Skip to content

Instantly share code, notes, and snippets.

@gdsosar
Created October 24, 2013 05:16
Show Gist options
  • Save gdsosar/7131738 to your computer and use it in GitHub Desktop.
Save gdsosar/7131738 to your computer and use it in GitHub Desktop.
Assign 2 for Machine Learning Class Bayesian Decision Theory and Graphical Models (Parametric Classification)
{
"metadata": {
"name": "assigment2 - 1"
},
"name": "assigment2 - 1",
"nbformat": 2,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"source": "# Assign 2\n\n## 1. Parametric Classificattion\n\na) Download the dataset from the course website. The dataset is a text \nle with a number of data samples, \none per line. Each line has the following structure\n\n$$x_i,y_i,C_i$$\n\nwhere\n\n$x_i,y_i \\in \\mathbb{R}$ and \n$C_i \\in$ \\{0,1,2\\}"
},
{
"cell_type": "code",
"collapsed": false,
"input": "import pylab as pl\nimport numpy as np\n\ndata = genfromtxt(open('notebooks/assign2_data/data.txt','r'), delimiter=',', dtype='f8')[:,0:2]\nlabels = genfromtxt(open('notebooks/assign2_data/data.txt','r'), delimiter=',', dtype='f8')[:,2]\n\n#plot the dataset\npl.plot(data[0:200,0],data[0:200,1],'ro',label='Class 1')\npl.plot(data[200:400,0],data[200:400,1],'bo',label='Class 2')\npl.plot(data[400:600,0],data[400:600,1],'go',label='Class 3')\npl.legend()\n\n#take data as columns\ndata=data.reshape(600,2)\nlabels=labels.reshape(600,1)+1",
"language": "python",
"outputs": [
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD5CAYAAADhnxSEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niDSAyZqISAOYrImINOD/AazRW5qLqqCeAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"source": "(b) Use a portion of the dataset (80% of the samples) to estimate the parameters of a\nbivariate Gaussian distribution for each class.\n\n###Create the train set corresponding to 80% of data"
},
{
"cell_type": "code",
"collapsed": true,
"input": "import random\ndata_len = len(labels)\n#randoms.sample(range, size) creates a vector with a random of number of elements \n##defined by 'size' with values between the interval defined by 'range'\n\n#in this case create a vector with the 80% of random indices taken from the 100% of the dataset indices\nrand_i= random.sample(xrange(len(labels)),(int(len(labels)*0.8)))\n#and create the train set with these indices\ntrain_data=data[rand_i]\ntrain_labels=labels[rand_i]\n\n#the remain will be used as test\ntest_data= np.delete(data,rand_i,0)\ntest_labels= np.delete(labels,rand_i,0)\n\nfeatures = 2",
"language": "python",
"outputs": [],
"prompt_number": 26
},
{
"cell_type": "markdown",
"source": "###Function createTwoClassSet(label_vector,label)"
},
{
"cell_type": "code",
"collapsed": true,
"input": "#this fuction convert the multiclass data problem in a two-class problem\n#given by 'label'\n\ndef createTwoClassSet(label_vector,label):\n\n new_labels=np.zeros((len(label_vector),1))\n for i in xrange(0,len(new_labels)):\n if (label_vector[i]!=label):\n new_labels[i]=0\n else:\n new_labels[i]=1\n \n return new_labels",
"language": "python",
"outputs": [],
"prompt_number": 27
},
{
"cell_type": "markdown",
"source": "(c) Write the parameters of the discriminant functions for each one of the three classes."
