{ "metadata": { "name": "", "signature": "sha256:f91dd1a830b4abe3feec5c7f523bfd6b7d159bcde85ed316f6abd2fb424457af" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import numpy.random as nr\n", "import matplotlib.pyplot as pl\n", "%matplotlib inline\n", "\n", "# Size matters in plots.\n", "pl.rcParams['figure.figsize'] = (12.0, 10.0)\n", "\n", "# Plotting with style! \n", "import seaborn as sb" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 52 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Playing around with the linear perceptron algorithm \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The linear perceptron algorithm can be used to classify data points according to pre-selected features they have. The idea is to find a curve (or hyperplane) that separates points with different features. Once we have the curve, we can use it to decide if future points are of feature A or B based on where they are with respect to the curve (above or below it). \n", "\n", "Below, I generate a collection of points and then paint them according to a line. If the points are above the line, they are blue, if they are below, green. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Generate some points\n", "N = 100\n", "xn = nr.rand(N,2)\n", "\n", "x = np.linspace(0,1);\n", "\n", "# Pick a line \n", "a = nr.rand();\n", "b = nr.rand();\n", "f = lambda x : a*x + b;\n", "\n", "fig =pl.figure()\n", "figa = pl.gca();\n", "\n", "pl.plot(xn[:,0],xn[:,1],'bo');\n", "pl.plot(x,f(x),'r')\n", "\n", "# Linearly separate the points by the line\n", "yn = np.zeros([N,1]);\n", "\n", "for i in xrange(N):\n", " if(f(xn[i,0])>xn[i,1]):\n", " # Point is below line\n", " yn[i] = 1;\n", " pl.plot(xn[i,0],xn[i,1],'go')\n", " else:\n", " # Point is above line\n", " yn[i] = -1;\n", " \n", " \n", "pl.legend(['Above','Separator','Below'],loc=0)\n", "pl.title('Selected points with their separating line.')\n", "figa.axes.get_xaxis().set_visible(False)\n", "figa.axes.get_yaxis().set_visible(False)\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ooz/Qd7/7A/3wh4/rxInj2r9/nzo62iRJW7Zs1qJFF2r58pVqa4tKkk6dOqUDB/Zp/vz5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\n6jXpGtN4bb0SFy2l0T4AYFyMtGUawar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"text": [ "" ] } ], "prompt_number": 54 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The curve naturally separates the space into two regions, one of green points and one of blue points. Thus, if I am given a new point, I can assign it a color based on where it is with respect to the curve. It is really that simple.\n", "\n", "What is not so simple is to find the curve given the points. However, if the points are linearly separable, i.e. if a line exists that does the job, then I can just move a line around until I get it to the correct position. This is what the linear perceptron algorithm is doing." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def perceptron(xn,yn,MaxIter=1000,w=np.zeros(3)):\n", " '''\n", " A very simple implementation of the perceptron algorithm for two dimensional data.\n", " \n", " Given points (x,y) with x in R^{2} and y in {0,1}, the perceptron learning algorithm searches for the best\n", " line that separates the data points according to the difference classes defined in y. \n", " \n", " Input: \n", " xn : Data points, an Nx2 vector. \n", " yn : Classification of the previous data points, an Nx1 vector. \n", " MaxIter : Maximum number of iterations (optional).\n", " w : Initial vector of parameters (optional).\n", " \n", " Output: \n", " w : Parameters of the best line, y = ax+b, that linearly separates the data. \n", " \n", " Note:\n", " Convergence will be slower than expected, since this implementation picks points\n", " to update without a specific plan (randomly). This is enough for a demonstration, not \n", " so good for actual work. \n", "'''\n", " \n", " N = xn.shape[0];\n", " \n", " # Separating curve\n", " f = lambda x: np.sign(w[0]+w[1]*x[0]+w[2]*x[1]);\n", "\n", " for _ in xrange(MaxIter):\n", " i = nr.randint(N);\n", " if(yn[i] != f(xn[i,:])): # If not classified correctly, adjust the line to account for that point.\n", " w[0] = w[0] + yn[i];\n", " w[1] = w[1] + yn[i]*xn[i,0];\n", " w[2] = w[2] + yn[i]*xn[i,1];\n", " \n", " return w;\n", " \n" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 14 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that I have a (working) implementation, here's a stab at our problem. Let's see how close it gets." ] }, { "cell_type": "code", "collapsed": false, "input": [ "w= perceptron(xn,yn)\n", "\n", "# Using weights w to compute a,b for a line y=a*x+b\n", "bnew = -w[0]/w[2];\n", "anew = -w[1]/w[2];\n", "y = lambda x: anew * x + bnew;\n", "\n", "# Computing the colors for the points\n", "sep_color = (yn+1)/2.0;\n", "\n", "pl.figure();\n", "figa = pl.gca()\n", "\n", "pl.scatter(xn[:,0],xn[:,1],c=sep_color, s=30)\n", "pl.plot(x,y(x),'b--',label='Line from perceptron implementation.')\n", "pl.plot(x,f(x),'r',label='Original line.')\n", "pl.legend()\n", "\n", "pl.title('Comparison between the linear separator and the perceptron approximation.')