{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Week 7. Convolutional Neural Networks and Clustering (Part I) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this session, we conclude on neural networks (You will finally get use convolutional neural networks for image classification), and we will start working with unsupervised learning models, and in particular clustering. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Supervised Learning (contd)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part I: Convolutional Neural Networks" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### I.1. Playing with convolutions..\n", "\n", "The idea behing convolutional neural nets is to extract high level features from the images in order to become better and better at discriminating them. When we are given two images, one could compare those images pixel-wise, but that could give us a relatively large number even if the images represent the same object. On top of comparing the pixels, one approach could be to average the pixels from, small, local neighborhoods and to compare those averages across the images. Consider the image shown below. \n" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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mXC7z0MOP8PrR13j3+76TOEp1ntpqnWpPGdOwSXQNLYkI/IhKtZTqV9kklckn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\nj9M4jdN4W3E6eZzGaZzG24r/H0dU0bZ5RIKdAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy import fftpack\n", "import matplotlib.pyplot as plt\n", "\n", "img = plt.imread('YannLeCun.jpg')\n", "plt.figure()\n", "plt.imshow(img)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1a. Turn this image into a black and white image by using the lines below__ " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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9Mky5fPmymlzxeBznz59HIpHA6tWrVdzc39+PSCSCr33ta5idncWmTZvg8Xiw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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from skimage import color\n", "from skimage import io\n", "\n", "img = color.rgb2gray(io.imread('YannLeCun.jpg'))\n", "plt.figure()\n", "plt.imshow(img,cmap='gray')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1b__ To understand how filters and convolutions can help us extract information from the image, we will use the following filters and compute their convolution with the image above. Use the function 'ndimage.filters.convolve' to compute the convolution of those filters with the image of Yann LeCun. \n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "from scipy import ndimage\n", "\n", "\n", "Kx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]], np.float32)\n", "Ky = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]], np.float32)\n", " \n", "# put your code here\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "plt.figure()\n", "plt.imshow(Iy,cmap='gray')\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__1c In your opinion, what do those convolutions return ?__\n", "If it is not yet clear, repeat the steps with the image below" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQUAAAD8CAYAAAB+fLH0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nICIRhYKIRBQKIhJRKIhI5P8BKbSbUIvQRtMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from skimage import color\n", "from skimage import io\n", "\n", "img = color.rgb2gray(io.imread('youTubeImage.png'))\n", "plt.figure()\n", "plt.imshow(img,cmap='gray')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And with the square image below" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAD8CAYAAABgtYFHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nMSwkdTEsJHUxLCR1MSwkdTEsJHX5f9ON205DpRctAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from skimage import color\n", "from skimage import io\n", "\n", "img = color.rgb2gray(io.imread('whiteSquare.png'))\n", "plt.figure()\n", "plt.imshow(img,cmap='gray')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the exercises above, you see that one can learn specific features from the images by taking their convolutions with appropriate filters. In this case, we had predefined our filters. Convolutional neural networks generalize this idea by learning the most appropriate filters for a particular classification task. If we want to discriminate between a dog and cat for example, the network will try to learn the best filters such that the convolution of the filter with the dog image is as far as possible from the convolution of the filter with the cat image. In the next exercise, we will use this idea to discriminate between shapes. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### I.4 The structure of a convolutional neural network\n", "\n", "Convolutional neural network are essentially made up of 3 blocks.\n", "\n", "- __Convolutional layers__. Those layers take as input the images from the previous layers and return the convolution of these images \n", "\n", "- __Pooling layers__. Pooling layers are often added to convolutional neural networks to reduce the representation and to improve the robustness. The Pooling step is usually defined by 2 parameters: the filter size and the stride (which indicates by how many pixels you want to move the filter before applying it to return the next value.). \n", "\n", "- __Fully connected layers__ Those are just regular layers similar to the one found in traditional neural networks. \n", "\n", "The two figures below respectively illustrate the convolution and the MaxPool steps. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### I.3. Recognizing shapes. \n", "\n", "Log on to Kaggle and download the 'four-shapes' dataset. Then modify the lines below to load a few images from any two shapes." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(200, 200)\n", "(100, 40000)\n" ] } ], "source": [ "# put the code here\n", "\n", "import numpy as np\n", "from PIL import Image\n", "import imageio\n", "import glob\n", "import cv2\n", "\n", "# checking the size of the images\n", "im = cv2.imread('/Users/acosse/Desktop/Teaching/MachineLearning2019Fall/ConvNets/four-shapes/shapes/circle/0.png')\n", "# converting to RGB\n", "r, g, b = im[:,:,0], im[:,:,1], im[:,:,2]\n", "gray = 0.2989 * r + 0.5870 * g + 0.1140 * b\n", "sz = np.shape(gray)\n", "num_circles = 100\n", "circle_images = np.zeros((num_circles,np.prod(sz)))\n" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# loading a few circles\n", "\n", "for filename in glob.glob('/Users/acosse/Desktop/Teaching/MachineLearning2019Fall/ConvNets/four-shapes/shapes/circle/*.png'): #assuming gif\n", " \n", " if iter_circles ACTIVATION => POOL' layers and then conclude with a fully connected layer and the ouptut layer. (Check for example the LeNet architecture below)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"\n" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from keras.models import Sequential\n", "from keras.layers import Dense, Conv2D, Flatten\n", "\n", "\n", "# put your code here " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Unsupervised Learning" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part II (Clustering).