1、 32 5 0 Vol.32No.5 2010 M 5 Journal of Electronics Non-negative Matrix Factorization(NMF); Projected gradient NMF; RBF network 1 + M 4 MYZEbtZE s i OV “ H ? | z MYrTb C L 3 4 | V+ “7“ V 4B “ MYZE dA1b “ MY5 Zhu1Gao2Li34+“ MYZEb ZE m 1 U n5“m vZ_asO q2009-04-28 l 2009-11-05 YT! gt_ Gaborlo roi4 | Z_a
2、 Gabor m GMM(Gabor Magnitude Map) Pg0d sZE4 | m NMF+| m + K RBF * ZE + MYs Yale ORL FERET o LV , “m HZE1.dsZE | MY qb4ZE/+ (1)g0d sr % d s HW5 P MYV L H1 pb (2)“K 44 | =+ 1122 0 32 m 1 GPGNMF m P PGNMFT“7 Y Gabor ro Fa?S K| Gabor ro0m PGNMF+ TK MY+b 2 Y Gabor ro +s 2 Gabor f f ?E VCBY ro O Z_ Vb Mar
3、celja n5 P Gabor ro E j$% l | bW q s ? b Daugman45Bs | bWabW qZ_ “ Gabor ro Br H 1“/f bY Gabor ro s 3 Z $bL ! BY 2222(, ) (, ) (, )(,) (,) (,)(,) (,) (,)eoeeooxy xy xyxy xy fxyxy xy fxy=+= = (1) (, )f xy m (,)exy (, )oxy sY Gabor ro b e P_ Gabor ro b (,) (,)cos(2 (cos sin)(,) (,)sin(2 (cos sin)eoxyf
4、 gxy fx yxyf gxy fx y = += +(2) (, )gxy f b 22221(, ) expxygxy += (3) f bW q bWM bW sY Gabor ro 1 b BY Gabor ro B+bW qZ_b+4 | H | qZ_ m MY A14 ro bW4b ro ql4 | +vbY q4 2 QZb E4 q 2, 4, 8, 16, 32 64 Hzb q4 4M 0o45o90o 135ob“ B 24 GaborroYb Y roT4 | TVY+byN B mY Gabor ro | 48+b 3 g0d s+ 3.1 NMF d s (N
5、on-negative Matrix Factorization NMF) Lee Seung 1999 M45bLee6 Gabriele7sY P NMFm+4 |V rT.d Eb d s VlB mn d nmVVs d nmW nmH1“ / T U nm nr rm=VWH(4) W H Vd s nrW rmH“ b V| V i V U ii=vWh5 iv5 W LF“ H b 3.2 IPGNMF | ro F(),()(, )Fi jexy (),()(,)Fi joxy 1, 2, 3, 4, 5, 6i = 1, 2, 3, 4j = (, )f xy“d roK V
6、BF rom(),()(, )Fi jxyeA (),()(,)Fi jxyoA b (),() (),()(,) abs(,) (,)Fi j Fi jexy fxy xy= eA (5) (),() (),()(,) abs(,) (,)Fi j Fi joxy fxy xy= oA (6) ZL4 |+| BF romZ 7B_ (, )ijoA (, )ijeA K Vm + Ab (1, 1), (1, 2), , (6, 4), (1, 1),(1,2), , (6,4)=ee e oooAA A A AAA“ (7) (, )ijeA (),()(, )Fi jxyeA _ (,
7、 )ijoA (),()(,)Fi jxyoA _ b Ac (, )f xy 1 (c 6 Z_ 4 )b 5 ! g0d s “+4 | 1123 NMF E HW E98 ?9yNA dKb y ?5 NMFZE4 E ?11bg0 (Projected GradientPG)ZEYVv NMF HWb PGNMFZEY il a ras 4 6# HWhv+8bLin84 Bg09 ZEvvh b E X / 221min ( ) ( ( ) )2s.t. 0, ,ij ijFHijbjfbj= = HVWH VWHH(8) 22TTT1min ( ) = ( ( ) )2s.t. 0
8、, ,ji jiW Fijibfib WVHW VWHW(9) T (8) T H T Pg0j()PfHH H -TH jH bg0()Pxl() max(,0)Px x= | x0WKvb g0 _ g0EK HsEnD 8b j()PfHH H 1 HW()Onmrb t H * HW5()Otnmrb Q HW|Hq ! jj jT(1 ) ( ),1,( )( ) 0 (10)2f+ HH HHHWWHHT (10)9 1jT()( )WW H H HW2()Omr b 4 s MY RBF * B ? z -_ * bX / Oi Kl5b RBF zw ?7 O9 91 B E
9、yb_f L bm 2_f mb 5 L !# T 5.1 L o Er ORL oaYALE o FERET o kb m 2 RBFm L MATLAB 7.0 CPUP4 3.6 G =i 512 Mb 5.2 “ MY qY “ MY qYORL o P.d PCA E ksY | “ 8 7 GQh“ k“ “ 10bV kTV A MY q “ “ “h t “v 4 H MY q 90% “ “ 3/ H MY qh “ H MY q 50%1K MYqr 40% Br“ MYE dA1b 5.3 qM MYTY L1 Gabor ro q! MY qY Gabor ro F !
