APLSSVM: Hybrid Entropy Models for Image Retrieval

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1 Internatonal Journal of Intellgent Informaton Systems 205; 4(2-2): 9-4 Publshed onlne Aprl 29, 205 ( do: 0.648/j.js.s ISSN: (Prnt); ISSN: (Onlne) APLSSVM: Hybrd Entropy Models for Image Retreval L Jun-y, L Jan-hua, Zhu Jn-hua 2, Chen Xao-hu 3 Shool of Eletron Informaton and Eletral engneerng, Shangha JaoTong Unversty, Shangha, Chna 2 College of Network Communaton Zhejang Yuexu Unversty of Foregn Languages, Zhe Jang, Chna 3 Informaton Engneerng Shool, Yuln Unversty, Yuln, Shanx, Chna Emal address: leejy2006@63.om (L Jun-y) To te ths artle: L Jun-y, L Jan-hua, Zhu Jn-hua, Chen Xao-hu. APLSSVM: Hybrd Entropy Models for Image Retreval. Internatonal Journal of Intellgent Informaton Systems. Speal Issue: C Content-based Image Retreval And Mahne Learnng. Vol. 4, No. 2-2, 204, pp do: 0.648/j.js.s Abstrat: Amng at propertes of remote sensng mage data suh as hgh-dmenson, nonlnearty and massve unlabeled samples, a knd of probablty least squares support vetor mahne (PLSSVM) lassfaton method based on hybrd entropy and L norm was proposed. Frstly, hybrd entropy was desgned by ombnng quas-entropy wth entropy dfferene, whh was used to selet the most valuable samples to be labeled from massve unlabeled sample set. Seondly, a L norm dstane measurng was used to further selet and remove outlers and redundant data from the sample set to be labeled. Fnally, based on orgnally labeled samples and sreened samples, PLSSVM was ganed through tranng. Expermental results on lassfaton of ROSIS hyperspetral remote sensng mages show that the overall auray and Kappa oeffent of the proposed lassfaton method reah 89.90% and respetvely. The proposed method an obtan hgher lassfaton auray wth few tranng samples, whh s muh applable to lassfaton problem of remote sensng mages. Keywords: Remote Sensng Image, L Norm, Atve Learnng, PLSSVM (Probablty Least Squares Support Vetor Mahne), Hybrd Entropy. Introduton Classfaton of remote sensng mages means to make eah pxel pont regon n the mage belong to a ategory n several ategores or one among several speal elements. The lassfaton results s to dvde mage spae nto several sub-regons, and eah sub-regon presents a pratal land objet [-2]. In atual lassfaton of remote sensng mages, there are usually massve unlabeled samples, whle the proporton of labeled samples s very small. Thus, t s very dffult to look for the nformaton n need of labelng from these massve unlabeled samples. Besdes, the st used to label these samples s very hgh. Atve learnng algorthm s a new method for sample tranng. It s dfferent from passve learnng algorthm where samples are seleted randomly [3-4]. In the proess of mahne learnng, learners an atvely hoose the data most benefal to mprovng propertes of a lassfer, automatally mark and add them n tranng samples for learnng so as to effetvely avod exessve manual nterventon and redue the number of labeled samples. The ore of atve learnng algorthm s that whh strateg seleton funton s used to selet the most valuable sample for labelng from unlabeled samples. Sne the evaluaton rtera for value are dfferent, multple atve learnng algorthms appear. Lterature [4] selets the samples for labelng whh urrent lassfer annot onfrm the ategory mostly. Generally, ths s alled unertan samplng. Ths method an fully selet the samples benefal to the lassfer, and gan better results than random algorthm. But t has large randomness, so only sub-superor samples set an be pked out. In addton, outlers and redundant data may be easly hosen [7]. The ntroduton of quas-entropy an redue samplng randomness to some extent. Lterature [8] proposes a heurst atve learnng algorthm whh selets the most possble mslassfed samples based on ommttee. Ths algorthm hooses the most possble mslassfed samples of urrent lassfer durng every samplng and elmnates the samples more than a half n the spae so as to gan faster onvergene speed than manstream seleton algorthm. Lterature [9] randomly selets unlabeled samples from unertan mslassfed samples on the verfaton set for labelng. Ths algorthm owns better auray rate than standard algorthm. But, these algorthms stll probably