\n", "### II.1. Market Basket analysis and the A priori algorithm\n", "\n", "One of the most basic clustering algorithm, market basket 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": { "collapsed": true }, "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 ($2^{num items}$) 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": { "collapsed": true }, "outputs": [], "source": [ "# put the code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "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", "### II.2. K-means and K-medoid from scratch\n", "\n", "__II.2.1.__ In this exercise, we will code the K-means and K-medoid algorithms. Consider the data shown below. \n", "\n", "- Code your own version of K-means for that particular dataset. \n", "- Modify your algorithm to get a implementation of K-medoid\n", "- Finally, compare the output of your implementation with the scikit learn version of K-means." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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SNaFwvvWljVsqbzfIxIUGcWAlV29jCpz4q2qySng3EVTK6RIUwe7Fyq4scnZt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\nwYICG4MkS7QwA4CQwYEughhwqk8IsSG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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.datasets import make_blobs\n", "\n", "plt.figure(figsize=(12, 12))\n", "\n", "n_samples = 500\n", "random_state = 170\n", "X, y = make_blobs(n_samples=n_samples, random_state=random_state)\n", "\n", "plt.subplot(221)\n", "plt.scatter(X[:, 0], X[:, 1])\n", "plt.title(\"Incorrect Number of Blobs\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__II.2.2.__ Load the Iris dataset, and plot the sample points on the 2D space according to the features 'sepal width' and 'sepal length'. Then apply your K-means algorithm to this 2D dataset. " ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from sklearn import datasets\n", "\n", "# import some data to play with\n", "iris = datasets.load_iris()\n", "X = iris.data[:, :2] # we only take the first two features.\n", "y = iris.target\n", "\n", "x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n", "y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n", "\n", "# Plot the training points\n", "plt.scatter(X[:, 0], X[:, 1])\n", "plt.show()" ] }, { "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": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Name: \n", "Type: Graph\n", "Number of nodes: 4039\n", "Number of edges: 88234\n", "Average degree: 43.6910\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/anaconda2/lib/python2.7/site-packages/networkx/drawing/nx_pylab.py:522: MatplotlibDeprecationWarning: The is_string_like function was deprecated in version 2.1.\n", " if not cb.is_string_like(edge_color) \\\n", "/anaconda2/lib/python2.7/site-packages/networkx/drawing/nx_pylab.py:543: MatplotlibDeprecationWarning: The is_string_like function was deprecated in version 2.1.\n", " if cb.is_string_like(edge_color) or len(edge_color) == 1:\n" ] }, { "data": { "image/png": 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6dGX9gexssvbqRdVC0AEh6qJdtiTpdLr2E8rXUfLz9fWouAMYD+Bn1A4LdpHv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\niCBbq/usk4U7jkF5YpAkiWz+fNtTRI8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" ] }, "metadata": {}, "output_type": "display_data" } ], "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. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.cluster import KMeans\n", "import numpy as np\n", "\n", "# put your code here\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.3.3.__ Try to detect the communities with your own version of K-means. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.cluster import KMeans\n", "import numpy as np\n", "\n", "# put your code here\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.3.4.__ Now instead of using the Fruchterman-Reingold force-directed algorithm as a black box, we will build our own community detection algorithm from scratch by combining K-means with a additional, more reasonable step called spectral clustering. Spectral clustering works as follows (also check out the [tutorial by Ulrike von Luxburg](https://arxiv.org/pdf/0711.0189.pdf))\n", "\n", "- We first want to build an adjacency matrix from list of edges provided in the 'txt' file. The Adjacency matrix is a matrix whose $(i,j)$ entry is defined as $1$ if there is an edge connecting vertex $i$ and $j$ and $0$ otherwise. The diagonal elements are all $0$. Build this matrix below. Then display it as an image. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "\n", "\n", "# put your code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- As a second step, we weight this matrix using the degree of each vertex. Define a diagonal matrix $D$ whose diagonal entries $D_{kk}$ are given by the sums\n", "\n", "$$D_{kk} = \\sum_{i=1}^N W_{ik}$$\n", "\n", "I.e. $D_{kk}$ encodes the degree of the vertex $k$.\n", "\n", "From $D$ and $A$, we can build the Laplacian of the graph. Build this Laplacian matrix below" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- The key idea of spectral clustering is to encode the points in the graph through the eigenvectors of the Laplacian. \n", "Using numpy compute the eigenvalue decomposition of the Laplacian and plot the eigenvalues. What do you notice?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "- To get appropropriate feature vectors that can then be fed to any clustering algorithm such as K-means, Spectral clustering then only retains the smallest $K$ eigenvectors and encode each vertex $i$ through the $K$ tuple $[v_1[i], v_2[i], \\ldots v_K[i]]$ where the $v_i$ are used to denote the eigenvectors. We then apply K-means on those newly defined feature vectors. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# put your code here\n", "\n", "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }