Heterogeneous Visual Features Fusion via Sparse Multimodal Machine

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1 013 IEEE Conference on Computer Vson and Pattern Recognton Heterogeneous Vsual Features Fuson va Sparse Multmodal Machne Hua ang, Fepng Ne, Heng Huang, Chrs Dng Department of Electrcal Engneerng and Computer Scence Colorado School of Mnes, Golden, Colorado 80401, USA Department of Computer Scence and Engneerng Unversty of Texas at Arlngton, Arlngton, Texas 76019, USA Abstract To better understand, search, and classfy mage and vdeo nformaton, many vsual feature descrptors have been proposed to descrbe elementary vsual characterstcs, such as the shape, the color, the texture, etc. How to ntegrate these heterogeneous vsual features and dentfy the mportant ones from them for specfc vson tasks has become an ncreasngly crtcal problem. In ths paper, e propose a novel Sparse Multmodal Learnng (SMML) approach to ntegrate such heterogeneous features by usng the jont structured sparsty regularzatons to learn the feature mportance of for the vson tasks from both group-wse and ndvdual pont of vews. A new optmzaton algorthm s also ntroduced to solve the non-smooth objectve wth rgorously proved global convergence. e appled our SMML method to fve broadly used object categorzaton and scene understandng mage data sets for both snglelabel and mult-label mage classfcaton tasks. For each data set we ntegrate sx dfferent types of popularly used mage features. Compared to exstng scene and object categorzaton methods usng ether sngle modalty or multmodaltes of features, our approach always acheves better performances measured. 1. Introducton Scene categorzaton and vsual recognton problem analyzes and classfes the mages nto semantcally meanngful categores. It s wthout doubts a dffcult task n computer vson research feld, because any scene/object category can be characterzed by a hgh degree of dversty and potental ambgutes. To enhance the vsual understandng, computer vson researchers have proposed many feature representaton methods to descrbe the vsual objects n Correspondng author. Ths work was partally supported by NSF IIS dfferent types of mages [1, 18, 3]. However, t s usually not clear what the best feature descrptor to solve a gven applcaton problem s. Because dfferent features descrbe dfferent aspects of the vsual characterstcs, one descrptor can be better than others under certan crcumstances. How to ntegrate heterogeneous features s becomng a challengng as well as attractve problem nowadays. Consderng dfferent feature representatons gve rse to dfferent kernel functons, the Multple Kernel Learnng (MKL) approaches [19, 9, 13] have been recently studed and employed to ntegrate heterogenous features or data and select mult-modal features. Partcularly, [5] surveyed several MKL methods, as well as ther varants usng boostng method, for computer vson tasks and appled them n object classfcaton. However, such models tran a weght for each type of features,.e., when multple types of features are combned together, all features from the same type are weghted equally. Ths crucal drawback often causes the low performance. To address the ntegraton of the heterogeneous mage features for vsual recognton tasks, n ths paper, we propose a novel Sparse Multmodal Learnng (SMML) method by utlzng a new mxed structured sparsty norms. In our method, we concatenate all features of one mage together as ts feature vector and learn the weght of each feature n the classfcaton decson functons. The man dffculty of ntegratng heterogeneous mage features s to smultaneously consder the feature group property (e.g. GIST s good at detectng natural scenes and the GIST features should have large weghts for classes related to outdoor natural scenes) and ndvdual feature property,.e., although a type of features are not useful to categorze certan specfc classes, a small number of ndvdual features from the same type can stll be dscrmnatve for these classes. e propose to utlze two structured sparsty regularzers to capture both group and ndvdual propertes of dfferent modaltes (types) of features. Meanwhle the sparse weght matrx provdes a natural feature selecton results. Our new /13 $ IEEE DOI /CVPR

