Data Mining: Practical Machine Learning Tools and Techniques, Second Edition

where f(x;mA,sA) is the normal distribution function for cluster A, that is:

The denominator Pr[x] will disappear: we calculate the numerators for both

Pr[A |x] and Pr[B |x] and normalize them by dividing by their sum. This whole

procedure is just the same as the way numeric attributes are treated in the Naïve

Bayes learning scheme of Section 4.2. And the caveat explained there applies

here too: strictly speaking,f(x;mA,sA) is not the probability Pr[x|A] because

the probability ofxbeing any particular real number is zero, but the normal-

fx e

x

;,ms.

ps

m

( )= s

(-)

1

2

2

22

Pr A

Pr A Pr A

Pr Pr

x x AAA

x

fx p

x

[]=

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264 CHAPTER 6| IMPLEMENTATIONS: REAL MACHINE LEARNING SCHEMES

data

A 51

A 43

B 62

B 64

A 45

A 42

A 46

A 45

A 45

B 62

A 47

A 52

B 64

A 51

B 65

A 48

A 49

A 46

A 48

B 64

A 51

B 63

A 43

B 65

B 66

B 65

A 46

A 51

A 48

B 64

A 42

A 48

A 41

B 64

A 51

A 52

B 62

A 49

A 48

B 62

A 43

A 40

A 39

B 62

B 64

A 52

B 63

B 64

A 48

B 64

A 48

(a)

model

(^304050)
mA = 50, sA = 5, pA = 0.6 mB = 65, sB = 2, pB = 0.4
AB
60 70
(b)
Figure 6.19A two-class mixture model.