Social Media Mining: An Introduction

P1: Sqe Trim: 6.125in×9.25in Top: 0.5in Gutter: 0.75in
CUUS2079-05 CUUS2079-Zafarani 978 1 107 01885 3 January 13, 2014 19:23

118 Data Mining Essentials

Table 5.2. Naive Bayes Classifier (NBC) Toy Dataset

No. Outlook (O) Temperature (T) Humidity (H) Play Golf (PG)

1 sunny hot high N

2 sunny mild high N

3 overcast hot high Y

4 rain mild high Y

5 sunny cool normal Y

6 rain cool normal N

7 overcast cool normal Y

8 sunny mild high?

Example 5.4.Consider the dataset in Table5.2.

We predict the label for instance 8 (i 8 ) using the naive Bayes classifer

and the given dataset. We have

P(PG=Y|i 8 )=

P(i 8 |PG=Y)P(PG=Y)

P(i 8 )

=P(O=Sunny,T=mild,H=high|PG=Y)

×

P(PG=Y)

P(i 8 )

=P(O=Sunny|PG=Y)×P(T=mild|PG=Y)

×P(H=high|PG=Y)×

P(PG=Y)

P(i 8 )

=

1

4

×

1

4

×

2

4

×

4

7

P(i 8 )

=

1

28 P(i 8 )

. (5.22)

Similarly,

P(PG=N|i 8 )=

P(i 8 |PG=N)P(PG=N)

P(i 8 )

=P(O=Sunny,T=mild,H=high|PG=N)

×

P(PG=N)

P(i 8 )

=P(O=Sunny|PG=N)×P(T=mild|PG=N)

×P(H=high|PG=N)×

P(PG=N)

P(i 8 )

=

2

3

×

1

3

×

2

3

×

3

7

P(i 8 )

=

4

63 P(i 8 )

. (5.23)