. ISSN ans net. Feature Fusion Using Automatic Generated RBF Neural Network. Liuzhou, China

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2 Informaton Technology Journal 14 (1): 16-3, 15. ISSN ans net 15 Asan Network for Scentfc Informaton Asan Network for Scentfc Informaton RESEARCH ARTICLE OPEN ACCESS Feature Fuson Usng Automatc Generated RBF Neural Network DOI: 1.393/tj ZhWen Wang and GongKun Luo 1 College of Computer Scence and Communcaton Engneerng, College of Electrcal and Informaton Engneerng, Guangx Unversty of Scence and Technology, Luzhou, Chna A R T I C L E I N F O Artcle Hstory: Receved: Aprl 13, 14 Accepted: January, 15 Correspondng Author: ZhWen Wang College of Computer Scence and Communcaton Engneerng, Guangx Unversty of Scence and Technology, 68 Dong Huan Road, Luzhou, Guangx, 5456, Chna A B S T R A C T In ths study, a strategy for feature fuson for team behavors recognton usng automatcally generated RBF neural network s proposed, for varous features need to be extracted n the course of team behavors recognton and t s dffcult to estmate the contrbuton of varous features for dentfyng and decryptng team behavors. The burden of hgh-level recognton algorthm s use eased by usng the underlyng features of movng target, such as the trajectory characterstcs extracted by usng the method of trajectory growth. KPCA algorthm s used to nonlnearly reduce dmensonalty of extracted characterstcs before feature fuson for extracted characterstcs of team behavors. Automatcally generated RBF neural network s constructed and feature fuson s realzed by usng Dempster-Shafer combnaton rules and network learnng. Parameters µ, α and γ are obtaned through networks learnng n the course of features fuson, s and p s decded by the decreased gradent of output error. The accuracy of behavor recognton s ncreased dramatcally and the processng tme s shorten sgnfcantly. Key words: Feature fuson, automatc generated RBF neural network, nonlnear dmensonalty reducton, recognzng of team behavor, KPCA algorthm INTRODUCTION Team behavor recognton usng sngle feature wll lead to unrelablty for the results, as t s dffcult for sngle feature to effectvely characterze the team behavor (Lazebnk and Ragnsky, 9; Wang and L, 11). Frstly, characterstc dmenson reducton for the extracted features wll be carred on after the characterstcs of clothng color of team, contour, trajectory are extracted n ths study. Secondly, we merge these features usng mult-feature fuson technques. Fnally, team behavor s descrbed and team behavor recognton s carred on by usng the fused characterstcs. Selecton of a learnng algorthm for a partcular applcaton s crtcally dependent on ts accuracy and speed. In practcal onlne applcatons, sequental learnng algorthms are generally preferred over batch learnng algorthms as they do not requre retranng whenever a new data s receved. Compared wth the batch learnng algorthms, the sequental learnng algorthms have the followng dstngushng features: C C C C All the tranng observatons are sequentally (one-by-one) presented to the learnng system At any tme, only one tranng observaton s seen and learned The learnng system has no pror knowledge as to how many total tranng observatons wll be presented A tranng observaton s dscarded as soon as the learnng procedure for that partcular observaton s completed Thus, f one strctly apples the above features of the sequental algorthms, many of the exstng algorthms are not sequental. One major bottleneck seems to be that they need the entre tranng data ready for tranng before the tranng procedure starts and thus, they are not really sequental. Ths pont s hghlghted n a bref revew of the exstng algorthms gven below. The RBF networks whch combnes forward subset selecton and zero-th-order regularzaton and acheves better generalzaton. Unlke other approaches nvolvng several 16

