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分類器 (ナイーブベイズ)

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Satoshi MATSUURA
Satoshi MATSUURA

This document discusses Bayesian probability and its application to text classification. It explains how to calculate the probability P(C|D) that a document D belongs to a class C using Bayes' theorem. Key terms like bag-of-words, term frequency, and maximum likelihood estimation are also introduced. Several examples are provided to illustrate how to classify documents into different topics based on word probabilities.

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- - MATSUURA Satoshi matsuura@is.naist.jp 1
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20% 35% 85% 4
P (C|D) D C P 5
P (C|D) 6
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P (D|C)P (C) P (C|D) = P (D) 8
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P (CD) D C 10
P (CD) = P (C|D)P (D) = P (D|C)P (C) • D C x D P (C|D) P (D) • C D x C P (D|C) P (C) 11
P (D|C)P (C) P (C|D) = P (D) 12
P (D|C)P (C) P (C|D) = P (D) P (D) P (C|D) 13
P (D|C)P (C) P (C|D) = P (D) P (C) C C / 14
P (D|C)P (C) P (C|D) = P (D) P (D|C) C D P (D|C) = 15
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D P (D|C) 17
bag of words 18
ick -k 0 FIFA hat relew nder-2 f ye lo u c Con fed er ar d tric k goal at i on s ke hooligan off ep er nte ring s i d ce e goal 19
P (D|C) = P (W1|C)P (W2|C) · · · P (Wn|C) P (Wi|C) = Wi D W 20
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P (D|C)P (C) P (C|D) = P (D) P (D|C) P (W1 |C)P (W2 |C) · · · P (Wn |C) P (Wi|C) = Wi • ★ ( ) ★ 22
Wa Wb Wc Wx Wy Wa Wy Wx Wc Wb Wb Wa W W W W W W W W bag of words bag of words 23
bag of words 24
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Wa Wz Wy Wb bag of words 26
Wa Wz Wa Wy Wb Wb bag of words Wc Wx Wy 4 P (Cs )P (D|Cs ) P (Wa |Cs )P (Wb |Cs )P (Wy |Cs )P (Wz |Cs ) 7 4 1 2 1 0 = × × × × ) Wz 7 4 4 4 4 =0 27
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Wnew P (Wnew |C) P (Wnew |C) = × popfile Wi P (Wi|C) = Wi α → α× α 30
popfile 31
Wa Wz Wa Wy Wb Wb bag of words Wc Wx Wy 4 P (Cs )P (D|Cs ) P (Wa |Cs )P (Wb |Cs )P (Wy |Cs )P (Wz |Cs ) 7 4 1 2 1 1 = × × × × ) 7 4 4 4 10 × 7 1 = 3920 3 P (Cp )P (D|Cp ) P (Wa |Cp )P (Wb |Cp )P (Wy |Cp )P (Wz |Cp ) 7 3 1 1 1 1 = × × × × ) 7 3 10 × 7 10 × 7 10 × 7 1 P (Cs )P (D|Cs ) P (Cp )P (D|Cp ) = 2401000 32
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DEMO 37
• ( ) • Web+DB vol.56 p.134-142, , May. 2010. • 4.2 • , p.101-117, , Aug, 2010. • ( ) • http://gihyo.jp/dev/serial/01/machine-learning/0003 • • http://d.hatena.ne.jp/kogecoo/20091103/1257281433 • ( ) • http://homepage3.nifty.com/DO/ensyu3_class2.pdf 38

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分類器 (ナイーブベイズ)

  • 1. - - MATSUURA Satoshi [email protected] 1
  • 2. 2
  • 3. 3
  • 4. 20% 35% 85% 4
  • 5. P (C|D) D C P 5
  • 7. 7
  • 8. P (D|C)P (C) P (C|D) = P (D) 8
  • 9. 9
  • 10. P (CD) D C 10
  • 11. P (CD) = P (C|D)P (D) = P (D|C)P (C) • D C x D P (C|D) P (D) • C D x C P (D|C) P (C) 11
  • 12. P (D|C)P (C) P (C|D) = P (D) 12
  • 13. P (D|C)P (C) P (C|D) = P (D) P (D) P (C|D) 13
  • 14. P (D|C)P (C) P (C|D) = P (D) P (C) C C / 14
  • 15. P (D|C)P (C) P (C|D) = P (D) P (D|C) C D P (D|C) = 15
  • 16. 16
  • 17. D P (D|C) 17
  • 19. ick -k 0 FIFA hat relew nder-2 f ye lo u c Con fed er ar d tric k goal at i on s ke hooligan off ep er nte ring s i d ce e goal 19
  • 20. P (D|C) = P (W1|C)P (W2|C) · · · P (Wn|C) P (Wi|C) = Wi D W 20
  • 21. 21
  • 22. P (D|C)P (C) P (C|D) = P (D) P (D|C) P (W1 |C)P (W2 |C) · · · P (Wn |C) P (Wi|C) = Wi • ★ ( ) ★ 22
  • 23. Wa Wb Wc Wx Wy Wa Wy Wx Wc Wb Wb Wa W W W W W W W W bag of words bag of words 23
  • 25. 25
  • 26. Wa Wz Wy Wb bag of words 26
  • 27. Wa Wz Wa Wy Wb Wb bag of words Wc Wx Wy 4 P (Cs )P (D|Cs ) P (Wa |Cs )P (Wb |Cs )P (Wy |Cs )P (Wz |Cs ) 7 4 1 2 1 0 = × × × × ) Wz 7 4 4 4 4 =0 27
  • 28. 28
  • 29. 29
  • 30. Wnew P (Wnew |C) P (Wnew |C) = × popfile Wi P (Wi|C) = Wi α → α× α 30
  • 31. popfile 31
  • 32. Wa Wz Wa Wy Wb Wb bag of words Wc Wx Wy 4 P (Cs )P (D|Cs ) P (Wa |Cs )P (Wb |Cs )P (Wy |Cs )P (Wz |Cs ) 7 4 1 2 1 1 = × × × × ) 7 4 4 4 10 × 7 1 = 3920 3 P (Cp )P (D|Cp ) P (Wa |Cp )P (Wb |Cp )P (Wy |Cp )P (Wz |Cp ) 7 3 1 1 1 1 = × × × × ) 7 3 10 × 7 10 × 7 10 × 7 1 P (Cs )P (D|Cs ) P (Cp )P (D|Cp ) = 2401000 32
  • 33. 33
  • 34. 34
  • 35. 35
  • 36. 36
  • 38. • ( ) • Web+DB vol.56 p.134-142, , May. 2010. • 4.2 • , p.101-117, , Aug, 2010. • ( ) • http://gihyo.jp/dev/serial/01/machine-learning/0003 • • http://d.hatena.ne.jp/kogecoo/20091103/1257281433 • ( ) • http://homepage3.nifty.com/DO/ensyu3_class2.pdf 38

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