2 objectve, employng the hnge loss and the two non-smooth regularzers, s hghly non-smooth and dffcult to solve n general. Thus, we derve a new effcent algorthm to solve t wth rgorously proved global convergence. e appled our new sparse multmodal learnng method to fve broadly used object categorzaton and scene understandng mage data sets for both sngle-label and mult-label mage classfcaton tasks. For each data set we ntegrate sx dfferent types of popularly used mage features. In all expermental results, our new method always acheves a better object and scene categorzaton performance than tradtonal classfcaton methods utlzng each sngle type descrptor and the wdely used MKL based feature ntegraton methods.. Sparse Multmodal Learnng In recent research, sparse regularzatons have been wdely nvestgated and appled nto dfferent computer vson and machne learnng studes [1, 16, 11]. The sparse representatons are typcally acheved by mposng nonsmooth norms as regularzers n the optmzaton problems. Because the structured sparsty regularzers can capture the structures exstng n data ponts and features, they are useful n dscoverng the underlyng patterns. e wll use a new jont structured sparsty regularzers to explore both group-wse and ndvdual mportance of each feature for dfferent classes..1. Jont Structured Sparsty Regularzatons In the supervsed learnng settng, we are gven n tranng mages {(x, y )} n [, where (x ) 1 T ( ) ] x =,, x k T T R d s the nput vector ncludng all features from a total of k modaltes and each modalty j has d j features (d = k j=1 d j). y R c s the class label vector of data pont x, where c s the number of classes. Let X = [x 1,, x n ] R d n and Y =[y 1,, y c ] R c n. In ths paper, we wrte matrces as boldface uppercase letters and vectors as boldface lowercase letters. For matrx =(w j ), ts -th row and j-th column are denoted by w and w j respectvely. Dfferent to MKL, we drectly learn a d c feature weght matrx = [w1, 1, wc; 1,, ; w1, k, wc k ] R d c, where wp q R dq ndcates the weghts of all features from the q-th modalty n the classfcaton decson functon of the p-th class. Typcally we can use a convex loss functon L(X, ) to measure the loss ncurred by on the tranng mages. e choose to use the hnge loss, because the hnge loss based SVM has shown state-of-the-art performance n classfcatons. Compared to MKL approaches that learn weght matrces n unsupervsed way, our method wll learn all weghts of features usng supervsed learnng model. Because the heterogeneous features come from dfferent vsual descrptors, we cannot only use the loss functon that equvalents to assgn the unform weghts to all features. The regularzer R has to be added to mpose the nterrelatonshps of modaltes and features as: mn n j=1 ( ) 1 y j(w T x j + b ) + γr, (1) + where γ>0s a trade-off parameter and the functon (a) + s defned as (a) + = max(0,a). For brevty, we denote f (w,b )= n ( (1 y j w T x j + b ) ) n the sequel. + j=1 In heterogeneous features fuson, from multmodal vewpont, the features of a specfc modalty can be more or less dscrmnatve for specfc classes. For nstance, the color features substantally ncreases the detecton of stop sgns whle they are almost rrelevant for fndng cars n mages. Thus, we propose a new group l 1 -norm (G 1 -norm) as regularzer n Eq. (1), whch s defned as G1 = k w j [17]. Then Eq. (1) becomes: j=1 mn f (w,b )+γ 1 G1. () Because the group l 1 -norm uses l -norm wthn each modalty and l 1 -norm between modaltes, t enforces the sparsty between dfferent modaltes,.e., f one modalty of features are not dscrmnatve for certan tasks, the objectve n Eq. () wll assgn zeros (n deal case, usually they are very small values) to them for correspondng tasks; otherwse, ther weghts are large. Ths group l 1 -norm regularzer captures the global relatonshps between modaltes. However, n certan cases, even f most features n one modalty are not dscrmnatve for certan vsual categores, a small number of features from the same modalty can stll be hghly dscrmnatve. From the mult-task learnng pont of vew, such mportant features should be shared by all tasks. Thus, we add one more l,1 -norm regularzer nto Eq. () and get the fnal objectve as: mn f (w,b )+γ 1 G1 +γ,1. (3) Because the l,1 -norm regularzer mposes the sparsty between all features and non-sparsty between classes, the features that are dscrmnatve for all classes wll get large weghts. Because of the mposed sparsty, the weghts of most features are close to zeroes and only the features mportant to classfcaton tasks have large weghts. Thus, our SMML results automatcally perform the feature selecton procedure

