{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Machine Learning\n", "# Unsupervised Learning and Clustering" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### [Luis Martí](http://lmarti.com)\n", "#### [Instituto de Computação](http://www.ic.uff)\n", "#### [Universidade Federal Fluminense](http://www.uff.br)\n", "$\\newcommand{\\vec}[1]{\\boldsymbol{#1}}$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "import random, itertools\n", "import numpy as np\n", "import pandas as pd\n", "import scipy\n", "import sklearn\n", "import matplotlib as mpl\n", "import matplotlib.pyplot as plt\n", "import matplotlib.cm as cm\n", "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "plt.rc('text', usetex=True); plt.rc('font', family='serif')\n", "plt.rcParams['text.latex.preamble'] ='\\\\usepackage{libertine}\\n\\\\usepackage[utf8]{inputenc}'\n", "\n", "import seaborn\n", "seaborn.set(style='whitegrid'); seaborn.set_context('talk')\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# fixing a seed for reproducibility, do not do this in real life. \n", "random.seed(a=42)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Unsupervised learning\n", "* A type of machine learning algorithm used to draw inferences from datasets consisting of input data without labeled responses.\n", "* The most common unsupervised learning method is cluster analysis,\n", " * used for exploratory data analysis to find hidden patterns or grouping in data.\n", "* Also usefull for [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction).\n", "* The clusters are modeled using a measure of similarity which is defined upon metrics such as Euclidean or probabilistic distance." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "We are going to present two approaches to unsupervised learning and present some sample applications:\n", "* *Dimensionality reduction* with *principal components analysis* (PCA)\n", "* *Clustering* with the *$k$-means algorithm*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Approaches\n", "\n", "* **Connectivity models**: for example, [hierarchical clustering](https://en.wikipedia.org/wiki/Hierarchical_clustering) builds models based on distance connectivity.\n", "* **Centroid models**: for example, the $k$-means algorithm represents each cluster by a single mean vector.\n", "* **Distribution models**: clusters are modeled using statistical distributions, such as multivariate normal distributions used by the Expectation-maximization algorithm.\n", "* **Density models**: for example, [DBSCAN](https://en.wikipedia.org/wiki/DBSCAN) and [OPTICS](https://en.wikipedia.org/wiki/OPTICS_algorithm) defines clusters as connected dense regions in the data space.\n", "* **Graph-based models**: a clique, that is, a subset of nodes in a graph such that every two nodes in the subset are connected by an edge can be considered as a prototypical form of cluster.\n", " * Relaxations of the complete connectivity requirement (a fraction of the edges can be missing) are known as quasi-cliques, as in the HCS clustering algorithm." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Common clustering algorithms include:\n", "\n", "* *Hierarchical clustering*: builds a multilevel hierarchy of clusters by creating a cluster tree\n", "* *$k$-Means clustering*: partitions data into k distinct clusters based on distance to the centroid of a cluster\n", "* *Gaussian mixture models*: models clusters as a mixture of multivariate normal density components\n", "* *Self-organizing maps*: uses neural networks that learn the topology and distribution of the data\n", "* *Hidden Markov models*: uses observed data to recover the sequence of states" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Cluster analysis or clustering\n", "\n", "* The task of grouping a set of objects in such a way that \n", "* objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters). \n", "* It is a main task of exploratory data mining, and a common technique for statistical data analysis," ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Dimensionality Reduction with Principal Component Analysis\n", "\n", "* Uses an **orthogonal transformation** to convert a set of observations of **possibly correlated variables** into a set of values of **linearly uncorrelated variables** called **principal components**. \n", "* Useful linear dimensionality reduction technique.\n", "\n", "We'll start with our standard set of initial imports:" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "### Flashback\n", "\n", "In linear algebra, an [orthogonal transformation](https://en.wikipedia.org/wiki/Orthogonal_transformation) is a linear transformation $T: V \\rightarrow V$ on a real inner product space $V$, that preserves the inner product. That is, for each pair $u$, $v$ of elements of $V$, we have\n", "$$\n", "\\langle u,v \\rangle = \\langle Tu,Tv \\rangle \\,.\n", "$$\n", "\n", "* Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them. \n", "* Orthogonal transformations map orthonormal bases to orthonormal bases.