Image classification

import matplotlib.pyplot as plt
import numpy as np
from numpy import array
import math
import Image

rt = lambda x:math.sqrt(x)
arr = lambda x : np.array(x)
def normal_function(mu,sigma):
    mu = np.array([mu])
    return lambda x:np.exp(-np.dot(np.dot((x-mu),np.linalg.inv(sigma)),(x-mu).T)/2.0)/((((2*math.pi)**mu.shape[1])*np.linalg.det(sigma))**.5)

def findClass(nos,classes):
    index = -1
    for i in range(classes.shape[0]):
        if nos < classes[i]:
            index = i
            break
    return index

def BayesClassfier(mu,sigma,prior,n,label):

    label1 = label+'_n'+str(n)
    data_set = np.zeros((n,mu.shape[1]))
    category = np.zeros(data_set.shape[0])
    Iprior = np.zeros(prior.shape)
    Iprior[0] = prior[0]
    for i in range(1,Iprior.shape[0]):
        Iprior[i] = Iprior[i-1] + prior[i]

    for i in range(data_set.shape[0]):
        index = findClass(np.random.rand(1)[0],Iprior)
        data_set[i] =  np.random.multivariate_normal(mu[index],sigma[index],1)
        category[i] = index+1

    train_set = data_set[:(data_set.shape[0]/2),:]
    train_cat = category[:(category.shape[0]/2)]
    test_set = data_set[(data_set.shape[0]/2):,:]
    test_cat = category[(category.shape[0]/2):]

    est_mu = np.zeros(mu.shape)
    est_sigma = np.zeros(sigma.shape)
    category_size = np.zeros(prior.shape)
    est_prior = np.zeros(prior.shape)

    for i in range(train_set.shape[0]):
        index = train_cat[i] - 1
        est_mu[index] = est_mu[index] + train_set[i]
        category_size[index] += 1

    for i in range(category_size.shape[0]):
        est_mu[i] = est_mu[i]/category_size[i]
        est_prior[i] = category_size[i]/train_set.shape[0]

    for i in range(train_set.shape[0]):
        index = train_cat[i]-1
        data = np.array([train_set[i]]) - est_mu[index]
        est_sigma[index] = est_sigma[index] + np.dot(data.T,data)

    for i in range(category_size.shape[0]):
        est_sigma[i] = est_sigma[i]/category_size[i]
    prob = [normal_function(est_mu[i],est_sigma[i]) for i in range(prior.shape[0])]
    misclassification_rate = 0.0
    for i in range(test_set.shape[0]):
        mix_density = np.zeros(prior.shape)
        for j in range(prior.shape[0]):
            mix_density[j] = est_prior[j]*prob[j](test_set[i])

        index = np.argmax(mix_density)+1
        if index != test_cat[i]:
            misclassification_rate += 1


    misclassification_rate /= test_set.shape[0]
    fo = open(label1+'.txt','wb')

    printLine = "misclassification rate of "+label1+" is "+str(misclassification_rate)
    print printLine
    fo.write(printLine+'\n')

    prob_or = [normal_function(mu[i],sigma[i]) for i in range(prior.shape[0])]

    misclassification_rate_or = 0.0
    for i in range(data_set.shape[0]):
        mix_density = np.zeros(prior.shape)
        for j in range(prior.shape[0]):
            mix_density[j] = prior[j]*prob_or[j](data_set[i])
        index = np.argmax(mix_density)+1
        if index != category[i]:
            misclassification_rate_or += 1.0

    misclassification_rate_or /= data_set.shape[0]
    printLine = "misclassification rate of (original) "+label1+" is "+str(misclassification_rate_or)
    print printLine
    fo.write(printLine+'\n\ndata: \n')
    #wr_pol = csv.writer(open('tr_pol.txt','wb'),delimiter=' ')

    imageMatrix = np.zeros((64,64),dtype=np.uint8)
    grayBW  = 255/(prior.shape[0]-1)
    for x in range(imageMatrix.shape[0]):
        ref_x = x*10.0/(imageMatrix.shape[0]-1) -5
        for y in range(imageMatrix.shape[1]):
            ref_y = y*10.0/(imageMatrix.shape[1]-1)-5
            ref_data = np.array([[ref_x,ref_y]])
            mix_density = np.zeros(prior.shape)
            for j in range(prior.shape[0]):
                mix_density[j] = est_prior[j]*prob[j](ref_data)

            index = np.argmax(mix_density)
            imageMatrix[x][y] = math.ceil(grayBW*index)

    image = Image.fromarray(imageMatrix).rotate(90)
    fname = label1+'.png'
    image.save(fname)

    if n == 3000:
        imageMatrix = np.zeros((64,64),dtype=np.uint8)
        grayBW  = 255/(prior.shape[0]-1)
        for x in range(imageMatrix.shape[0]):
            ref_x = x*10.0/(imageMatrix.shape[0]-1) -5
            for y in range(imageMatrix.shape[1]):
                ref_y = y*10.0/(imageMatrix.shape[1]-1)-5
                ref_data = np.array([[ref_x,ref_y]])
                mix_density = np.zeros(prior.shape)
                for j in range(prior.shape[0]):
                    mix_density[j] = prior[j]*prob_or[j](ref_data)

                index = np.argmax(mix_density)
                imageMatrix[x][y] = math.ceil(grayBW*index)

        image = Image.fromarray(imageMatrix).rotate(90)
        fname = label+'_original.png'
        image.save(fname)
    '''
    fig = plt.figure()
    plt.imshow(image)
    fig.suptitle(label)
    plt.gray()
    plt.show()
    '''
#Given Data
mu1 = arr([0,0])
mu2 = arr([0,1])
mu3 = arr([1,0.5])
sigma1 = arr([[1,0],[0,1]])
sigma2 = arr([[2,-1],[-1,2]])
sigma3 = arr([[1,0.5],[0.5,2]])

mu = arr([mu1,mu2])
sigma = arr([sigma1,sigma1])
prior = arr([0.5,0.5])

cases = [[arr([mu1,mu2]),arr([sigma1,sigma1]),arr([0.5,0.5]),'case1'],[arr([mu1,mu2]),arr([sigma1,sigma1]),arr([0.6,0.4]),'case2'],\
    [arr([mu1,mu2]),arr([sigma1,sigma2]),arr([0.6,0.4]),'case3'],[arr([mu1,mu2,mu3]),arr([sigma1,sigma2,sigma3]),arr([0.3,0.4,0.3]),'case4']]
nos = [200,500,1000,3000]

for case in cases:
    for n in nos:
        BayesClassfier(case[0],case[1],case[2],n,case[3])