3 .. A New Effcent Optmzaton Algorthm The objectve of Eq. (3) s a hghly non-smooth problem and cannot be easly solved n general. Thus, we derve a new effcent algorthm to solve ths problem as summarzed n Algorthm 1, whose convergence to the global optmum s guaranteed by the followng theorem. Theorem 1 In Algorthm 1, the value of the objectve n Eq. (3) s monotoncally decreased n each teraton. Proof: In each teraton t, accordng to the Step 3 n the Algorthm 1, we have: t+1 = mn f (w,b ) (4) ) + γ 1 D t w ( + γ tr T D t, by whch we can derve f ((w t+1), (b t+1) ) k (w t+1) j + γ 1 j=1 (w t) j + γ f ((w t), (b t) ) + γ 1 j=1 k (w t) j (w t) j + γ w t+1 w t w t w t. Because t can verfed that for functon g (x) =x x α, gven any x α R n, g (x) g (α) holds, we can derve: k γ 1 (w t+1) j k (w t+1) j γ 1 j=1 j=1 (w t) j (6) k γ 1 (w t) j k (w t) j γ 1 j=1 j=1 (w t) j ; γ w t+1 γ w t+1 wt wt γ wt γ. w t Addng Eqs. (5)-(7) n both sdes, we have k f ((w t+1), (b t+1) )+γ 1 (w t+1) j j=1 j=1 + γ k f ((w t), (b t) )+γ 1 (w t) j + γ w t (5) (7) wt+1. (8) Therefore, the algorthm decreases the objectve value n each teraton. Because the problem (3) s a convex problem, Algorthm 1 wll converge to the global optmum. Input: X =[x 1, x,, x n] R d n, Y =[y 1, y,, y c] R n c. 1. Let t =1. Intalze t R d c. whle Not converges do. Calculate the block dagonal matrces D t the j-th dagonal block of D t s 1 (w t) j (1 c), where I j. Calculate the dagonal matrx D t, where the -th dagonal element s 1 wt. 3. For each w (1 c), calculate (w t+1 ) = D 1 ( w t), where w =argmnf ( w,b ; X)+ w w T w, X = D 1 X and D = γ 1 D + γ D. 4. t = t +1. end Output: t R d c. Algorthm 1: An effcent teratve algorthm to solve the optmzaton problem n Eq. (3). 3. Expermental Results In ths secton, we expermentally evaluate the proposed Sparse Mult-Modal Learnng (SMML) approach n both sngle-label mage classfcaton tasks and mult-label mage classfcaton tasks Evaluaton n Sngle-Label Image Classfcaton e frst evaluate the proposed approach n sngle-label mage classfcaton, n whch each mage belongs to one and only one class. e experment wth the followng three benchmark sngle-label mult-modal mage data sets, whch are broadly used computer vson studes. NUS-IDE-Object data set 1 contans 30,000 mages and 31 classes. Followng [4], we select to use a subset of 6 classes n our experments. Anmal data set contans mages for 50 anmals (classes). MSRC-v1 data set 3 contans 40 mages wth 9 classes. Followng [], we refne the data set to get 7 classes ncludng tree, buldng, arplane, cow, face, car, bcycle, and each refned class has 30 mages. All the three data sets are descrbed by a set of 6 dfferent mage descrptors, whch are lsted n Table 1. Expermental setups. e classfy the mages n the above three data sets usng the proposed methods by ntegratng the sx types of mage features of each of them. e compare the proposed method aganst several most recent multple

4 Type Table 1. Image feature descrptors of mage data sets used n experments. NUS-IDE-Object Anmal MSRC-v1 / MSRC-v / TRECVID 005 Features Dmenson Features Dmenson Features Dmenson 1 Color moments 55 Self-Smlarty 000 Color moment 48 Color hstogram 64 Color hstogram 688 LBP 56 3 Color correlogram 144 PyramdHOG 5 HOG avelet texture 18 SIFT 000 SIFT Edge dstrbuton 73 colorsift 000 GIST 51 6 Vsual words 500 SURF 000 Centrst 130 kernel learnng (MKL) methods that are able to make use of multple types of data: (1) SVM l MKL method [13], () SVM l 1 MKL [9], (3) SVM l MKL method [8], (4) least square (LSSVM) l MKL method [19], (5) LSSVM l 1 MKL method [14] and (6) LSSVM l MKL method [0]. Besdes, we also compare our method to three most recent mult-model mage classfcaton methods publshed n computer vson communty, ncludng Gaussan process (GP) method [7], LPBoost-β method [5] and LPBoost-B method [5], whch have demonstrated