},
{
"cell_type": "markdown",
"source": "###Function parEstimation(train_set,label_set,classes)"
},
{
"cell_type": "code",
"collapsed": true,
"input": "#The following function estimate the parameters for a bayesian classificator\ndef parEstimation(train_set,label_set,classes):\n N=len(labels1)\n \n #P(Ci): prior estimation\n pCi=np.sum(label_set)/N\n \n #mi: mean estimation\n #mi= sum(r(t)*x(t))/sum(r(t) -- where 'r' is the label_set and 'x' the train set\n #mi=|--------------r(t)'-----------|--x(t)------|----sum(r(t))--|\n mi =np.dot( label_set.reshape(1,N) , train_set )/np.sum(label_set)\n \n #Si: covariance matrix estimatoion\n #Si= sum(r(t)*[x(t)-mi]*[x(t)-mi]')/sum(r(t) -- where 'r' is the label_set and 'x' the train set\n Si=np.zeros((classes,classes))\n #the for loop will do the sum over all t\n #the linalg.multiply module do the matrix multiplication between (xt-m)*(xt-m)'\n for t in xrange(0,N):\n #Si= |--r(t)--| |-----------------------(x(t)-m1)'-----------------------|-----(x(t)-m1)-----|\n Si =Si+label_set[t]*np.linalg.linalg.multiply( train_set[t,:].reshape(classes,1)-mi.reshape(classes,1) , train_set[t,:]-mi )\n #and divide by sum(r(t))\n Si=Si/np.sum(label_set)\n \n return (pCi,mi,Si)\n \n ",
"language": "python",
"outputs": [],
"prompt_number": 28
},
{
"cell_type": "markdown",
"source": "###Parameter estimation for class 1 and plot"
},
{
"cell_type": "code",
"collapsed": false,
"input": "\ntrain1=train_data\nlabels1=createTwoClassSet(train_labels,1)\n\npl.plot(data[0:200,0],data[0:200,1],'bo',label='Class 1')\npl.plot(data[200:400,0],data[200:400,1],'wo',label='Class 2')\npl.plot(data[400:600,0],data[400:600,1],'wo',label='Class 3')\npl.legend()\n\npC1,m1,S1 = parEstimation(train1,labels1,2)\n\nprint 'P(C1)=',pC1\nprint 'm1=',m1\nprint 'S1=',S1",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "P(C1)= 0.34375\nm1= [[ 3.80115593 5.0850681 ]]\nS1= [[ 0.64049069 0.57017316]\n [ 0.57017316 1.70043608]]"
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD5CAYAAADhnxSEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkgDLmohIAixrIiIJsKyJiCTAsiYiksB/W6wNEx/0eyUAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"source": "###Parameter estimation for class 2 and plot"
},
{
"cell_type": "code",
"collapsed": false,
"input": "\ntrain2=train_data\nlabels2=createTwoClassSet(train_labels,2)\n\npl.plot(data[0:200,0],data[0:200,1],'wo',label='Class 1')\npl.plot(data[200:400,0],data[200:400,1],'bo',label='Class 2')\npl.plot(data[400:600,0],data[400:600,1],'wo',label='Class 3')\npl.legend()\n\npC2,m2,S2 = parEstimation(train2,labels2,2)\n\nprint 'P(C2)=',pC2\nprint 'm2=',m2\nprint 'S2=',S2",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "P(C2)= 0.34375\nm2= [[ 9.1770428 5.92874719]]\nS2= [[ 1.45936251 -0.80617977]\n [-0.80617977 1.06550933]]"
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD5CAYAAADhnxSEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 30
},
{
"cell_type": "markdown",
"source": "###Parameter estimation for class 3 and plot"
},
{
"cell_type": "code",
"collapsed": false,
"input": "\ntrain3=train_data\nlabels3=createTwoClassSet(train_labels,3)\n\npl.plot(data[0:200,0],data[0:200,1],'wo',label='Class 1')\npl.plot(data[200:400,0],data[200:400,1],'wo',label='Class 2')\npl.plot(data[400:600,0],data[400:600,1],'bo',label='Class 3')\npl.legend()\n\npC3,m3,S3 = parEstimation(train3,labels3,2)\n\nprint 'P(C3)=',pC3\nprint 'm3=',m3\nprint 'S3=',S3",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "P(C3)= 0.3125\nm3= [[ 7.05727169 3.56001065]]\nS3= [[ 1.29937667 0.03468753]\n [ 0.03468753 1.26230882]]"
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD5CAYAAADhnxSEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 31
},
{
"cell_type": "markdown",
"source": "(d) Write a program that calculates the discriminant function for each class, \ntaking into account the possibility of rejection with a cost \"lambda\"\nand cost 1 for misclassi\ncation"
},
{
"cell_type": "markdown",
"source": "###Function discFunction(train_set,pC,m,S)"
},
{
"cell_type": "code",
"collapsed": true,
"input": "#The following function estimates the values for the discriminant function g(x)\n#for the train values based on the estimated PC,m and S\n\n# gi(x)=(-1/2)*log|Si| - (1/2)*(x-mi)*Si\u207b\u00b9*(x-mi)' + log(PCi)\n\ndef discFunction(train_set,pC,m,S):\n gi=zeros(N)\n for t in xrange(0,N):\n #(x-mi) as matrix\n xmi= np.asmatrix(train_set[t,:]-m)\n #(x-mi)' as matrix\n xmit= xmi.T\n #S1 as matrix\n Si=np.asmatrix(S)\n #inv(S1)\n inv_Si=np.linalg.pinv(Si)\n #print (1.0/2)*np.asscalar(xm1*invS1*xm1t)#xm1*invS1*xm1t\n gi[t]= -(1.0/2)*np.log(np.linalg.det(Si)) - (1.0/2)*xmi*inv_Si*xmit + np.log(pC)\n \n return gi",