3 preset parameters and thresholds (used for addng new centers and performng gradent descent) that must be tuned wth each new problem. Thus, n ths study, a strategy for feature fuson for team behavors recognton usng automatcally generated RBF neural network s proposed, because t can overcome to the complexty of the network learnng, to acheve the requrements of real-tme mage processng. MATERIALS AND METHODS In order to mprove the accuracy of team behavor recognton and recognton effcency, feature dmenson reducton has been done for varous extracted features and then use the RBF neural network s used to ntegrate these features. Characterstcs dmenson reducton: In order to obtan compact descrpton and effcent calculaton of the team behavors, KPCA algorthm s used to nonlnearly reduce the dmenson of the extracted feature. Two aspects are manly consdered: (1) KPCA algorthm provdes an effectve learnng method for subspace to dscover the nonlnear structure of behavoral space, () KPCA algorthm can be easly appled to any new data pont and some nonlnear dmensonalty reducton methods are stll unclear how to descrbe the new data ponts, such as ISOMAP, LLE, etc. In the space of U D, a gven tranng feature set T x = {X 1, X,, X M } whch has M elements, the goal of subspace learnng s to fnd a embedded data set E y = {Y 1, Y,, Y M } n low-dmensonal space U D (d<d). For the method of kernel prncpal component analyss, each vector X s frstly mapped to a non-lnear Hlbert space H by N:U D 6H. Then, n the space H, prncpal component analyss s appled to the mappng data T N = {N(X 1 ), N(X ),...,N(X M )}. Due to the use of core sklls, the mappng process can be omtted. Let k s a postve sem-defnte kernel functon, nonlnear relatonshps of two feature vectors s defned by Eq. 1: k(x,x ) ( (x ) (x )) j j In the space H, the problem for searchng the coeffcents of man components can be attrbuted to dagonalzaton of kernel matrx κ: Where: If: ee k(x,x ), e [e,e,,e ] j j 1 Z e (x ) 1 T s used to represent spndle, a new pont X s mapped to the j spndle Z j can be expressed as: (1) () (Z (x)) e ( (x ) (x )) e k(x,x ) j j j j j 1 1 Gaussan kernel functon s used n our experments. After obtanng embeddng space whch ncludes frst man component d, any vdeo v can be mapped to a assocated track T o = {O 1, O,, O T } n a d dmensonal feature space. Feature fuson strategy for team behavor recognton: Three questons need to be consdered n feature fuson of team behavor recognton: (1) Whch features nformaton need to be fused? Dfferent characterstcs nformaton s reasonably selected to be fused, dependng on the dfferent applcaton scenaro, () At what level that feature ntegraton s carred on? Feature fuson can choose to be mplemented on the bottom level feature, md-level keyword and senor-level semantc and (3) Whch strategy s chosen n the course of features fuson? We need to select strategy for data normalzaton processng and fuson probablty expresson. Selectng feature fuson strategy: Currently mult-feature fuson strategy have multplcatve ntegraton, weghted fuson and dscrete Karhunen-Loeve (K-L) transform fuson. For multplcatve ntegraton, the jont dstrbuton of multple features s calculated by usng feature weghts Quadrature method whch can effectvely mprove the accuracy of trackng movng targets and may amplfy the nose. Weghted fuson adjusts weght coeffcent of each feature accordng to the credblty of dfferent characterstcs and then calculates the total feature weghts usng weghted sum of each feature. Weghted feature fuson s not senstve to nose, but can not rase the credblty of the fuson track (Wang and Yung, 1). K-L transform fuson s a adaptve mult-feature fuson strategy whch has the advantages of characterstcs of remaned entropy, energy, decorrelaton, as well as energy re-allocaton and concentraton, etc., but the calculaton s more complex and the learnng process s lack. In ths study, automatc generaton of RBF neural network shown n Fg. 1 s used to ntegrate varous features. A wde class of multple-nput-sngle-output systems can be modeled by the RBF neural networks gven by: ŜRBF(X,,c,w) w (X,,c ) m 1 where, Ŝ denotes the network output, X s the nput vector to the network, N (X, σ, c ) denotes the radal bass functon (e.g., Gaussan bass functon) of the -th hdden node wth the center c U n and the wdth σ U 1 and w s the lnear output weght. The adjustable parameters n network (Eq. 4) are therefore, the center vector c = (c 1, c,, c m ), the wdth vector σ = (σ 1, σ,, σ m ) and the lnear output weght vector W = (w 1, w,, w m ) T. For the Gaussan radal bass functon N (X, σ, c )-exp(-x-c /σ, where, C denotes the Eucldean norm. Input layer of network s consttuted of N neurons whch use the same actvaton functon N, d s the dstance calculated (3) (4) 17

