フィッシャーの線形判別ーフィッシャーのアヤメを例にー tokyoscipy

1. NUMPY
- -
gerumanium3_2

2. .....

3. https://gist.github.com/
gerumanium

4. twitter
ID gerumanium3_2

5. numpy

7. (Pattern Recognition)

8. :
:

10. Discriminant Analysis
z
Fisher (FDA)
(discrimination)
(classification)
(LDA)
(QDA)

11. 1. -
2.

12. fisher(1890 1962)

13. 1. W
B
−1
2. X =W B
3. X λ
4. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4

14. x1:
x2:
x3:
x4:
L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4
L ” L ” l1 , l2 , l3 , l4

15. K
W = Sk
L k=1
W T B Sk = (xn − mk )(xn − mk )T
n∈Ck
1
W: mk = xn
Nk
n∈Ck
T: N
B: T = (xn − mn )(xn − m)T
m=1
T =W +B

16. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4
l Bl
Q≡ → max
l Wl
L
l’Bl l’Wl

17. Q L
−1
X=W B
X λ
l1 , l2 , l3 , l4

18. 1. W
B
−1
2. X =W B linalg.inv()
3. X λ
linalg.eig()
4. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4

19. numpy

20. numpy
python
numpy
“iris.txt”

21. >>from numpy import *
>>data=loadtxt("iris.txt")
>>

22. >>>#
>>>Vi=array([data[i] for i in range(0,50)])
>>>#Vi Vi.T transpose(Vi)
>>>Vi=Vi.T
>>>Vi=array([Vi[i] for i in range(1,5)])
>>>
 
x 1
x2 
x = x1 , x2 , x3 , x4 , x5 →x= 
x3 
x4

23. >>#
>>Ve=array([data[i] for i in range(50,100)])
>>Ve=Ve.T
>>Ve=array([Ve[i] for i in range(1,5)])
>>
>>#
>>Se=array([data[i] for i in range(100,150)])
>>Se=Se.T
>>Se=array([Se[i] for i in range(1,5)])
>>

24. >>> #
>>> data=data.T
>>> #(4,150)
>>> data=array([data[i] for i in range(1,5)])
>>>

25. 1. W
B
−1
2. X =W B linalg.inv()
3. X λ
linalg.eig()
4. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4

26. 1. W
B

27. 3
W = Sk
k=1
= (V in − V¯i)(V in − V i)T
¯
n∈V i
+ (V en − V¯e)(V en − V¯e)T
n∈V e
+ ¯ ¯ T
(Sen − Se)(Sen − Se)
n∈Se

28. >W=zeros((4,4))
>#Vi
>m1=array([[mean(i) for i in Vi]])
>m1=m1.T
>W+=dot(Vi-m1,transpose(Vi-m1))
(V in − V¯i)(V in − V i)T
¯
n∈V i

29. #Ve
>m2=array([[mean(i) for i in Ve]])
>m2=m2.T
>W+=dot(Ve-m2,transpose(Ve-m2))
>
(V en − V¯e)(V en − V¯e)T
n∈V e

30. #Se
>m3=array([[mean(i) for i in Se]])
>m3=m3.T
>W+=dot(Se-m3,transpose(Se-m3))
¯ ¯ T
(Sen − Se)(Sen − Se)
n∈Se

31. T
N
T
T = (xn − x)(xn − x)
¯ ¯
n=1
B=T−W

32. >>#
>>M=array([[mean(i) for i in
data]]).T
>>T=dot(data-M,transpose(data-M))
#
>>B=T-W
>>

33. 1. W
B
2. −1 linalg.inv()
X=W B
3. X λ
linalg.eig()
4. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4

34. >># linalg.inv()
>>X=dot(linalg.inv(W),B)
>>

35. 1. W
B
−1
2. X =W B linalg.inv()
3. X λ
linalg.eig()
4. L = l 1 x 1 + l 2 x 2 + l 3 x 3 + l4 x 4

36. >>>#
>>>#la
>>>#v la
>>>la,v = linalg.eig(X)
>>> la
array([3.21919292e
+01,2.85391043e-01,
3.25093377e-15,
3.08736744e-14])
>>>

37. (1)
L = −0.20874182x1
−0.38620369x2
+0.55401172x3
+0.7073504x4

38. L ( L(1) L(x) )
(2) (1)
L = −0.20874182x1 L = −0.20874182x1
−0.38620369x2 −0.38620369x2
+0.55401172x3 +0.55401172x3
+0.7073504x4 +0.7073504x4

40. <http://d.hatena.ne.jp/
gerumanium/> ...

41. R
5 (2009)
(2007)
(2008)