1_995505573 - 1 K_L Karhumen-Loeve T x = [ x(1), , x(n)] u...

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Unformatted text preview: 1 K_L Karhumen-Loeve T x = [ x(1), , x(n)] u i , i = 1,2, , x = ci u i i =1 1 u uj = 0 T i i= j i j ^ x = ci u i i =1 2 d ^ ^ = E[( x - x) ( x - x)] T = E[( ci ui ) i = d +1 T j = d +1 c u j j = E[ c ] i = d +1 2 i u x = u c k u k = ci = x u i T i k =1 T i T 3 = E[ u xx ui ] i = d +1 T i T j T = = i = d +1 u E[ xx ]ui i T i = d +1 u u T i 4 g (u i ) = i = d +1 u u T i i - i = d +1 [u i T i u i - 1] g = 2(u j - j u j ) = 0 u j ( - j I )u j = 0, j = d + 1, ,+ u j = j u j 5 u1 , x u1 , ' , ud : K_L , ud xK_L x = [c1 , c 2 , K_L T i , cd ] T E[ci c j ] = E[u xx u j ] = i u u j = i ij T T i 6 u = [u1 , u2 , u u = [u1 , u2 , T T u1 = [u1 , T u D , uD ] , u D ] [u1 , u2 , T , uD ] 0 D K_L 1 2 x u1 , u 2 , i K_L 1 ,uD ] = 0 ,uD D 7 x2 S2 S1 A2 C x1 A1 8 9 K_L-, 10 K_L- SVD 11 x2 S2 S1 A1 C x1 12 x u1 , ' , ud x = [c1 , c 2 , u = [u1 , u2 , T T , cd ] , uD ] T x ui = ci T x u = c = [c1 , c2 ,..., cd , cd +1 ,..., cD ] T -1 x = [c1 , c2 ,..., cd , cd +1 ,..., cD ]u x = u[c1 , c2 ,..., cd , cd +1 ,..., cD ] x = u[0..., ci , 0] " T 13 T Principal Component Analysis ( PCA ) 16 Principal Component Analysis ( PCA ) 17 K_L- 18 19 20 K-L x y xy 21 22 23 24 25 26 27 28 29 30 ...
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