A Non-Negative Sparse Neighbor Representation for Multi-Label Learning Algorithm

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1 44 6 Vo.44 No.6 05 Journa of Unversty of Eectronc Scence and Technoogy of Chna Nov. 05 ( 3060) k-lasso k(ml-knn)(ml-src) ; ; LASSO; TP39.4 A do:0.3969/.ssn A Non-Negatve Sparse Neghbor Representaton for Mut-Le Learnng Agorthm CHEN S-bao, XU Dan-yang, and LUO Bn (Schoo of Computer Scence and Technoogy, Anhu Unversty Hefe 3060) Abstract In order to avod the nfuence of the nonnear manfod structure n tranng data and preserve more dscrmnant nformaton n the sparse representaton based mut-e earnng, a new mut-e earnng agorthm based on non-negatve sparse neghbor representaton s proposed. Frst of a, the k-nearest neghbors among each cass are found for the test sampe. Secondy, based on non-negatve the east soute shrnkage and seectonator operator (LASSO)-type sparse mnmzaton, the test sampe s non-negatve neary reconstructed by the k-nearest neghbors. Then, the membershp of each cass for the test sampe s cacuated by usng the reconstructon errors. Fnay, the cassfcaton s performed by rankng these membershps. A fast teratve agorthm and ts correspondng anayss of convergng to goba mnmum are provded. Expermenta resuts of mut-e cassfcaton on severa pubc mut-e datases show that the proposed method acheves better performances than cassca ML-SRC and ML-KNN. Key words LASSO sparse mnmzaton; mut-e earnng; non-negatve reconstructon; sparse neghbor representaton [-] [3] ML-KNNk- [4] [5] Rank-SVM [6] [7] (SRC) [8] (non-negatve SRC, NSRC)[9] (sparse neghbor representaton dassfcaton, SNRC) (04AA0504)( )(KJ0A004) (979 ).

2 [0]SRC, (ML-SRC) ML-SRC LASSO [] (ML-NSNRC). n y R,,, n T {,,, L} D[ y, y,, yn ] d n R d n y b y b b 0 D L n B [ b, b,, bn ] R h : y L, y ML-SRC D y sˆ arg mn yds s () s s 0 ML-SRC [0] f ( y, ) : n f ( y, ) ( b sˆ ) sˆ,,, L () n s, s 0 sˆ,,,, n f ( y, ) 0, s 0 y h( y). (SNRC) [9] d k- k- k- SNRC s y s argmn yψ s s (3) s ψ y D k-,,, cc 0 SNRC, SNRC [8] (NSNRC). NSNRC NSNRCKNN y D k- ψ ψ y ψ sˆ arg mn yψs s s s.t.,,, c (4) k s s, s 0,,, k 0 D ψ. NSNRC NSNRC(4) [](4) : ( t) ( t) ψ y s s (5) ( ψ ψ s )

3 6 : 90 s s (5).3 NSNRC G( s, s ) F( s ) G( s, s ) F( s) G( s, s) F( s ) (6) ( K s ) T ( t) ( ψψs ) a K ( s ) (7) s F( s ) G( s, s ) F( s ) ( s s ) F( s ) ( ) ( )( s s K s s s ) (8) G( s, s) F( s) G( s, s ) F( s) F( s) F( s ) ( s s ) F( s ) ( ) ( )( s s ψψ s s ) (9) (8) () () () 0 ( s s t ) [ K( s t ) ψψ]( s s t ) (0) (0) () () () () M ( s t ) s t ( K( s t ) ψψ) s t () a b M K ψψ x Mx x M x s ( ψψ) s x x s ( ψψ) s x a b a a a b b ( ψψ) s s a b a b a b a a b x x x x ψψ s s x x () ( ) a b ( a b ) 0 ()M(0) G( s, s ) F( s) G F ( t) ( t) s arg mn G( s, s ) (3) s ( t) ( t) (3) G( s, s ) G( s, s ) G( s, s ) F() s ( t) ( t) ( s ) ( s, s ) ( s, s ) ( s ) F G G F (4) s G( s, s ) ( t ( ) ) ( ( t F s ) F s ) F( s ) s (3) ( t) ( t) 0 F( smn ) F( s ) F( s ) F( s ) (5) 0 G( s, s ) s ψ ( ψs y) K( s )( s s ) 0 (6) () () s ( t )( t s k s ψψs ψ y ) () () T () T () T s t ( t /( t ) )( t s ψψs ψψs ψ y ) s ( ψ y)/( ψψs ) (7) (5).4 NSNRC (5) ( ψ ) y ( ψ ) ψ ( kd) ( kd ) d k y ( k k k) NSNRC O( kd+k d+t(3 k+k )) t (fast teratve shrnkage-threshodng agorthm, FISTA)SRC [3] O( tn d) n D 3 ) ML-SRC 0 ) ML- SRC y D k-