state-of-the-art object categorzaton performance. In addton, we also report the classfcaton performances by SVM on each ndvdual type of features and a straghtforward concatenaton of all sx types of features as baselnes. e mplement three versons of the proposed method. Frst, we set γ n Eq. (3) as 0, whch only uses the G 1 - norm as regularzaton thereby only takes nto account the structure over modaltes. e denote t as Our method (G 1 -norm only). Second, we set γ 1 n Eq. (3) as 0 to only use l,1 -norm regularzaton, whch thereby select feature shared across tasks yet modalty structure s not consdered. e denote ths degenerate verson of the proposed method as Our method (l,1 -norm only). Fnally, the full verson of the proposed method by Eq. (3) s mplemented and denoted as Our method. e conduct standard 5-fold cross-valdaton and report the average results. For each of the 5 trals, wthn the tranng data, an nternal 5-fold cross-valdaton s performed to fne tune the parameters. The parameters of our method (γ 1 and γ n Eq. (3)) are optmzed n the range of { 10 5, 10 4,...,10 4, 10 5}. For SVM method and MKL methods, one Gaussan kernel s constructed ( for each type of features (.e., K (x, x j )=exp γ x x j ) ), where the parameter γ s fne tuned n the same range used as our method. e mplement the compared MKL methods usng the codes publshed by [0]. Followng [0], n LSSVM l and l methods, the regularzaton parameter λ s estmated jontly as the kernel coeffcent of an dentty matrx; n LSSVM l 1 method, λ s set to 1; n all other SVM approaches, the C parameter of the box constrant s fne tuned n the same range as γ. For LPBoost-β and LPBoost- B methods, we use the codes publshed by the authors 4.e 4 pgehler/projects/ccv09/ Table. Classfcaton accuraces (mean ± std) of the compared methods n three sngle-label mage classfcaton tasks. Methods NUS-IDE Anmal MSRC-v1 SVM (Type 1) 0.15± ± ±0.019 SVM (Type ) 0.149± ± ±0.018 SVM (Type 3) 0.146± ± ±0.0 SVM (Type 4) 0.150± ± ±0.06 SVM (Type 5) 0.141± ± ±0.03 SVM (Type 6) 0.149± ± ±0.01 SVM (all by concatenaton) 0.138± ± ±0.05 SVM l MKL method 0.11± ± ±0.03 SVM l 1 MKL method 0.07± ± ±0.019 SVM l MKL method 0.0± ± ±0.0 LSSVM l MKL method 0.00± ± ±0.05 LSSVM l 1 MKL method 0.195± ± ±0.07 LSSVM l MKL method 0.187± ± ±0.018 GP method 0.181± ± ±0.015 LPboost-β 0.0± ± ±0.010 LPboost-B 0.19± ± ±0.013 Our method (G 1-norm only) 0.± ± ±0.01 Our method (l,1-norm only) 0.3± ± ±0.013 Our method 0.45 ± ± ± 0.05 use LIBSVM 5 software package to mplement SVM n all our experments. Expermental results. Because we are concerned wth sngle-label mage classfcaton, we employ the most wdely used classfcaton accuracy to assess the classfcaton performance. The results of all compared methods n the three mage classfcaton tasks are reported n Table. A frst glance at the results shows that our methods generally outperform all other compared methods, whch demonstrate the effectveness of our methods n sngle-label mage classfcaton. In addton, the methods usng multple data sources are sgnfcantly better than SVM usng one sngle type of data. Ths confrms the usefulness of data ntegraton n mage classfcaton. Moreover, the results that our methods are always better than the MKL methods and boostng enhanced MKL methods s consstent wth the prevous theoretcal analyss n that, although both of them take advantage of the nformaton from multple dfferent sources, our method not only assgns proper weght to each type of features, but also rewards the relevances of the ndvdual features nsde a gve feature type. In contrast, the MKL methods and boostng enhanced MKL methods only address the former whle not beng able to take nto account the latter. 5 cjln/lbsvm/