2 0 L Jun-y et al.: APLSSVM: Hybrd Entropy Models for Image Retreval hoose outlers and redundant data, and alulaton omplexty s hgh. The ntroduton of entropy dfferene an help pk up mslassfed samples more onvenently. In order to get more refned sample set, hybrd entropy s ganed through fusng quas-entropy and entropy dfferene. Sne the algorthm may result n seletng outlers and redundant data, L norm dstane measurement s used to hoose these data and elmnate them. Ths paper proposes an atve learnng algorthm based on hybrd entropy and L norm. Ths algorthm mproves seleton funton from two aspets: ) the most valuable samples are seleted wth hybrd entropy, and a rough sample set to be labeled s ganed; L norm dstane measurement s used to hoose and elmnate possble outlers and redundant data; 2) remote sensng mage data usually own suh features as hgh dmenson, nonlnearty and massve data, so support vetor mahne a be used to analyze and treat them. But tradtonal support vetor mahne lassfaton method only takes nto aount of two extreme ases durng dedng sample lassfaton,.e. the label for the sample belongng to the ategory s + and the label for the sample whh does not belong to the ategory s -. However, n pratal applaton, due to the exstene of unertanty and nfluene of external fators, every sample has dfferent dvson methods. Espeally form some problems, due to sample randomness and fuzzness, they annot be lassfed nto a lass expltly, but an only lassfed nto a lass aordng to ertan probablty or ertan membershp degree. So, t s mproper to + [0]. Thus, for the samples seleted on the bass of atve learnng algorthm, PLSSVM s adopted as the lassfer to lassfy and dentty hyperspetral remote sensng mages. empress lass nformaton only wth {, } 2. Plssvm Amng at lassfaton nauray and unertanty of tradtonal support vetor mahne as well as defets of nterferene samples, Lterature [0] desgns PLSSVM to lassfy the samples whh annot be expltly lassfed nto a lass aordng to ertan probablty. In ths way, sample lassfaton has qualtatve nterpretaton and quanttatve evaluaton. Posteror probablty of sample x belongng to eah lass s: p( 2) p( ) p(2 ) p(2 ) p( ) p( 2) T T ( p, p, p ) = (0,0,,0), 2 Where, s the number of lasses; p( ) s posteror probablty that sample x belongs to the th lass under the ondton where sample x belongs to the frst lass. Smlarly, p( ) ; p m s posteror probablty that sample x belongs to the mth lass ( m =,2,, ). () Formula () an be regarded as equaton sets used to solve unknown varables p m. Through solvng Formula (), n output probablty modelng of mult-lassfaton problem, deson funton of pm of sample x n eah lass an be ganed,.e. take the lass wth the largest posteror probablty as the sample. The lass that x belongs to s as follows: y( x) = argmax( p ). m=,2,, 3. Atve Learnng Based on Hybrd Entropy and L Norm Labeled sample setl = {( x, y),( x2, y2),,( xl, yl)} from unknown dstrbuton and an unlabelled sample set U = { xl +, xl + 2, xn} are gven. Overall sample set s χ = L U. There are lasses. x R d ( =,2,, n; d refers to the number of dmensons of samples) and y {,2,, } s the label of sample x. The system adopts labeled sample set L as the tranng set to gan ntal PLSSVM lassfer, and atvely selets some samples wth large nformaton quantty from unlabelled sample set U aordng to a strategy. Then, experts label them and add them n the tranng set. Thus, new PLSSVM lassfer s obtaned. After repeated yles, lassfaton results wll fnally reah the threshold value of an evaluaton ndex or spefed yle tmes. A. Sample seleton strategy based on hybrd entropy The lassfer may easly make mstakes durng judgng the most unertan sample lassfaton, thus