4 Feature one Feature two Feature L Input layer L1 layer L layer Output layer Fg. 1: RBF neural network for fusng mult-features by usng tranng data. α[, 1] s weakenng parameters of correspondng neuron (Wang et al., 1). There are: s (d ) (d ) exp( (d ) ) L1 layer s used to calculate the trust blocks m of -th module connected to -th neuron of prevous level: m( w q ) u q,(d) m( ) 1 (d) where, u q, s the member degree of each category of characterstc, q = {1,,, M}. L layer merges N dfferent functon blocks usng the fuson composton rule of Dempster-Shafer n a sngle block, the combnatons rules of shown n Eq. 7: m(a) (m m m ) m (B ) 1 N B1BBN A 1 Defnng an exctaton vector u of -th module and u s obtaned by Eq. 8 usng recursve calculaton: N (5) (6) (7) The output of output layer of RBF neural network are very senstve to the number of orgnal features, small changes n the number of features may cause large change of output fused characterstcs (Laptev, 5; Wang and L, 1; Boman and Iran, 7), thus exctaton vector of orgnal characterstcs are consdered to calculate output to reduce the mpact caused by number change of features n the course of block calculaton. Equaton 9 s specfc expresson of calculaton: O p O O N u 1,j j N M1 u 1 j1,j q q M1 Estmaton of fuson parameter: The RBF has only three preset parameter, the bass functon wdth. The computaton cost (number of floatng pont operatons) for parameters adjustment at each learnng cycle can be up to O(n 3 ), where, n s the number of tranng data whch s usually very large. u, α, γ are the mportance factor of each feature n the process of characterstc ntegraton whch we can get through network learnng. RESULTS (9) u1 m1 u u m u m u m u,m u 1,Mm,M1,j 1,j,j 1,j,M1 1,M1,j (8) The result of characterstc reducton usng KPCA algorthm for two-dmenson orgn features s shown n Fg.. Where, gray expresses nput characterstc vectors and red+ s the reduced feature vectors. Fgure 3 shows mappng 18

5 1 8 Input vectors Reconstructed 6 Second dmenson Frst dmenson Fg. : Result of feature reducton for two-dmenson characterstcs Frst dmenson Pck up onject Jog n place Push Squat Wave Kck Bend to the sde Throe Tum around Talk on cellphone.1 Second dmenson Thrd dmenson.1 Fg. 3: Three-dmensonal vew of mappng track for behavor n KPCA derved subspace H Fg. 4: Learnng process of RBF neural network trajectores (PTM) of behavor of the dataset n lterature (Veeraraghavan et al., 5) and the tme sequence of frame s marked unclearly. Learnng of RBF neural network s shown as Fg. 4. The s and p are determned by the gradent descent of the output error. DISCUSSION Radal Bass Functon (RBF) neural networks have been wdely used n many areas, such as data mnng, pattern recognton, sgnal processng, tme seres predcton and nonlnear system modelng and control, because of the smple topologcal structure and unversal approxmaton ablty (Park and Sandberg, 1991). Ths s also stated n prevous studes (Adams and Payandeh, 1996; Chen and Bllngs, 199; Er et al., 5; Gonzalez et al., 3; Hong et al., 3; Peng et al., 6; L and Wang, 14; L et al., 4, 6; 19