\n", "\n", "figa.axes.get_xaxis().set_visible(False)\n", "figa.axes.get_yaxis().set_visible(False)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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4LQB79+7h5MmTVYq1Z89eAMTFNSU9PZ3ExC1s2rSeTZs2AJCbm0N+fj7BwUpb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\n0aNHtHz5m7rxxhuUlpamN99cIsmj/PyLnC6txRm1NfKuKZW3uCiyCcr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"text": [ "" ] } ], "prompt_number": 55 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not bad, right? The algorithm should have managed to converge to a good approximation of the separating line. If it didn't, try running the last piece of code again. Remember that this implementation updates randomly picked points, so in some cases convergence will be worse.\n", "\n", "Also, note that the line that separates the points is not unique, given the dataset we have available. Would it be so if we had all of the possible information? My guess is that this depends on the data. \n", "\n", "In any case, it can be proven that this process works every time, given a sufficient number of steps. This assumes that the data is linearly separable, a fact that is quite powerful on its own. We may be good at finding patterns in $\\mathbb{R}^2$ but what about $\\mathbb{R}^d$? Is there a way to show that a collection of points can be separated by \"inserting\" planes between them? We take a look at that next." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# What if the dataset is not linearly separable?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the data is not separable by a line, then, in most cases, this process will not work perfectly. Some points will be classified correctly and some will not. Then, we can think about two more questions. \n", "\n", "1. How much will it cost us if we missclassify a point? Is the cost an extra spam e-mail in our inbox or is it a patient not getting the correct medicine?\n", "2. If we don't want to take the risk with a line, which is the best curve to use instead?\n", "\n", "We are not going to answer those here. Instead, I will just show you an example where the classification can fail, if the points are not separable by a line. Then, if you download this notebook, you can try with other curves and see what happens. \n", "\n", "Remember that, in our case, given a point $x=(x_1,x_2)$, classification is done according to $\\text{sign}(f(x_1)-x_2)$, which can either be -1 or 1." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Change this function to select points with respect to a different curve.\n", "f = lambda x: x**2;\n", "\n", "x = np.linspace(0,1);\n", "\n", "# Generate some data points to play with.\n", "N = 100\n", "xn = nr.rand(N,2)\n", "\n", "fig = pl.figure()\n", "figa = pl.gca();\n", "\n", "# Plot classifier \n", "pl.plot(x,f(x),'r')\n", "\n", "# Classify based on f(x)\n", "yn = np.sign(f(xn[:,0])-xn[:,1])\n", "\n", "colors = (yn+1)/2.0;\n", "\n", "pl.scatter(xn[:,0],xn[:,1],c=colors,s=30);\n", "pl.title('Classification based on f(x)')\n", "\n", "figa.axes.get_xaxis().set_visible(False)\n", "figa.axes.get_yaxis().set_visible(False)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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o33+w1dFERIKOY+sWEvt0x1erDik/rgTdYjfonOkCK5VVkQpu+/Zt7Nmzi2bNWlC3bj2r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\n888UDofNjmVZ7qmTlNi3h2y+bKUPHynvw4+xh2oEuvPOv+m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"text": [ "" ] } ], "prompt_number": 46 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, we can see that $x^2$ colours some points as black and others as white. Let us find a linear separator now." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Try percepton with that data.\n", "w = perceptron(xn,yn,MaxIter=1000)\n", "\n", "# Re-scale the weights to construct a new representation\n", "bnew = -w[0]/w[2];\n", "anew = -w[1]/w[2];\n", "y = lambda x: anew * x + bnew;\n", "\n", "figa = pl.gca()\n", "pl.scatter(xn[:,0],xn[:,1],c=colors,s=50);\n", "pl.title('Classification based on f(x)')\n", "\n", "pl.plot(x,f(x),'r',label='Separating curve.')\n", "pl.plot(x,y(x),'b--',label = 'Curve from perceptron algorithm.')\n", "\n", "pl.legend()\n", "\n", "figa.axes.get_xaxis().set_visible(False)\n", "figa.axes.get_yaxis().set_visible(False)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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XCgxRkAtjKWwcCMDx46mFbxQRERHx4ciRwzz33JN8+unnRX7uX35ZR82atalSpSpvvfVP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\ntPqY0+lkxozpjBs3kvHjRzF37mzcbrfasYQIODINQIgA1a7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cd7hFLbzzeDx89tknxMVt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\nO1716hWId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"text": [ "" ] } ], "prompt_number": 45 }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this case, our classifier cannot get all the cases right (white points should be above the blue line, black points below). This situation will probably become worse as we add more and more points. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#This notebook is a work in progress\n", "\n", "More details to be added soon(-ish). " ] } ], "metadata": {} } ] }