Dscrmnatve Dctonary Learnng wth Parwse Constrants Humn Guo Zhuoln Jang LARRY S. DAVIS UNIVERSITY OF MARYLAND Nov. 6 th,
Outlne Introducton/motvaton Dctonary Learnng Dscrmnatve Dctonary Learnng wth Parwse Constrants Experments Face verfcaton Face recognton Summary
Applcatons Par-matchng type problems, only bnary class nformaton Face Verfcaton (same/dfferent) Par-matchng (same/dfferent, smlar/dssmlar) Image Retreval (relevant/rrelevant) Classfcaton problems, category labels provded Face Recognton Image Classfcaton 3
Motvatons Par matchng problems are common n many practcal applcatons; we can use provded parwse constrants explctly DDL-PC: the learned dctonary encourages feature ponts from the same class (or a smlar par) to have smlar sparse codes, dscrmnatve+ DDL-PC: furthermore add n a classfcaton error term n classfer constructon for a unfed objectve functon, dscrmnatve++ 4
Dctonary Learnng fnd optmzed dctonares A* that provdes a succnct representaton for most statstcally representatve nput sgnals Solvng l-mnmzaton Reconstructon Term Regularzaton Term ( N y... y ) : tranng sgnals; x... x ) : sparse codes for y... y ) ( N ( N 5
DDL-PC The objectve functon of Dctonary Learnng A*, X* arg mn arg mn A, X arg mn A, X A, X N N y Ax x N, j x x T T y ( ) ( ) Ax x Tr X XD Tr X XM N T y ( ) Ax x Tr X XL Reconstructon Term Regularzaton Term Dscrmnaton Term j M j y... y ) : tranng sgnals; ( x... x N ) : sparse codes for ( y... y N ) M: Adjacency (weght) matrx; N D dag( d... d N ) : degree matrx, where d M j j L=D-M : Laplacan matrx ( N 6
Optmzaton The objectve functon s not convex for A and X smultaneously, but fortunately, t s convex n A (whle holdng X fxed) and convex n X (whle holdng A fxed). When A s fxed, we optmze each alternately and fx the other x j ( j ) for other sgnals. Optmzng the objectve functon s equvalent to T x ( XL ) mn L( x ) y Ax x x Here we modfy feature sgn search algorthm* to solve ths convex problem. x x T x L *H. Lee, A. Batte, R. Rana and A. Y. Ng, Effcent Sparse Codng Algorthm. NIPS6 7
Optmzaton (cont.) Gven all the sparse codes X, Optmzng the objectve functon s equvalent to mn L( A) A N y Ax Ths s L constraned least square problem. We can optmze t usng Newton s method or conjugate gradent., s. t. a a T 8
DDL-PC The objectve functon of Dctonary Learnng 9
Matchng approach Face Verfcaton (gven same/not same) y, y are the same person, y3, y4 are the same person, y5 y6 are dfferent person M y y y3 y4 y5 y6
Matchng approach Face Recognton class labels are gven for each mage n the tranng set. The par relatonshps are derved from the category labels Matrx M encodng the (ds)smlarty nformaton can be defned as
Experments: Face Verfcaton LFW (Labeled Faces n the Wld) dataset Remarkable varatons caused by Pose, facal appearance, age, lghtng, expresson, occluson, scale, camera, msalgnment, harstyle, etc. 333 mages 5749 people
Expermental Results Face Verfcaton on LFW Examples of some mage pars from the LFW dataset and the smlarty scores obtaned from KSVD dctonary learnng and proposed DDL-PC respectvely. Top row: Fve examples of same pars; Bottom row: Fve examples of dfferent pars. 3
Evaluaton on LFW ROC curve 4
Experments: Face Recognton Extended Yale-B Recognton results usng random-face features on the Extended YaleB. AR face database Recognton results usng random-face features on the Extended AR. 5
Summary a novel dctonary learnng approach that tackles the par matchng and classfcaton problem n a unfed framework a dscrmnatve term called parwse sparse code error based on parwse constrants + the classfcaton error term for better dscrmnatng power. 6
Thanks! Q&A 7