6 Second dmenson (a) Second component (b) Frst dmenson Frst component 6 (c) (d) 4. Second component - Second component Frst component Frst component Fg. 5(a-d): Comparng of PCA and KPCA, (a) Orgn, (b) Kernel PCA (Poly), (c) Tradtonal PCA and (d) Kernel PCA (Gaussan) Oyang et al., 5; Park and Sandberg, 1991; Polycarpou, 1; Xe and Leung, 5; Zhang et al., 4; Zhu and Bllngs, 1996). Gaussan radal bass functons have also been wdely used n support vector machnes, an mportant class of machne learnng algorthms. One of the most mportant ssues n the RBF neural network applcatons s the network learnng,.e., to optmze the adjustable parameters whch nclude the center vectors, the varances (or the wdths of the bass functons) and the lnear output weghts connectng the RBF hdden nodes to the output nodes. Another mportant ssue s to determne the network structure or the number of RBF nodes based on the parsmonous prncple (Huang et al., 5; Leung et al., 3). Both the ssues to determne the network sze and to adjust the parameters on the contnuous parameter space are closely coupled. It s a mxed nteger hard problem f the two ssues are consdered smultaneously. Evolutonary algorthms have been used to address ths problem (Gonzalez et al., 3; Leung et al., 3), however, they are computatonally very expensve to mplement and t s also well known that these algorthms suffer the slow and premature convergence problems. Despte that no analytc method s avalable to effcently and effectvely address ths ntegrated problem, the two separate ssues have been studed extensvely n the lterature. Wth respect to the RBF neural network learnng, conventonal approach takes a two stage procedure,.e., unsupervsed learnng of both the centers and wdths for the RBF nodes and supervsed learnng of the lnear output weghts. Wth respect to the center locaton, clusterng technques have been proposed. For the wdth learnng, f the nput samples are unformly dstrbuted, an dentcal wdth can be set for all the bass functons, otherwse a partcular wdth has to be set for each ndvdual bass functon to reflect the nput dstrbuton (Park and Sandberg, 1991). Once the centers and the wdths are determned, the lnear output weghts can be obtanable usng Cholesky factorzaton, orthogonal least squares, or sngular value decomposton. In contrast to the conventonal two stage learnng procedure, supervsed learnng methods am to optmze all the network parameters (Neruda and Kudova, 5). To mprove the convergence, varous technques have been ntroduced. For example, hybrd algorthms combne the gradent-based search for the nonlnear parameters (the wdths and centers) of the

7 RBF nodes and the least squares estmaton of the lnear output weghts (Panchapakesan et al., ; Peng et al., 3). Second-order algorthms have also been proposed whch use an addtonal adaptve momentum term to the Levenberg-Marquardt algorthm n order to mantan the contumacy between successve mnmzaton drectons, resultng n good convergence for some well-known hard problems. Neruda and Kudova (5), the performances of three dfferent RBF learnng methods are compared a gradent-based algorthm (gradent descent wth a momentum term), a three-step hybrd learnng algorthm and a genetc algorthm. Generally speakng, although supervsed learnng s thought to be superor to conventonal two stage approaches, t can be computatonally more demandng. Nevertheless, these above learnng methods are only applcable to RBF networks of fxed structure. If the network sze also has to be determned, one of the smplest ways s to repeat these above learnng procedures wth dfferent network sze untl the optmal one s acqured based on some network selecton crteron such as the Akake Informaton Crteron (AIC). Ths method s, however, computatonally too demandng. Wth respect to the determnaton of the RBF neural network structure, a popular approach s to formulate t as a lnear-n-the parameters problem, where all the tranng patterns (or samples) are usually used as the canddate RBF centers and the RBF wdths are chosen a pror. A parsmonous network s then determned from these canddates usng an effcent forward subset selecton method, such as the Orthogonal Least Squares (OLS) algorthms (Zhu and Bllngs, 1996) or the Forward Recursve Algorthm (FRA) (L et al., 5). To mprove the network generalzaton, the Regularzed Forward Selecton (RFS) algorthm has been proposed (Orr, 1995) whch combnes subset selecton wth zero-order regularzaton. Backward selecton methods have also been used n RBF center selecton (L et al., 4, 6). However, forward selecton algorthms are thought to be superor to backward methods n terms of computatonal effcency, snce they do not need to solve the equatons explctly wth