Numpy発表資料 tokyoscipy
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1) The document discusses Fisher's linear discriminant analysis (LDA) and how it can be implemented using NumPy. 2) LDA aims to find the vectors that best discriminate between classes of objects. It calculates a linear combination of features that separates cases into classes. 3) The document provides code to load iris data, calculate the within-class and between-class scatter matrices W and B, and derive the projection matrix X by taking the inverse of W and multiplying it by B. It then computes the eigenvalues and eigenvectors of X.
![>>>#
>>>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](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-22-320.jpg)
![>>#
>>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)])
>>](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-23-320.jpg)
![>>> #
>>> data=data.T
>>> #(4,150)
>>> data=array([data[i] for i in range(1,5)])
>>>](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-24-320.jpg)
![>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](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-28-320.jpg)
![#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](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-29-320.jpg)
![#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](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-30-320.jpg)
![>>#
>>M=array([[mean(i) for i in
data]]).T
>>T=dot(data-M,transpose(data-M))
#
>>B=T-W
>>](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-32-320.jpg)
![>>>#
>>>#la
>>>#v la
>>>la,v = linalg.eig(X)
>>> la
array([3.21919292e
+01,2.85391043e-01,
3.25093377e-15,
3.08736744e-14])
>>>](https://image.slidesharecdn.com/numpy-110827191006-phpapp01/85/Numpy-tokyoscipy-36-320.jpg)
Numpy発表資料 tokyoscipy
- 1. NUMPY - - gerumanium3_2
- 2. .....
- 5. numpy
- 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
- 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
- 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
- 41. R 5 (2009) (2007) (2008)