5 Fnally, the performances of the full verson of the proposed method s consstently better than those of ts two degenerate versons, whch demonstrate that both taskspecfc modalty selecton and across-task feature selecton are necessary n mage categorzaton, no one less. 3.. Evaluaton n Mult-Label Image Classfcaton Now we evaluate the proposed method n mult-label mage classfcaton, n whch each mage can be assocated wth more than one class label. e evaluate the proposed approach on the followng two benchmark mult-label mage data for mage annotaton tasks. TRECVID data set contans mages and labeled wth 39 concepts (labels). As n most prevous works [15], we randomly sample the data such that each concept has at least 100 mages. MSRC-v 7 data set s an extenson of MSRC-v1 data set, whch has 591 mages annotated by classes. Same as the MSRC-v1 data set, we extract sx types of mage features for these two data sets as detaled n the last column of Table 1 followng []. Expermental setups. e stll mplement the three versons of our method and compare them aganst the MKL methods used n the above experments wth the same settngs. For our method and MKL methods, we conduct classfcaton for every class ndvdually. For each class, we consder t as a bnary classfcaton task by usng onevs.-others strategy. For the classfcaton on each ndvdual data type and the smple mxture of all types of features, nstead of usng SVM as n the prevous subsecton for sngle-label data, we use mult-label k-nearest Neghbor (Mk-NN) [1] method to classfy the mages, whch s a broadly used mult-label classfcaton method. In addton, we also mplement two most recent mult-label classfcaton methods ncludng mult-label correlated Green s functon (MCGF) [15] method and Mult-Label Least Square (MLLS) [6] method. However, these two methods are desgned for data wth sngle type of features, therefore we use the concatenaton of all types of features as ther nput. e mplement the two mult-label classfcaton methods usng the codes publshed by the authors. The conventonal classfcaton performance metrcs n statstcal learnng, precson and F1 score, are used to evaluate the compared methods. For every class, the precson and F1 score are computed followng the standard defnton for a bnary classfcaton problem. To address the multlabel scenaro, followng [10], macro average and mcro average of precson and F1 score are computed to assess the overall performance across multple labels. Expermental results. The classfcaton results by standard 5-fold cross-valdaton on TRECVID 005 data set (a) Face, meetng, person, studo. (b) Crowd, face, person. (d) Outdoor, face, person, vegetaton. (c) Bus, car, person. (e) Buldng, crowd, (f) Outdoor, person, person. Sports, vegetaton. Fgure 1. Sample mages from TRECVID 005 data set, whose labels can only be correctly and completely predcted by the proposed method, not other compared methods. The bolded and underlned labels can only be correctly predct by our method. and MSRC-v data set are reported n Table 3. From the results, we can see that our method stll performs the best on the both data sets. Besdes, MKL methods usng multple types of features are generally better than the methods usng sngle type of features. Although Mk-NN, MCGF and MLLS methods are desgned for mult-label data, they can only work wth one type of features. hen usng the feature concatenaton as nput, they assume all types of features as homogenous wth no dstncton, whch, however, s not true n both our experments as well as most real world applcatons. Although our method and MKL methods do not purposely address the mult-label settngs, we stll acheve better performance due to properly makng use of the avalable nformaton from varous types of features. By further checkng the detaled labelng results, we notce that many mages can only be correctly annotated by our method, some of whch are shown n Fgure 1. The bolded and underlned labels can only be correctly predct by our method, but not the other compared methods. All these observatons, agan, confrm the effectveness of the proposed approach n feature ntegraton for mult-label mage classfcaton tasks. 4. Conclusons e proposed a novel Sparse Multmodal Learnng method to ntegrate dfferent types of vsual features for scene and object classfcatons. Instead of learnng one parameter for all features from one modalty as n multple kernel learnng, our method learned the parameters for each feature on dfferent classes va the jont structured sparsty regularzatons. Our new combned convex regularzatons consder the mportance of both feature modalty and ndvdual feature. The natural property of sparse regularzaton automatcally dentfes the mportant vsual features for dfferent vsual recognton tasks. e derved an eff