leadng to low lassfaton auray rate. Therefore, unertanty s an mportant fator that experts should onsder when seletng the samples to be labeled. Sample unertanty algorthms an be based on Shannon entropy, posteror probablty and the nearest boundary et. The algorthm based on Shannon entropy has ganed good results n many applatons, but t annot selet the optmal samples so that alulaton omplexty s hgh durng tranng the set. Thus, optmzaton seleton standard (.e. quas-entropy wth hgh qualty fator) s needed to measure sample unertanty. Lterature [] a ponts out that qualty fator of p (0 < a < ) onvex funton s hgher than that of plogp. If the qualty fator s larger, quas-entropy s more senstve to probablty dstrbuton evenness near the mnmum value, and the shape of mnmum value of quas-entropy s shaper. So, quas-entropy surpasses Shannon entropy n terms of sgnfane ndex of mnmum value. Therefore, quas-entropy wth hgh qualty fator replaes Shannon entropy. Assumng posteror probabltes that sample x belongs to every lass are p, p2, p, and m m= (2) pm = s met, unertanty measure of samplex an be expressed as λ = f ( p ) (3) m= m

3 Internatonal Journal of Intellgent Informaton Systems 205; 4(2-2): 9-4 a Where, f ( pm) = pm; λ has the followng propertes: Property : when posteror probablty dstrbuton s most even (.e. all p m are equal), λ s the mnmum and equal to f (/ ). Ths s also the stuaton where unertanty s the largest. It an be known from Property that when posteror probabltes p m that sample x belongs to every lass are equal, sample unertanty s the largest, and the value of quas-entropy λ s the smallest. So, quas-entropy an be sued to fgure out unertanty measurement value of eah sample. If quas-entropy value of samples s smaller, the nformaton quantty s larger. In nformaton entropy, the samples whh may be easly mslassfed an be expressed wth the absolute value of dfferenes of two absolute values: d = H( p ) H( p ), max se H( p ) = p log p, max max max H( p ) = p log p, se se se Where, p max s the maxmum posteror probablty that samplex belongs to every lass; pse s the seond largest posteror probablty that samplex belongs to every lass. Entropy dfferene dstane metr funton of densty funtons p max and pse of the two posteror probabltes have the followng haraterst [2] (4) pmax pse = L pmax pse (5) 2 Where, pmax pse L s standard Mnkowsk L norm dstane measurement, then H p H p p p (6) ( max) ( se) max se L Ths haraterst shows retreval results of Entropy dfferene dstane metr s nluded n retreval results of L norm dstane measurement, and the retreval range narrows. It an be seen from Formula (4), when posteror probablty of samples hanges slghtly, and the hange n entropy value wll also be small. When entropy dfferene value s smaller, the possblty that sample x belongs to some two lasses s lose,.e. ths sample may be mslassfed most easly, and the nformaton quantty s also the largest. Aordng to analyss of quas-entropy and entropy dfferene, the followng onlusons an be drawn: f quas-entropy value s smaller, sample unertanty s larger; entropy dfferene value s smaller, the sample may be mslassfed more easly. If the values of quas-entropy and entropy dfferene are smaller, nformaton quantty s larger and there are larger mpats n lassfaton effets. In massve data sets, the sample sze seleted purely by quas-entropy or entropy dfferene strategy s also large. In order to pk out more refned samples and redue labelng ost, quas-entropy and entropy dfferene are fused to gan a new sample seleton measurement strategy - hybrd entropy. u = λd. (7) M samples wth the hghest nformaton quantty are worked out aordng to Formula (7),.e. M samples wth the smallestu value. B. Sample smlarty measurement based on L norm The samples seleted by hybrd entropy may have outlers and redundant data. These data make lttle ontrbutons to lassfaton auray of the lassfer and even wll affet ts lassfaton auray. Therefore, L norm dstane measurement wll be adopted to work out smlarty among samples. Outlers and redundant data wll be removed aordng to smlarty value. Lterature [3] adopts L norm, L 2 norm and quadr expresson to ompare data retreval propertes. The testng results show these dstane measurement methods dffer lttle n retreval property. L norm dstane measurement s more robust than L 2 norm dstane measurement, and L norm dstane measurement s the most smplest n alulaton. So, L norm dstane measurement s adopted to alulate smlarty among samples to be labeled. s d = x x hj hk jk k = ( h, j =,2,, v), Where, x hk andx jk are the kth attrbute n the hth and jth samples; v s the number of samples. Assumng mean spae dstane of samples of the same lass s θ, a = θ /00, β = θ. If shj < a, samplex j s judged to be redundant nformaton and elmnated; f mns hj > β, samplex j s judged to be an outler and deleted. Then, the remanng samples are seleted and submtted to experts for labelng. Ths deletes outlers, elmnates redundant data, further narrows sale of sample set to be labeled and redues ost of manual labelng. 4. Algorthm Steps Input: labeled sample set s expressed as L and unlabelled sample set s expressed as U; the number of samples s expressed as M; endng ondton s expressed as S; the parameter s expressed as a. Algorthm proess: ) Tran lassfer PLSSVM wth labeled sample set; 2) Carry out a~g repeatedly untl endng ondton S s met; a) Posteror probablty that unlabeled sample set U belongs to eah lass s alulated wth lassfer PLSSVM; b) Calulate quas-entropy λ and entropy dfferene d of unlabeled samples aordng to posteror probablty ganed, Formula (3) and (4); ) Calulate hybrd entropyu aordng to Formula (7);, (8)

4 2 L Jun-y et al.: APLSSVM: Hybrd Entropy Models for Image Retreval d) Selet m samples wth the smallest u value and add them n the sample set to be labeled; e) Calulate smlarty of M samples aordng to Formula (8), elmnate the samples meetngs hj < a and mns hj > β, and make the remanng samples form new sample subset A; f) Submt A to experts for labelng and add labeled samples n L; g) PLSSVM. Utlze L to tran lassfer PLSSVM agan. Output: tran sample set L fnally labeled and gan lassfer PLSSVM. 5. Experment and Analyss A. ROSIS hyperspetral expermental data ROSIS hyperspetral expermental data ome from Lterature [4]. Spetral regon s 0.43~0.86 µm, wth pxel, 03 wave bands and.3 spatal resoluton. Besdes, tranng regon and testng regon atually measured synhronously are provded. The tranng samples nlude 9 lasses of land objets: btumnous (548 pxel), tree (524 pxel), brk (54 pxel), shadow (23 pxel), pth roof (375 pxel), bare land (532 pxel), metal plate (265 pxel), grt (392 pxel) and grassland (540 pxel). Testng samples nlude 9 lasses of land objets: btumnous (6592 pxel), tree (3064 pxel), brk (3682 pxel), shadow (942 pxel), pth roof (330 pxel), bare land (5029 pxel), metal plate (345 pxel), grt (2099 pxel) and grassland (8675 pxel). ENVI4.7 software s utlzed to transform orgnal data orrespondng to the regons ROSIS hyperspetral mage tranng sample and testng sample are nterested n to ASCII data so as to proess data n Matlab 7.8 envronment. B. Calfaton results of remote sensng mage and analyss of results Atve learnng algorthm s adopted to selet tranng samples for the lassfer and to onstrut two types of APLSSVM, expressed as APLSSVM and APLSSVM2 n ths paper. In the experment proess, parameter settng s as follows: kernel funton of PLSSVM adopts polynomal kernel funton; the optmal values of penalty parameter C and kernel parameter γ are onfrmed wth ross valdaton method, a=0.6 and M=00. ) Based on the same ntal sample set, hange the number of newly-added tranng samples, evaluate effets of the number of newly-added tranng samples on lassfaton auray of two type of APLSSVM; the endng ondton S s that the dfferene between adjaent two lassfaton auraes s less than or the number of teraton tmes reahes 5. Ths Btumnous Tree Br k