"language": "python",
"outputs": [],
"prompt_number": 32
},
{
"cell_type": "markdown",
"source": "### Compute the g(x) function with the 3 train sets\n### And set lambda value for misclassification"
},
{
"cell_type": "code",
"collapsed": false,
"input": "\nN=len(labels1)\ng1=discFunction(train_data,pC1,m1,S1)\ng2=discFunction(train_data,pC2,m2,S3)\ng3=discFunction(train_data,pC3,m3,S3)\n\n#Have seen before that g(x) function takes values around (-inf,-1)\n#so lets define a lambda that takes vales between that interval\n# replace the value of lambda in the logaritm argument of following expression\n\nlamda=np.log(0.3)-1",
"language": "python",
"outputs": [],
"prompt_number": 33
},
{
"cell_type": "markdown",
"source": "(e) Draw a plot where the regions corresponding to the di\nerent classes, including the rejection 'class',\nare shown with di\nfferent colors. A region corresponding to a class is the set\nof points where the particular class discriminant function is maximum (decision regions,\n[Alp10] Sect. 3.4)"
},
{
"cell_type": "markdown",
"source": "###Plot the results on train set"
},
{
"cell_type": "code",
"collapsed": false,
"input": "pl.plot(train1[:,0],train1[:,1],'wo',label='misclasification')\npl.legend()\nfor t in xrange(0,N):\n if (g1[t]>lamda):\n pl.plot(train1[t,0],train1[t,1],'ro')\n if (g2[t]>lamda):\n pl.plot(train1[t,0],train1[t,1],'bo')\n if (g3[t]>lamda):\n pl.plot(train1[t,0],train1[t,1],'go')\n\nprint \"red=C1, blue=C2, green=C3\"",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "red=C1, blue=C2, green=C3"
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD5CAYAAADhnxSEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"source": "(f) Classify the rest of the dataset that was not used for training, using a classi\ner based on\nthe discriminant functions. Evaluate the results using a confusion matrix"
},
{
"cell_type": "markdown",
"source": "###Plot the results on test set"
},
{
"cell_type": "code",
"collapsed": false,
"input": "pl.plot(test_data[:,0],test_data[:,1],'wo',label='misclasification')\npl.legend()\n\n#find the g(x) values for test_set using estimators computed previoulsy\nN=len(test_labels)\ng1=discFunction(test_data,pC1,m1,S1)\ng2=discFunction(test_data,pC2,m2,S3)\ng3=discFunction(test_data,pC3,m3,S3)\n\n#create the new_test_labels vector for the predicted values on test_set\n#by default the 4 value is misclassification. will be updated in on next\nnew_test_labels=np.zeros((N,1))+4\n\n#and plot the regions. at the same time assign the predicted value to new_test_labels\nfor t in xrange(0,N):\n if (g1[t]>lamda):\n pl.plot(test_data[t,0],test_data[t,1],'ro')\n new_test_labels[t]=1\n if (g2[t]>lamda):\n pl.plot(test_data[t,0],test_data[t,1],'bo')\n new_test_labels[t]=2\n if (g3[t]>lamda):\n pl.plot(test_data[t,0],test_data[t,1],'go')\n new_test_labels[t]=3\n\nprint \"red=C1, blue=C2, green=C3\"",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "red=C1, blue=C2, green=C3\n(120, 1)\n(120, 1)"
},
{
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWsAAAD9CAYAAAB6DlaSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmhBCFOD/Axy16a8MTgQbAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 35
},
{
"cell_type": "markdown",
"source": "###Compute the confusion matrix"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#Now build the confusion matrix\n## will be 3x4 for the 3 classes plus the misclassification column\nconf_matrix=np.zeros((3,4))\n\nfor t in xrange(0,N):\n for i in xrange(0,3):\n if(test_labels[t]==i+1):\n if(new_test_labels[t]==1):\n conf_matrix[i,0]=conf_matrix[i,0]+1\n if(new_test_labels[t]==2):\n conf_matrix[i,1]=conf_matrix[i,1]+1\n if(new_test_labels[t]==3):\n conf_matrix[i,2]=conf_matrix[i,2]+1\n if(new_test_labels[t]==4):\n conf_matrix[i,3]=conf_matrix[i,3]+1\n\nprint \"\"\"\n |C2|C2|C3|mis|\nC1|__|__|__|___|\nC2|__|__|__|___|\nC3|__|__|__|___|\n\"\"\"\nprint conf_matrix",
"language": "python",
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "\n# |C2|C2|C3|mis|\n#C1|__|__|__|___|\n#C2|__|__|__|___|\n#C3|__|__|__|___|\n\n[[ 29. 0. 0. 6.]\n [ 0. 18. 0. 17.]\n [ 1. 1. 29. 19.]]"
}
],
"prompt_number": 36
}
]
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment