In the below example I implemented a “Naive Bayes classifier” in python and in the following I used “sklearn” package to solve it again:
and the output is:
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male posterior is: 1.54428667821e-07 female posterior is: 0.999999845571 Then our data must belong to the female class Then our data must belong to the class number: [2] |
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import numpy as np import matplotlib.pyplot as plt #------------------------------------------------------------------------------------------------------------------------------- #Example taken from https://en.wikipedia.org/wiki/Naive_Bayes_classifier#Examples #Sex height(feet) weight(lbs) foot size(inches) #male 6 180 12 #male 5.92 (5'11") 190 11 #male 5.58 (5'7") 170 12 #male 5.92 (5'11") 165 10 #female 5 100 6 #female 5.5 (5'6") 150 8 #female 5.42 (5'5") 130 7 #female 5.75 (5'9") 150 9 def gaussian_pdf_function(mu,sigma,x): pi=np.pi e=np.e denominator=1/((2*pi*sigma**2)**0.5 ) y=denominator * e** (-(x-mu)**2/(2*sigma**2)) return y #Training Data, male height_male=[6, 5.92, 5.58, 5.92] weight_male=[180,190,170,165] foot_size_male=[12,11,12,10] #Training Data, female height_female=[5,5.5,5.42,5.75] weight_female=[100,150,130,150] foot_size_female=[6,8,7,9] #Mean, Var male height_male_variance= np.var(height_male) weight_male_variance= np.var(weight_male) foot_size_male_variance= np.var(foot_size_male) height_male_mean=np.mean(height_male) weight_male_mean=np.mean(weight_male) foot_size_male_mean=np.mean(foot_size_male) #Mean, Var female height_female_variance= np.var(height_female) weight_female_variance= np.var(weight_female) foot_size_female_variance= np.var(foot_size_female) height_female_mean=np.mean(height_female) weight_female_mean=np.mean(weight_female) foot_size_female_mean=np.mean(foot_size_female) #male data ploting x_min_range=4 x_max_range=7 step=0.05 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( height_male_mean ,height_male_variance**(0.5),x) fig = plt.figure() ax1 = fig.add_subplot(231) #ax1.text(1,1,"sssss", fontdict=None, withdash=False) ax1.set_ylabel('height male') ax1.plot(x, y, 'r-') x_min_range=40 x_max_range=220 step=1 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( weight_male_mean ,weight_male_variance**(0.5),x) ax2 = fig.add_subplot(232) ax2.set_ylabel('weight male') ax2.plot(x, y, 'k-') x_min_range=4 x_max_range=20 step=0.1 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( foot_size_male_mean ,foot_size_male_variance**(0.5),x) ax3 = fig.add_subplot(233) ax2.set_ylabel('foot size male') ax3.plot(x, y, 'b-') #female data ploting x_min_range=4 x_max_range=7 step=0.05 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( height_female_mean ,height_female_variance**(0.5),x) ax4 = fig.add_subplot(234) ax4.plot(x, y, 'k-') ax4.set_ylabel('height female') x_min_range=40 x_max_range=220 step=1 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( weight_female_mean ,weight_female_variance**(0.5),x) ax5 = fig.add_subplot(235) ax5.set_ylabel('weight female') ax5.plot(x, y, 'k-') x_min_range=4 x_max_range=20 step=0.1 x=np.arange(x_min_range,x_max_range,step) y=gaussian_pdf_function( foot_size_female_mean ,foot_size_female_variance**(0.5),x) ax6 = fig.add_subplot(236) ax6.set_ylabel('foot size female') ax6.plot(x, y, 'b-') plt.show() #Testing height=6 weight=130 foot_size=8 #Calculating the probabilities P_male=0.5 P_female=0.5 #P(height|male) P_height_male=gaussian_pdf_function(height_male_mean,height_male_variance**(0.5),height) #P(weight|male) P_weight_male=gaussian_pdf_function(weight_male_mean,weight_male_variance**(0.5),weight) #P(foot_size|male) P_foot_size_male=gaussian_pdf_function(foot_size_male_mean,foot_size_male_variance**(0.5),foot_size) #P(height|female) P_height_female=gaussian_pdf_function(height_female_mean,height_female_variance**(0.5),height) #P(weight|female) P_weight_female=gaussian_pdf_function(weight_female_mean,weight_female_variance**(0.5),weight) #P(foot_size|female) P_foot_size_female=gaussian_pdf_function(foot_size_female_mean,foot_size_female_variance**(0.5),foot_size) #evidence=P(male)*P(height|male)*P(weight|male)*P(foot_size|male) + P(female)*P(height|female)*P(weight|female)*P(foot_size|female) evidence=P_male*P_height_male*P_weight_male*P_foot_size_male + P_female*P_height_female*P_weight_female*P_foot_size_female #male posterior: male_posterior=(P_male*P_height_male*P_weight_male*P_foot_size_male)/evidence female_posterior=(P_female*P_height_female*P_weight_female*P_foot_size_female)/evidence print "male posterior is:" print male_posterior print "female posterior is:" print female_posterior print "Then our data must belong to the female class" #Solving problem using sklearn package height_male=[6, 5.92, 5.58, 5.92] weight_male=[180,190,170,165] foot_size_male=[12,11,12,10] #Training Data, female height_female=[5,5.5,5.42,5.75] weight_female=[100,150,130,150] foot_size_female=[6,8,7,9] #our data is expected to be tabular form 8x3 height=np.hstack((height_male,height_female)) weight=np.hstack((weight_male,weight_female)) foot_size=np.hstack((foot_size_male,foot_size_female)) record=zip(height,weight,foot_size) record=np.array(record) class_labels=np.array([1,1,1,1,2,2,2,2]) test_data=np.array([6,130,8]) test_data=test_data.reshape(1, -1) from sklearn.naive_bayes import GaussianNB clf = GaussianNB() clf.fit(record, class_labels) GaussianNB() print "Then our data must belong to the class number:" print clf.predict(test_data) |