Table. Confuson matrx obtaned by APLSSVM Shadow Pth roof ndates hgh lassfaton auray an be ganed when PLSSVM s used to proess remote sensng mages; when the number of newly-added tranng samples s less than 300, lassfaton auray of APLSSVM boots rapdly wth the rse n the number of labeled samples; when the number of newly-added tranng samples exeeds 300, lassfaton auray of APLSSVM basally tends to be stable and mantans about 90% wth the rse n the number of labeled samples; for APLSSVM2, ts lassfaton auray nreases slowly wth the rse n the number of labeled samples; to reah the same lassfaton auray wth APLSSVM, APLSSVM2 needs more labeled samples, whh wll onsumes more tme and energy of experts. So, the ost s expensve. 2) In the experment, gven tranng samples serve as the ntal sample set. Under the ondton where the number of newly-added tranng samples s the same, lassfaton effets of two APLSSVM lassfers and passve PLSSVM lassfer are ompared. APLSSVM and APLSSVM2 selets newly-added tranng samples for labelng through teraton of atve learnng algorthm; passve PLSSVM dretly selets samples of the same number as newly-added samples for tranng. The number of tranng samples the three lassfers selet s: orgnal sample set newly-added samples. The endng ondton S s that the number of teratons reahes 3. Table, Table 2 and Table 3 are onfuson matrx and Kappa oeffent orrespondng to eah fgure. It an be seen that APLSSVM2 and passve PLSSVM lassfy most grassland nto bare land, and the mslassfaton phenomenon s serous; APLSSVM performs relatvely well n ths aspet and an well lassfy the two types of land objets; mslassfaton auray of other land objets approahes for the three lassfers. The followng an be ganed aordng to Table -3: User s auray: among all knds of land objets, user s auray dffers mostly for bare land. User s auray of APLSSVM s 80.04%, up over 30% ompared wth user s auray of APLSSVM2 and passve PLSSVM. Aordng to onfuson matrx n Table 2 and Table 3, APLSSVM2 and passve PLSSVM mslassfy most grassland nto bare land. Thus, the proporton of grassland n bare land samples exeeds a half. For pth roof, the largest user s auray of APLSSVM2 s 83.90%, followed by APLSSVM (70.29%), and passve PLSSVM has the smallest user s auray (65.58%). For the three lassfers, user s auray dffers lttle among other land objets. Bare land Metal plate Grt Grassland User s auray/% Btumnous Tree Brk Shadow

5 Internatonal Journal of Intellgent Informaton Systems 205; 4(2-2): Btumnous Br Bare Metal Tree Shadow Pth roof k land plate Grt Grassland User s auray/% Pth roof Bare land Metal plate Grt Grassland Produer s Overall auray=89.90% auray/% Kappa= Btumnous Tree Brk Table 2. Confuson matrx obtaned by APLSSVM 2 Shado w Pth roof Bare land Metal plate Gr t Grassla nd Btumnous Tree Brk Shadow Pth roof Bare land Metal plate Grt Grassland Produer s auray/% Btumnous Tre e Table 3. Confuson matrx obtaned by passve PLSSVM Br k Shadow Pth roof Bare land Metal plate Gr t Grasslan d User s auray/% Overall auray=8.56% Kappa=0.769 Btumnous Tree Brk Shadow Pth roof Bare land Metal plate Grt Grassland Produer s auray/% User s auray/% Overall auray=78.48% Kappa= Produer s auray: produer s auray of grassland dffers most greatly. Produer s auray of APLSSVM s 9.90%, up over 20% ompared wth produer s auray of APLSSVM2 and passve PLSSVM. Aordng to onfuson matrxes n Table 2 and Table 3, nearly /3 grassland samples are mslassfed nto bare land. Produer s auray of other land objets approahes for the three lassfers. Overall auray and Kappa oeffent: sne overall auray takes nto aount of orrespondng weght relatonshp of eah lass, t s relatvely objetve; sne Kappa oeffent onsders the prelateshp between user s auray and produer s auray, t has beome lassfaton auray evaluaton ndex of remote sensng mages together wth overall auray. Based on analyss of Table -3, overall auray and Kappa oeffent of APLSSVM are the hghest, followed by APLSSVM2. Passve PLSSVM performs most poorly. Experment results show, APLSSVM over onsders sample unertanty and samples whh may be easly mslassfed, and elmnates outlers and redundant data from samples to be seleted. Fnally, more refned tranng sample set s ganed. Therefore, under the same number of tranng samples, APLSSVM has hgher lassfaton auray than other lassfers. 6. Conlusons a) Hybrd entropy ganed through fusng quas-entropy and