10、 f bW q M k ! f V | 2F (2,4)4 F (2,4,8,16),6 F (2,4,8,16,32,64),8 F (2,4,8,16,32, 64,128,256)sYS U2468,FFFF V | 2F (0, ) 4 F (0, /4, /2,3 /4),6 F (0, /6, /3, /2,2 /3,5 /6),8 F (0, /8, /4,3 /8, /2,5 /8,3 /4,7 /8),sYS U2468, 16FS U22 24 88,FF F “ b k o4 FERET o o4 50 | 2 mT “ 6 mT kb LT m 3 U Gabor sO
11、 q qM |Fb YV kT V A f | 6 F | 4 F H MY qK qMs ?4 q + +V%J % VCD W Vsb 5.4 1+4 | HW L n5 L1 NMF 1 fsY NMF PGNMF IPGNMF HWT1 o ORL o LT m 4 1124 0 32 m 3 “ q MYTY m 4 +4 | HW + M UbVm V A PGNMF HWK NMF HWK IPGNMF HW)W MY q1 NMF PGNMF1nV 1b V 1 MY MY q MYZE ORLMY q YEL MY q FERETMY q ( MY q GABOR 0.572
12、 0.520 0.556 0.549 GABOR+PCA 0.644 0.640 0.623 0.636 GABOR+ICA 0.733 0.727 0.653 0.704 GABOR+2DPCA 0.797 0.820 0.676 0.764 GABOR+NMF 0.721 0.785 0.747 0.751 GABOR+PGNMF 0.704 0.816 0.787 0.769 GABOR+IPGNMF 0.824 0.833 0.8433 0.833 Q L GaborMB m4 | Gabor+ HW) 1+ omT V 2 UbYVT V A Gabor+4 | HW ( 188 m
13、s MYL H YT1B HWb 5.5 +4 |ZE MY q1 L !1n MYZEZE MY qS1 LT V 1 UbY V 2 Gabor +4 | HW o HW ORL 183 msYALE 175 ms FERET 206 msV kT V AZE1 PGABOR Mss (PCA) s s(ICA) NMF(d s ) PGNMF(0gd s ) E MYrTzb 6 .d MYZE “ MY5 J4 Bg0d s “+4 |ZEbZE IPGNMF - n5“m vZ_asO q Gaborlo roi4 | Z_a Gabor m GMM(Gabor Magnitude
14、Map) Pg0d sZE4 | m NMF +| m + K RBF * ZE + MYs K *s MYb o ORLaYELaFERETMY L GREY, PCA, ICA, NMF, PGNMFZE1 Vr % “ MY5bHq/ “+4 | b I D 1 Zhu Yulian, Liu Jun, and Chen Songcan. Semi-random subspace method for face recognitionJ. Image and Vision Computing, 2009, 9(26): 113. 2 Gao Quan-xue, Zhang Lei, an
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16、ors applicable to face recognition with one training image per personJ. Journal of ZheJiang University, 2008, 35(2): 181184. 4 Daugman J G. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two2dimensional visual cortical filters J. Journal of the Optical
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