6 Table 3. Mult-label classfcaton performances (mean ± std) of the compared methods. Data set TRECVID 005 data set MSRC-v data set Methods Macro average Mcro average Macro average Mcro average Precson F1 Precson F1 Precson F1 Precson F1 Mk-NN (Color moment) ± ± ± ± ± ± ± ± 0.01 Mk-NN (DoG-SIFT) 0.41 ± ± ± ± ± ± ± ± 0.00 Mk-NN (LBP) ± ± ± ± ± ± ± ± 0.00 Mk-NN (HOG) ± ± ± ± ± ± ± ± 0.01 Mk-NN (GIST) ± ± ± ± ± ± ± ± 0.0 Mk-NN (CENTRIST) 0.45 ± ± ± ± ± ± ± ± 0.04 Mk-NN (all by concatenaton) 0.47 ± ± ± ± ± ± ± ± 0.03 MCGF (all by concatenaton) ± ± ± ± ± ± ± ± 0.0 MLLS (all by concatenaton) ± ± ± ± ± ± ± ± 0.05 SVM l MKL method ± ± ± ± ± ± ± ± 0.0 SVM l 1 MKL method ± ± ± ± ± ± ± ± 0.03 SVM l MKL method ± ± ± ± ± ± ± ± 0.01 LSSVM l MKL method 0.45 ± ± ± ± ± ± ± ± 0.0 LSSVM l 1 MKL method ± ± ± ± ± ± ± ± 0.04 LSSVM l MKL method ± ± ± ± ± ± ± ± 0.05 GP method ± ± ± ± ± ± ± ± 0.01 LPboost-β ± ± ± ± ± ± ± ± LPboost-B ± ± ± ± ± ± ± ± Our method (G 1-norm only) 0.47 ± ± ± ± ± ± ± ± Our method (l,1-norm only) ± ± ± ± ± ± ± ± Our method ± ± ± ± ± ± ± ± 0.06 cent optmzaton algorthm to solve our non-smooth objectve and provded a rgorous proof on ts global convergence. Extensve experments have been performed on both sngle-label and mult-label mage categorzaton tasks, our approach outperforms other related methods n all benchmark data sets. References [1] A. Argyrou, T. Evgenou, and M. Pontl. Mult-task feature learnng. In NIPS, 007. [] X. Ca, F. Ne, H. Huang, and F. Kamangar. Heterogeneous mage feature ntegraton va mult-modal spectral clusterng. In CVPR, 011. [3] N. Dalal and B. Trggs. Hstograms of orented gradents for human detecton. In CVPR (1), pages , 005. [4] S. Gao, L. Cha, and I. Tsang. Mult-layer group sparse codngłfor concurrent mage classfcaton and annotaton. In CVPR, 011. [5] P. Gehler and S. Nowozn. On feature combnaton for multclass object classfcaton. In ICCV, 009. [6] S. J, L. Tang, S. Yu, and J. Ye. A shared-subspace learnng framework for mult-label classfcaton. ACM Transactons on Knowledge Dscovery from Data (TKDD), 4():1 9, 010. [7] A. Kapoor, K. Grauman, R. Urtasun, and T. Darrell. Gaussan processes for object categorzaton. Internatonal journal of computer vson, 88(): , 010. [8] M. Kloft, U. Brefeld, P. Laskov, and S. Sonnenburg. Nonsparse multple kernel learnng. In NIPS. [9] G. Lanckret, N. Crstann, P. Bartlett, L. Ghaou, and M. Jordan. Learnng the kernel matrx wth semdefnte programmng. JMLR, 5:7 7, 004. [10] D. Lews, Y. Yang, T. Rose, and F. L. Rcv1: A new benchmark collecton for text categorzaton research. The Journal of Machne Learnng Research, 5: , 004. [11] F. Ne, H. ang, H. Huang, and C. Dng. Unsupervsed and sem-supervsed learnng va l 1-norm graph. In ICCV, pages 68 73, 011. [1] A. Olva and A. B. Torralba. Modelng the shape of the scene: A holstc representaton of the spatal envelope. Internatonal Journal of Computer Vson, 4(3): , 001. [13] S. Sonnenburg, G. Rätsch, C. Schäfer, and B. Schölkopf. Large scale multple kernel learnng. JMLR, 7: , 006. [14] J. Suykens, T. Van Gestel, and J. De Brabanter. Least squares support vector machnes. orld Scentfc Pub Co Inc, 00. [15] H. ang, H. Huang, and C. Dng. Image annotaton usng mult-label correlated Green s functon. In ICCV, 009. [16] H. ang, F. Ne, H. Huang, S. L. Rsacher, C. Dng, A. J. Saykn, L. Shen, and ADNI. A new sparse mult-task regresson and feature selecton method to dentfy bran magng predctors for memory performance. ICCV 011: IEEE Conference on Computer Vson, pages , 011. [17] H. ang, F. Ne, H. Huang, S. L. Rsacher, A. J. Saykn, L. Shen, et al. Identfyng dsease senstve and quanttatve trat-relevant bomarkers from multdmensonal heterogeneous magng genetcs data va sparse multmodal multtask learnng. Bonformatcs, 8(1):17 136, 01. [18] J. u and J. M. Rehg. here am : Place nstance and category recognton usng spatal pact. In CVPR, 008. [19] J. Ye, S. J, and J. Chen. Mult-class dscrmnant kernel learnng va convex programmng. JMLR, 9: , 008. [0] S. Yu, T. Falck, A. Daemen, L. Tranchevent, J. Suykens, B. De Moor, and Y. Moreau. L -norm multple kernel learnng and ts applcaton to bomedcal data fuson. BMC bonformatcs, 11(1):309, 010. [1] M. Zhang and Z. Zhou. ML-KNN: A lazy learnng approach to mult-label learnng. Pattern Recognton, 40(7): ,