\n", "* Orthogonal transformations in two- or three-dimensional Euclidean space are stiff rotations, reflections, or combinations of a rotation and a reflection (also known as improper rotations). \n", "* Reflections are transformations that exchange left and right, similar to mirror images. \n", "* The matrices corresponding to proper rotations (without reflection) have determinant +1. \n", "* Transformations with reflection are represented by matrices with determinant −1. \n", "* This allows the concept of rotation and reflection to be generalized to higher dimensions." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Consider a data matrix, $\\vec{X}$, of shape $n\\times p$ such that:\n", "* column-wise zero empirical mean (the sample mean of each column has been shifted to zero), \n", "* each of the $n$ rows represents a different repetition of the experiment, \n", "* and each of the $p$ columns represents a given input feature feature (say, the results from a particular sensor).\n", "\n", "The transformation is defined by a set of $p$-dimensional vectors of weights or loadings\n", "$$\n", "\\vec{w}_{(k)} = (w_1, \\dots, w_p)_{(k)}$$\n", "that map each row vector $\\vec{x}_{(i)}$ of $\\vec{X}$ to a new vector of principal component scores $\\vec{t}_{(i)} = (t_1, \\dots, t_k)_{(i)}$, given by\n", "$$\n", "{t_{k}}_{(i)} = \\vec{x}_{(i)} \\cdot \\vec{w}_{(k)}\n", "$$\n", "such that individual variables of $\\vec{t}$ considered over the data set successively inherit the maximum possible variance from $\\vec{X}$, with each loading vector $\\vec{w}$ constrained to be a unit vector." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## First component\n", "\n", "The first loading vector $\\vec{w}_{(1)}$ has to satisfy\n", "$$\n", "\\vec{w}_{(1)}\n", " = \\underset{\\Vert \\vec{w} \\Vert = 1}{\\operatorname{\\arg\\,max}}\\,\\left\\{ \\sum_i \\left(t_1\\right)^2_{(i)} \\right\\}\n", " = \\underset{\\Vert \\mathbf{w} \\Vert = 1}{\\operatorname{\\arg\\,max}}\\,\\left\\{ \\sum_i \\left(\\vec{x}_{(i)} \\cdot \\vec{w} \\right)^2 \\right\\}\n", "$$\n", "\n", "Rewriting it in matrix form gives\n", "$$\n", "\\vec{w}_{(1)}\n", " = \\underset{\\Vert \\vec{w} \\Vert = 1}{\\operatorname{\\arg\\,max}}\\, \\{ \\Vert \\vec{Xw} \\Vert^2 \\}\n", " = \\underset{\\Vert \\vec{w} \\Vert = 1}{\\operatorname{\\arg\\,max}}\\, \\left\\{ \\vec{w}^\\intercal \\vec{X}^\\intercal \\vec{X w} \\right\\}\n", "$$\n", "\n", "* The quantity to be maximised can be recognised as a Rayleigh quotient.\n", "* A standard result for a symmetric matrix such as $\\vec{X}^\\intercal\\vec{X}$ is that the quotient's maximum possible value is the largest eigenvalue of the matrix.\n", "* This occurs when $\\vec{w}$ is the corresponding eigenvector." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Remaining components\n", "\n", "The $k$th component can be found by subtracting the first $k − 1$ principal components from $\\vec{X}$:\n", "$$\n", "\\hat{\\vec{X}}_{k} = \\vec{X} - \\sum_{s = 1}^{k - 1} \\vec{X} \\vec{w}_{(s)} \\vec{w}_{(s)}^{\\intercal}\n", "$$\n", "and then finding the loading vector which extracts the maximum variance from this new data matrix\n", "$$\n", "\\vec{w}_{(k)} = \\underset{\\Vert \\vec{w} \\Vert = 1}{\\operatorname{arg\\,max}} \\left\\{ \\Vert \\vec{\\hat{X}}_{k} \\vec{w} \\Vert^2 \\right\\} = {\\operatorname{\\arg\\,max}}\\, \\left\\{ \\tfrac{\\vec{w}^\\intercal\\vec{\\hat{X}}_{k}^\\intercal \\mathbf{\\hat{X}}_{k} \\vec{w}}{\\vec{w}^\\intercal\\vec{w}} \\right\\}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Interestingly, this produces the remaining eigenvectors of $\\vec{X}^\\intercal\\vec{X}$, with the maximum values for the quantity in brackets given by their corresponding eigenvalues. \n", "\n", "* the loading vectors are eigenvectors of $\\vec{X}^\\intercal\\vec{X}$.\n", "* The $k$th component of a data vector $\\vec{x}_{(i)}$ can therefore be given as a score $t_{k(i)} = \\vec{x}_{(i)} \\cdot \\vec{w}_{(k)}$ in the transformed co-ordinates,\n", "* or as the corresponding vector in the space of the original variables, $\\left\\{\\vec{x}_{(i)}\\cdot\\vec{w}_{(k)}\\right\\}\\cdot\\vec{w}_{(k)}$, where $\\vec{w}_{(k)}$ is the $k$th eigenvector of $\\vec{X}^\\intercal\\vec{X}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "The full principal components decomposition of X can therefore be given as\n", "\n", "$$\\vec{T} = \\vec{X} \\vec{W}$$\n", "where $\\vec{W}$ is a $p\\times p$ matrix whose columns are the eigenvectors of $\\vec{X}^\\intercal\\vec{X}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Demonstrating PCA\n", "\n", "Principal Component Analysis is a very powerful unsupervised method for *dimensionality reduction* in data." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "It's easiest to visualize by looking at a two-dimensional dataset:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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c3Ot7APoGfJXL5Rvlcvmzcrncmzz8DAN2Fcrl8sfhP356yNslIiI6czKWgeur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