the full set of ntal canddate centers. Generally speakng, exstng (forward and backward) subset selecton methods have several major dsadvantages. Frst, snce the RBF wdths are set a pror and the centers of the RBF nodes are selected from a set of tranng samples wth lmted sze, the optmal values on the contnuous parameter space for the center and wdth parameters of RBF nodes can be easly mssed out on. Ths means that the stepwse forward or backward procedures can easly mss out on a good RBF neural network. Second, n order to ncrease the chance of obtanng a satsfactory RBF network, one has to use a very large set of canddate RBF nodes of dfferent centers and wdths. Ths s, however, sometmes computatonally too expensve or mpossble to mplement, snce all the canddate RBF nodes have to be stored for batch operatons and the number of all canddates wll ncrease exponentally as the search space dmenson ncreases. Part of ths s usually referred to as the curse of dmensonalty problem n the lterature. In order to optmze the RBF center and wdth parameters along wth the network structure determnaton process, a Sparse Incremental Regresson (SIR) modelng method was proposed n Chen et al. (5). Ths method appends repressor n an ncremental modelng process. For each repressor to be appended, the nonlnear parameters are tuned usng a boostng search base d on a correlaton crteron. In ths way, the network structure and the assocated nonlnear parameters are determned smultaneously. However, the search for the optmal values of the nonlnear parameters (RBF centers and wdths) s a contnuous optmzaton problem. The boostng approach n SIR whch employs a stochastc search process, tends to be slower n convergence than calculus-based optmzaton technques. In addton, all the nonlnear parameters are treated equally n SIR and the dfference between the center and wdth parameters of a RBF node s gnored; ths s agan another factor that slows down the search process. Fnally, the boostng search n SIR has three to fve parameters that need to be tuned emprcally. All the above potental problems wth SIR are llustrated n the smulaton examples at the end of ths study. Dfferent from exstng methods n RBF neural network constructon, ths study proposes a novel Hybrd Forward Algorthm (HFA) whch performs smultaneous network growng and parameter optmzaton wthn an ntegrated analytc framework, leadng to two man techncal advantages. Frst, the network performance can be sgnfcantly mproved through the optmzaton of the nonlnear RBF parameters on the contnuous parameter space. Second, conventonal forward selecton algorthms tend to use all tranng samples to produce a very large set of canddate RBF nodes from whch the fnal RBF network s selected (Adams and Payandeh, 1996; Gonzalez et al., 3). The currently proposed method, however, only uses a very small number of tranng samples just for the ntalzaton of the RBF centers, amng to speed up the contnuous optmzaton procedure. We use KPCA to reduce the dmenson of nput features n ths study. As a result, the memory requrement s sgnfcantly reduced. Fgure 5 shows the results of two-dmensonal features reducton usng the methods of tradtonal PCA and KPCA (usng kernel functon poly and Gaussan) whch are shown n Fg. 5c and 5d, respectvely. Fgure 5b shows the orgnal features. Automatcally generated RBF neural network s constructed and extracted features of team behavor are merged by usng combnaton rule of Dempster-Shafer and network learnng. The accuracy of behavor recognton s ncreased dramatcally and the processng tme s shorten sgnfcantly n ths study. 1

8 CONCLUSION Strategy of feature fuson for team behavor recognton usng automatcally generated RBF neural network s presented n ths study. Frstly, the underlyng characterstcs are extracted to reduce the burden of hgh-level recognton algorthm, such as trajectory feature of movng targets s extracted by usng the growth method of trace. Secondly, nonlnear dmensonalty reducton for extracted characterstcs s mplemented usng KPCA algorthm. Fnally, automatcally generated RBF neural network s constructed and extracted features of team behavor are merged by usng combnaton rule of Dempster-Shafer and network learnng. Parameters u, α, γ are obtaned through network learnng n the ntegraton process, s and p are calculated by the gradent descent algorthm of output error. ACKNOWLEDGMENT Ths study was supported n part by Natonal Natural Scence Foundaton of Chna (61468) and a grant from Natural Scence Foundaton of Guangx (13GXNSFAA19336) and the Foundaton of Doctor of Guangx Unversty of Scence and Technology (1z14). REFERENCES Adams, J. and S. Payandeh, Methods for low velocty frcton compensaton: Theory and expermental study. J. Robot. Syst., 13: Boman, O. and M. Iran, 7. Detectng rregulartes n mages and n vdeo. Int. J. Comput. Vson, 74: Chen, S. and S.A. Bllngs, 199. Neural network for nonlnear dynamc system modellng and dentfcaton. Int. J. Control, 56: Chen, S., X.X. Wang and D.J. Brown, 5. Sparse ncremental regresson modelng usng correlaton crteron wth boostng search. IEEE Sgnal Process. Lett., 1: Er, M.J., W. Chen and S. Wu, 5. Hgh-speed face recognton based on dscrete cosne transform and RBF neural networks. IEEE Trans. Neural Networks, 16: Gonzalez, J., I. Rojas, J. Ortega, H. Pomares, F.J. Fernandez and A.F. Daz, 3. Multobjectve evolutonary optmzaton of the sze, shape and poston parameters of radal bass functon networks for functon approxmaton. IEEE Trans. Neural Networks, 14: Hong, X., C.J. Harrs, S. Chen and P.M. Sharkey, 3. Robust nonlnear model dentfcaton methods usng forward regresson. IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum., 33: Huang, G.B., P. Saratchandran and N. Sundararajan, 5. A generalzed growng and prunng RBF (GGAP-RBF) neural network for functon approxmaton. IEEE Trans. Neural Networks, 16: Laptev, I., 5. On space-tme nterest ponts. Int. J. Comput. Vson, 64: Lazebnk, S. and M. Ragnsky, 9. Supervsed learnng of quantzer codebooks by nformaton loss mnmzaton. IEEE Trans. Pattern Anal. Mach. Intell., 31: Leung, F.H.F., H.K. Lam, S.H. Lng and P.K.S. Tam, 3. Tunng of the structure and parameters of a neural network usng an mproved genetc algorthm. IEEE Trans. Neural Networks, 14: L, Y., S. Qang, X. Zhuang and O. Kaynak, 4. Robust and adaptve backsteppng control for nonlnear systems usng RBF neural networks. IEEE Trans. Neural Networks, 15: L, K., J.X. Peng and G.W. Irwn, 5. A fast nonlnear model dentfcaton method. IEEE Trans. Autom. Control, 5: L, K., J.X. Peng and E.W. Ba, 6. A two-stage algorthm for dentfcaton of nonlnear dynamc systems. Automatca, 4: L, S.Z. and Z.W. Wang, 14. Adaptve fractal-wavelet mage denosng based on multvarate statstcal model. Chn. J. Comput., 7: Neruda, R. and P. Kudova, 5. Learnng methods for radal bass functon networks. Future Gen. Comput. Syst., 1: Orr, M.J.L., Regularzaton n the selecton of radal bass functon centers. Neural Comput., 7: Oyang, Y.J., S.C. Hwang, Y.Y. Ou, C.Y. Chen and Z.W. Chen, 5. Data classfcaton wth radal bass functon networks based on a novel kernel densty estmaton algorthm. IEEE Trans. Neural Network, 16: Panchapakesan, C., M. Palanswam, D. Ralph and C. Manze,. Effects of movng the center's n an RBF network. IEEE Trans. Neural Networks, 13: Park, J. and I.W. Sandberg, Unversal approxmaton usng radal-bass-functon networks. Neural Comput., 3: Peng, H., T. Ozak, V. Haggan-Ozak and Y. Toyoda, 3. A parameter optmzaton method for radal bass functon type models. IEEE Trans. Neural Networks, 14: Peng, J.X., K. L and D.S. Huang, 6. A hybrd forward algorthm for RBF neural network constructon. IEEE Trans. Neural Networks, 17: Polycarpou, M.M., 1. Fault accommodaton of a class of multvarable nonlnear dynamcal systems usng a learnng approach. IEEE Trans. Autom. Control, 46: Veeraraghavan, A., A.K. Roy-Chowdhury and R. Chellappa, 5. Matchng shape sequences n vdeo wth applcatons n human movement analyss. IEEE Trans. Pattern Anal. Mach. Intell., 7: Wang, L. and N.H. Yung, 1. Extracton of movng objects from ther background based on multple adaptve thresholds and boundary evaluaton. IEEE Trans. Intell. Transp. Syst., 11:

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