4 d kl Ψ [ φ, φ, φ, φ,, φl, φl] R d kl φ KNNyD k- 0 φ y φ sˆ arg mn yφ s s s s. t. s 0,,,, k, 0,,,,, L (8) k s s 0 NSNRC ( t) ( t) () t s s (( φ ) y) (( φ ) φ s ) (9) t 0 y ( x) φ s y (0) 3. y g( y, ) y ( y) e g( y, ) 0 ( y) ( y) e e () y h( y) { g( y, )> p( y), T} p( y) 3. ML-NSNRC ML-NSNRC y k- y y d n ) D [ y, y,, yn ] R L n B R d y R ) y g( y, ) 3 ) D KNN y K-Ψ ) (0) y φ s s /n 3) (0) () y 4 4. ML-NSNRC 3 [3] Yeastscene [4] ) 000 %.4± ) Yeast Yeast YeastYeast Yeast4 [5] ) scene scene [4] ML-NSNRC ML-NSNRC /n N(0,) (0,) ML-NSNRC5

5 6 : 903 ML-NSNRC s /n /n (0,) ML-NSNRC 4.3 ML-NSNRCk k- k kml-nsnrck n,n n <<n k n k ML-NSNRCk5 scene ML-NSNRCML-KNN k ML-SRCML-NSRC k0ml-nsnrc k5ml-knn ML-KNN ML-NSNRC ML-SRC ML-NSRC k kml-nsnrcml-knn 4.4 [3] -5 4 ML-SRC (ML-NSRC) ML-NSNRC3 3k- ML-KNN ML-SRC ML-NSRCML-KNN ML-SRC ML-NSNRC 00k400Yeast k5scenek0 4-3 ML-KNN9.4%ML-KNN4.7% ML-KNN4.3% 4 - ML-KNN ML-SRC ML-NSRC ML-NSNRC Yeast ML-SRCML-NSRC Yeast 4 3 ML-KNN8.5%ML-KNN 9%ML-KNNML-SRC.6% 4Yeast - ML-KNN ML-SRC ML-NSRC ML-NSNRC

6 scene 3 ML-KNN ML-SRC8.%.4%ML- KNN3.6%ML-KNNML-SRC 4.3%5.6% 3 4scene - ML-KNN ML-SRC ML-NSRC ML-NSNRC Yeast scene ML-NSNRCML-KNN ML-SRCML-NSRC4 k- 5 (NSNRC) ML-NSNRC k- Yeastscene3 [] SCHAPIRE R E, SINGER Y. Boostexter: a boostng-based system for text categorzaton[j]. Machne Learnng, 000, 39(-3): [] UEDA N, SAITO K. Parametrc mxture modes for mut-e text[j]. Advances n Neura Informaton Processng, 003(5): [3] ZHANG M L, ZHOU Z H. ML-KNN: a azy earnng approach to mut-e earnng[j]. Pattern Recognton, 007, 40(7): [4] SANDEN C, ZHANG J Z. Enhancng mut-e musc genre cassfcaton through ensembe technques[c] //Proceedngs of the 34th nternatona ACM SIGIR Conference on Research and deveopment n Informaton Retreva. New York: ACM, 0: [5] ELISSEEFF A, WESTON J. A kerne method for muteed cassfcaton[j]. Advances n Neura Informaton Processng, 00(4): [6] CANDÈS E J, ROMBERG J, TAO T. Robust uncertanty prncpes: Exact sgna reconstructon from hghy ncompete frequency nformaton[j]. IEEE Transactons on Informaton Theory, 006, 5(): [7] WRIGHT J, YANG A Y, GANESH A, et a. Robust face recognton va sparse representaton[j]. IEEE Transactons on Pattern Anayss and Machne Integence, 009, 3(): 0-7. [8] JI Y, LIN T, ZHA H. Mahaanobs dstance based nonnegatve sparse representaton for face recognton[c]// Internatona Conference on Machne Learnng and Appcatons. Mam, FL: IEEE, 009: [9] HUI K, LI C, ZHANG L. Sparse neghbor representaton for cassfcaton[j]. Pattern Recognton Letters, 0, 33(5): [0],. [J]., 0, 5(): 4-9. SONG Xang-fa, JIAO L-cheng. A mut-e earnng agorthm based on sparse representaton[j]. Pattern Recognton and Artfca Integence, 0, 5(): 4-9. [] TIBSHIRANI R. Regresson shrnkage and seecton va the asso[j]. Journa of the Roya Statstca Socety (Seres B, Methodoogca), 996, 58(): [] LEE D D, SEUNG H S. Agorthms for non-negatve matrx factorzaton[j]. Advances n Neura Informaton Processng, 00(): [3] BECK A, TEBOULLE M. A fast teratve shrnkagethreshodng agorthm for near nverse probems[j]. SIAM Journa on Imagng Scences, 009, (): [4] BOUTELL M R, LUO J, SHEN X, et a. Learnng mut-e scene cassfcaton[j]. Pattern Recognton, 004, 37(9):

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