陽明大學放射醫(yī)學科學研究所(4)-文庫吧
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【正文】 E 1 ) ( 1 } { y y Q Fixedpoint algorithm using kurtosis wk+1 = wk + ? Note that adding the gradient to wk does not change its direction, since Convergence : |wk+1 , wk|=1 since wk and wk+1 are unit vectors ) ( ? ? wk F wk = ( + ? 1 l 2 ) ) ( ? ? wk F wk 2 3 3 } ] [ { w w z w z Therefore, w ? ? T E w w w / ? wk+1 = wk ?( wk ) l 2 = (1 2? l ) wk Fixedpoint algorithm using kurtosis 1. Centering 2. Whitening 3. Choose m, No. of ICs to estimate. Set counter p ? 1 4. Choose an initial guess of unit norm for wp, eg. randomly. 5. Let 6. Do deflation decorrelation 7. Let wp ? wp/||wp|| 8. If wp has not converged (|wpk+1 , wpk| 1), go to step 5. 9. Set p ? p+1. If p ? m, go back to step 4. ?????1p1jjjTppp )ww(xmxx ~~ ??IzzVxz ?? }{, TE23 3}][{ppTpp E wwzwzw ???Fixedpoint algorithm using negentropy The kurtosis is very sensitive to outliers, which may be erroneous or irrelevant observations Need to find a more robust measure for nongaussianity Approximation of negentropy ex. . with sample size=1000, mean=0, variance=1, contains one value = 10 ? kurtosis at least equal to 104/10003=7 kurtosis : E{x4}3 Fixedpoint algorithm using negentropy 0?Entropy ??? dppH yy )(lo g)()( ???yNegentropy )()()( yyy HHJ g a u s s ??Approximation of negentropy 0?21 ,c os hlog1)( 1111 ??? ayaayG)2/e x p ()( 22 yyG ???4)(43yyG ?yayg 11 ta nh)( ?)2/e x p ()( 22 yyyg ??33 )( yyg ?2) }]({)}({[)( ?GEyGEyJ ??w ? E{zg(wTz)} ? E{g 39。(wTz)} w w ? w/||w|| Fixedpoint algorithm using negentropy 21 ,c o s hlog1)( 1111 ??? ayaayG)2/e x p ()( 22 yyG ???4)(43yyG ?yayg 11 ta nh)( ?)2/e x p ()( 22 yyyg ??33 )( yyg ?)](t a n h1[)( 1211 yaayg ???)2/e x p ()1()( 222 yyyg ????23 3)( yyg ??Convergence : |wk+1 , wk|=1 Max J(y) Fixedpoint algorithm using negentropy 1. Centering 2. Whitening 3. Choose m, No. of ICs to estimate. Set counter p ? 1 4. Choose an initial guess of unit norm for wp, eg. randomly. 5. Let 6. Do deflation decorrelation 7. Let wp ? wp/||wp|| 8. If wp has not converged, go back to step 5. 9. Set p ? p+1. If p ? m, go back to step 4. ?????1p1jjjTppp )ww(pTpTpp gEgE wzwzwzw )}({)}({ ???xmxx ~~ ??IzzVxz ?? }{, TEImplantations ? Create two uniform sources Implantations ? Create two uniform sources Implantations ? Two mixed observed signals Implantations ? Two mixed observed signals Implantations ? Centering Implantations ? Centering Implantations ? Whitening Implantations ? Whitening Implantations ? Fixedpoint iteration using kurtosis Implantations ? Fixedpoint iteration using kurtosis Implantations ? Fixedpoint iterati
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