6 4 L Jun-y et al.: APLSSVM: Hybrd Entropy Models for Image Retreval entropy dfferene an measure sample unertanty and avod sample mslassfaton. Sample seleton strategy based on hybrd entropy an hoose more refned samples and redue the ost of manual labelng. b) Sample smlarty measurement method based on L norm an sreen out outlers and redundant data, whh further redues the sale of sample set to be labeled and ost of manual labelng. ) Compared wth heurst atve learnng algorthm whh selets the most possble mslassfed samples based on ommttee, atve learnng algorthm based on hybrd entropy and L norm an pk out more valuable samples to be labeled and gan hgh lassfaton auray wth few tranng samples. d) PLSSVM owns both qualtatve explanaton and quanttatve evaluaton durng lassfyng unertan samples, sutable for lassfyng remote sensng mage data. e) For remote sensng mage data wth massve unlabelled samples, atve learnng an help fnd out the most valuable nformaton from massve unlabeled samples. Compared wth passve PLSSVM whh selets samples randomly, APLSSVM owns hgher lassfaton auray. Referenes [] WANG Yuan-yuan, CHEN Yun-hao, LI Jng. Applaton of model tree and support vetor regresson n the hyperspetral remote sensng [J]. Journal of Chna Unversty of Mnng & Tehnology, (6): [2] CHEN Shao-je, LI Guang-l, ZHANG We, et al. Land use lassfaton n oal mnng area usng remote sensng mages based on multple lassfer ombnaton [J]. Journal of Chna Unversty of Mnng & Tehnology, 20, 40(2): [3] HAMANAKA Y, SHINODA K, TSUTAOKA T, et al. Commttee-based atve learnng for speeh reognton [J]. IEICE Transatons on Informaton and Systems, 20, 94(0): [4] ZHANG L J, CHEN C, BU J J, et al. Atve learnng based on loally lnear reonstruton[j]. IEEE Transatons on Pattern Analyss and Mahne Intellgene, 20, 33(0): [5] SUN Z C, LIU Z G, LIU S H, et al. Atve learnng wth support vetor mahnes n remotely sensed mage lassfaton[c]//qiu P H. YIU C. ZHANG H. et al. Proeedngs of the 2nd Internatonal Congress on Image and Sgnal Proessng. Psataway: IEEE Computer Soety. 2009: -6. [6] TUIA D. RATLE F. PACIFICI F. et al. Atve learnng methods for remote sensng mage lassfaton [J]. IEEE Transatons on Geosene and Remote Sensng, 2009, 47(7): [7] CHEN Y, HE Z. Blnd separaton usng a lass of new ndependene measures[c]//ieee. Proeedngs of IEEE Internatonal Conferene on Aousts, Speeh, and Sgnal Proessng. Psataway: IEEE Sgnal Proess, 2003: [8] LONG J, YIN J P, ZHU E. An atve learnng method based on most possble mslassfaton samplng usng ommttee [J]. Leture Notes n Computer Sene : [9] BRUZZONE L, PERSELLO C. Atve learnng for lassfaton of remote sensng mages[c]//ieee. Proeedngs of IEEE Internatonal Geosene and Remote Sensng Symposum. Psataway: IEEE In-orporated, 2009: [0] GAO Y, WANG X S, CHENG Y H, et al. Fault dagnoss usng a probablty least squares support vetor lassfaton mahne [J]. Mnng Sene and Tehnology, 200, 20(6) : [] CHEN Yang. Propertes of quas-entropy and ther applaton [J]. Journal of Southeast Unversty: Natural Sene Edton, 2006, 36(2): [2] COX I J,MILLER M L, MINKA T P, et al. The bayesan mage retreval system, PeHunter: theory, mplementaton, and psyehophyseal experments [J]. IEEE Transatons on Image Proessng, 2000, 9(): [3] JOHN R S. Integrated spatal and feature mage systems: retreval, analyss, and ompresson [D]. New York: Columba Unversty, 997. [4] WEI L, SAURABH P. JAMES E F. et al. Loalty-preservng dmensonalty reduton and lassfaton for hyperspetral mage analyss [J]. IEEE Transatons on Geosene and Remote Sensng, 202, 50(5):