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@nipunbatra
Created March 6, 2013 08:29
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{
"metadata": {
"name": "SVM"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For SVM based classification the margin is given by 2/||w||. For the given problem, the weight vector, W is: [1,2,2]. Thus, the margin is given by:"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"margin=2.0/(math.sqrt(1+2*2+2*2))\n",
"margin"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 3,
"text": [
"0.6666666666666666"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we plot the separating plane in a 3 dimensional space."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib as mpl\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"mpl.rcParams['legend.fontsize'] = 10\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"z = np.linspace(-5, 5, 1000)\n",
"y=np.linspace(-5,5,1000)\n",
"x=-3-2*y-2*z\n",
"ax.plot(x, y, z, label='Margin Plane')\n",
"ax.legend()\n",
"plt.show()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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XLxzHSVMsuWAYuVisfPJnq+8ubVHp9XqTPjvSaSVfbEznl0rMgYhheqr0RLNm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\n/w+XxICzW9eq0QAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we plot the locus of all the points which lie on the margin plane. The margin plane would consist of all such points which are at a distance of \"margin\" away from the separating plane. The locus of such points is given by:\n",
"$$L(x,y,z)=\\frac{|x+2y+2z+3|}{\\sqrt{1*1+2*2+2*2}}=\\frac{margin}{2}=\\frac{1}{\\sqrt{1*1+2*2+2*2}}$$\n",
"Thus,\n",
"$$|x+2y+2z+3|=1$$\n",
"or the solutions are:\n",
"$$ x+2y+2z=-4$$\n",
"and\n",
"$$x+2y+2z=-2$$\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"figsize(15,10)\n",
"x2=-4-2*y-2*z\n",
"x3=-2-2*y-2*z\n",
"import matplotlib.pyplot as plt\n",
"mpl.rcParams['legend.fontsize'] = 10\n",
"fig = plt.figure()\n",
"ax = fig.gca(projection='3d')\n",
"z = np.linspace(-5, 5, 1000)\n",
"y=np.linspace(-5,5,1000)\n",
"x=-3-2*y-2*z\n",
"ax.plot(x, y, z, label='Margin Plane')\n",
"ax.plot(x2, y, z, label='SV Plane 1')\n",
"ax.plot(x3, y, z, label='SV Plane 2')\n",
"ax.legend()\n",
"\n",
"ax.plot([-1],[-1],[-2],'ro',ms=15)\n",
"ax.plot([2],[-2],[-1],'ro',ms=15)\n",
"ax.plot([-2],[-2],[2],'g+',ms=15);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "display_data",
"png": 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tAnw+eJ58Eury5RP+Tie/b+pRWVDc/O/k40CtZaLpgrIsl+6VFTiSRVQ9hiki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16Nj910E+bOnW3Wm1+Sx/b/bzv++0f/O2KS/e+cmNDwv/+34iimAECdmIA8OdmzmGo0Gi1LF9s1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JaW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\nMAUAAAAAASBMAQAAAEAA/g/3uhIOtIEWGQAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We next observe the given points and check if they are lying on support planes or not.\n",
"Point P1 (-1,-1,-2) does not satisfy either of the two SV planes and thus does not lie on the same.\n",
"Point P2 (2,-2,2) and P3(2,-2,-1) lie on SV planes."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next we highlight the similarities between SVM's and Perceptrons.\n",
"\n",
"* Both are discriminative classifiers\n",
"* Both involve class equations of the form: $$y=w.x+b$$"
]
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"The differences between the two are:\n",
"\n",
"* Ignoring multi-layer perceptron, perceptron can be used only for linear classification, whereas with SVM's variety of kernel functions allow non-linear classification.\n",
"* SVM's allow for projection to higher dimensions, which the Perceptron does not allow for.\n",
"* Typical Perceptron implementation would do a search through the possible state space, whereas SVM allow for solutions in the dual space.\n",
"* SVM's focus on maximizing the margin, which is not a case with Perceptron."
]
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