAPw0gKtV9YDj3N0A/huAGQD/XVWfNHx+EYAdAJYCeBHALaoaPVuHdBRRwhu9xpocyc2i6u1EtifZRk0+YbEy0lAIrABMGiMN06xp6FsAbgLwNedBEXkryo3rrwDwXgB/JSKmzt/DAP5JVS8H8E+V94QEEtcKXVFf5sE2R7WigX0Qb5rfW3f/IATAbWv66R8gDdPUjkBVnwUAqTee3gjgi6p6FsALInIUwNUA/q9h3Dsrr/83gH8G8AfNyES6g2aK1gWhKGf7epmuovokslYG51k9xrLY7ryDqKWz8wwdJS0gLh9BHsB+x/vjlWNuflxVXwEAVX1FRN7idUER2QRgEwD09/e3UFTSiZhq6gQRNnegmZIPeUeWszvu31QDqJk+Ba0uTUG6l0BFICJfBXCh4dQ9qvplr48ZjjUVVKGq2wBsA8q1hpq5Ful8nI7kMDuDsEogqOSDHdrphb0691qhuxXEnQ1GPLGQHGklgYpAVd/dwHWPA7jE8f5iACcM474nIhdVdgMXAXi1gXuRLsU54Q784VOeZpWgyp9Ogko++Pkm1l7mXybCpCC8FNnCPgt983qrSmPdisXYe+QkM4lJLMRlGnoMwN+LyJ8BWALgcgDf8Bj3awBGKv/32mEQ4sukj209akMYv+QsL9/EgnkZbP/Nd0S6D+BdNtpUaoKQuGgqakhEPiAixwG8A8BuEXkSAFT1MICdAL4N4B8B/I6qzlQ+87ciYpdBHQHwHhH5DoD3VN4TEhm/GPpMUCaYAa+VvylySFAuRbF2ZA/uHT2EtSN7sGx4N9aO7MHoWMH3PoMDeTxw00rkc9nQzWcIaTXsR0DmBKNjBQx9aaIuBt/qEWy8+hLsOliI5JT1c8TaReDC+CayVib0xM4+AiRuvPoRsMQEmRMMDuSx9YNXYmGfVT2Wy1rY+ktX4mODK2tW3bmshQXzvPMBghyxgwN5DG1YHire3zYzBWFnShcmi1C8UWYiaEdBSCvgjoB0HabyFHZUUdi4/LUje0LnMQiAF0auq97btOr3cnYzRJS0EnYoI6SCqTyFrQTCTrpRMpt7RKore1NTngMvveYZ8cRCcqQdUBGQriNKnwMvomQ2z6ji7kcO1bTctCmWZvD5/cd870NI3NBHQLoOr8k1yqTrFT209rJFxiilYmkmcvkI+z6ExA0VAek6ovRE8MIU9vngxlXY/pvvwGyL/G65rMWoIdIWaBoiXUeUnghB14mSdBalsX3WylT7HxMSN1QEpCuJ0hMhKl7ZwvbEftfOCd9s54V9VlOZxcxHIFGhIiCkxYTZcfhVTn29NNvwvU3N7tnYngTBPAJCEiAoO7nR/AGv/AbmIxCAmcWEpIrBgTz2Da/3zE5uNH+gFaGxpPugIiAkQVoRyhrn9Uh3QEVASIK0IpQ1zuuR7oDOYkISpFWhrHFdj3QHdBYTQkiXQGcxIYQQI1QEhBDS5VAREEJIl0NFQAghXQ4VASGEdDkdGTUkIicBvJS0HAAuAPAfSQthgHKFJ40yAZQrCmmUCUinXJeq6mL3wY5UBGlBRA6YQrGShnKFJ40yAZQrCmmUCUivXCZoGiKEkC6HioAQQrocKoLm2Ja0AB5QrvCkUSaAckUhjTIB6ZWrDvoICCGky+GOgBBCuhwqAkII6XKoCBpARH5JRA6LyKyIrHYcf4+IHBSRQ5X/t603oJdMlXN3i8hREXlORDa0SyaDjKtEZL+IjIvIARG5OilZ3IjI71Z+P4dF5E+SlseJiPy+iKiIXJACWbaKyBEReUZEHhWRXMLyvLfy73ZURIaTlMVGRC4Rkb0i8mzlefofScsUiKryJ+IPgJ8GsBzAPwNY7Tg+AGBJ5fXPACikQKa3ApgAMB/AMgDfBZBJ6Pf2FID3VV5fC+Cfk/63rMiyDsBXAcyvvH9L0jI5ZLsEwJMoJ1BekAJ5rgHQW3n9xwD+OEFZMpXn+ScAzKs8529Nwe/oIgBvq7x+M4B/T4Ncfj/cETSAqj6rqs8Zjo+p6onK28MAzhOR+UnKBOBGAF9U1bOq+gKAowCSWokrgB+rvD4fwAmfse3ktwCMqOpZAFDVVxOWx8mDAP4nyr+7xFHVp1R1uvJ2P4CLExTnagBHVfV5VT0H4IsoP++JoqqvqOrTldc/BPAsgFR3BqIiiI+bAYzZk0uC5AG87Hh/HMk9lJsBbBWRlwH8KYC7E5LDzU8B+AUR+bqI/IuI/FzSAgGAiNyA8q5yImlZPPgNAP+Q4P3T9GwbEZGlKFsKvp6wKL6wVaUHIvJVABcaTt2jql8O+OwVKG+br0mBTGI4Ftvq0k9GAO8CcKeq7hKRWwD8HYB3xyVLBLl6ASwEsAbAzwHYKSI/oZW9fYJyfQQtfobCEOY5E5F7AEwD2N5O2Vy09dmOioi8CcAuAJtV9QdJy+MHFYEHqtrQBCUiFwN4FMCvqup3UyDTcZTtzDYXI0aTjJ+MIvI5ALbj7GEAfxuXHG4C5PotAI9UJv5viMgsygXDTiYll4isRNmnMyEiQPnf7WkRuVpV/18SMjlk+zUA7wfwrnYoSx/a+mxHQUQslJXAdlV9JGl5gqBpqIVUIih2A7hbVfclLI7NYwBuFZH5IrIMwOUAvpGQLCcA/GLl9XoA30lIDjejKMsDEfkplB2PiVaNVNVDqvoWVV2qqktRnvTeFrcSCEJE3gvgDwDcoKpTScoC4JsALheRZSIyD8CtKD/viSJlzf13AJ5V1T9LWp4wMLO4AUTkAwD+AsBiAJMAxlV1g4jci7Ld2znBXdMO56OXTJVz96Bsz51GeZuaiF1XRP4zgD9HeSf6OoDfVtWDScjipDKJfBbAKgDnAPy+qu5JVCgXIvIiytFgiSooETmKcgTa9yuH9qvqHQnKcy2Ah1COIPqsqn48KVlsKs/5vwI4BGC2cvgjqvpEclL5Q0VACCFdDk1DhBDS5VAREEJIl0NFQAghXQ4VASGEdDlUBIQQ0uVQERBCSJdDRUAIIV3O/wc2mgSfH1bZgQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.datasets import make_blobs\n", "import matplotlib.pyplot as plt\n", "\n", "n_samples = 500\n", "random_state = 170\n", "X, y = make_blobs(n_samples=n_samples, centers = 4,random_state=random_state)\n", "\n", "plt.scatter(X[:,1], X[:,0])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "def Agglomerative_Clustering(data, Linkage, numClusters):\n", " \n", " \n", " '''function should implement agglomerative clustering with single linkage, complete linkage and \n", " group average objective'''\n", " \n", " \n", " \n", " \n", " return clusters\n", "\n", "\n", "\n", "def Divisive_Clustering(data, Linkage, numClusters):\n", " \n", " '''function should implement divisive clustering'''\n", " \n", " \n", " \n", " return clusters\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### II.3. Detecting communities on facebook\n", "\n", "__Exercise II.3.1__ Log on to the Stanford Network Analysis Project webpage and load the ['facebook_combined.txt' file ](https://snap.stanford.edu/data/egonets-Facebook.html)\n", "\n", "In this exercise, we will cheat a little. Although K-means is, in general, absolutely not suited to perform community detection, we will use the embedding (i.e the projection) of the graph provided by the 'networkx' module to get 2D coordinates, and we will then use those coordinates as our feature vectors. Use the lines below to load and plot the facebook graph" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import networkx as nx\n", "import matplotlib.pyplot as plt\n", "\n", "g = nx.read_edgelist('facebook.txt', create_using=nx.Graph(), nodetype=int)\n", "print nx.info(g)\n", "\n", "sp = nx.spring_layout(g)\n", "nx.draw_networkx(g, pos=sp, with_labels=False, node_size=35)\n", "# plt.axes('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.3.2.__ How many communities would you guess there are ? Initialize K means (first use the sklearn version) with 7 centroids. " ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }