Odor Recognition in Multiple E-nose Systems with Cross-domain Discriminative Subspace Learning

Transcription

1 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Odor Reognton n ultple E-nose ystems wth Cross-doman Dsrmnatve ubspae Learnng Le Zhang, ember, IEEE, Yan Lu, and nglng Deng Abstrat In ths paper, we propose an odor reognton framework for multple eletron noses (E-nose, mahne olfaton odor perepton systems. traght to the pont, the proposed transferrng odor reognton model s alled ross-doman dsrmnatve subspae learnng (CDL. General odor reognton problems wth E-nose are sngle doman orented, that s, reognton algorthms are often modeled and tested on the same one doman dataset (.e., from only one E-nose system. Dfferent from that, we fous on a more realst senaro: the reognton model s traned on a prepared soure doman dataset from a master E-nose system A, but tested on another target doman dataset from a slave system B or C wth the same type of the master system A. he nternal deve parameter varane between master and slave systems often results n data dstrbuton dsrepany between soure doman and target doman, suh that sngle doman based odor reognton model may not be adapted to another doman. herefore, we propose doman adaptaton based odor reognton for addressng the realst reognton senaro aross systems. pefally, the proposed CDL method onssts of three merts: an ntra-lass satter mnmzaton and nter-lass satter maxmzaton based dsrmnatve subspae learnng s solved on soure doman. a data fdelty and preservaton onstrant of the subspae s mposed on target doman wthout dstorton. 3 a mn-path feature weghted doman dstane s mnmzed for losely onnetng the soure and target domans. Experments and omparsons on odor reognton tasks n multple E-noses demonstrate the effeny of the proposed method. Index erms Odor reognton, eletron nose, doman adaptaton, ross-doman learnng, subspae learnng O I. IRODUCIO DOR reognton by usng an eletron nose (E-nose s an nterestng but hallengng ssue n mahne olfaton. he hallengng aspet les n the tehnal gap of olfatory sensors, wth respet to the vson sensors (e.g., magng sensor. In mahne olfaton ommunty, E-nose plays an mportant role n odor pereptron and data analyss based on pattern reognton algorthms [, ]. E-nose, as a ross-senstve odor pereptron deve wth ntellgent sgnal proessng and pattern hs work was supported n part by atonal atural ene Foundaton of Chna (Grant 6448 and n part by the researh fund for Central Unverstes. L. Zhang, Y. Lu and. Deng are wth the College of Communaton Engneerng, Chongqng Unversty, Chongqng 444, Chna. (e-mal: lezhang@qu.edu.n; yanlu@qu.edu.n; dengpl@qu.edu.n Known Odors Unknown Odors erepton erepton E-nose system A (master E-nose system B (slave Data aquston odel ranng hase on ystem A Data aquston odel estng hase on ystem B attern Reognton Cross-doman Learnng odel arameters Deson Fg.. Dagram of the proposed odor reognton framework. he model tranng (ross-doman learnng s mplemented n C based on the aqured odor data from master system A, and the well-traned model parameters wll be used to reognze the odors from slave B. reognton unts, has wtnessed a wde progress n systems, applatons, and algorthms durng the past two deades [3-6]. pefally, Flammn et al. proposed a low-ost nterfae to hgh-value resstve sensors over a wde range, suh that a wde deteton range s possble [7]. Brudzewsk et al. [8] proposed a dfferental eletron nose for reognton of offees. Herrero-Carrόn et al. [9] proposed an atve and nverse temperature modulaton E-nose for odorant lassfaton. Gosang and Guterrez-Osuna [] proposed an atve temperature programmng method for odor reognton. Yn et al. [] also proposed a temperature modulaton method n E-nose for gases reognton, and the reognton auray wth fewer sensors an also be guaranteed by modulaton. In odor reognton, a number of pattern reognton algorthms for lassfaton and regresson have been presented for E-nose [-5], suh as support vetor mahnes (V, neural networks (A, dsrmnant analyss (DA, learnng vetor quantzaton (LVQ, et. udu et al. [6] proposed an nremental fuzzy approah for lassfaton of blak tea qualty wth an E-nose, suh that the newly presented patterns an be automatally nluded n the tranng set beause of the nremental learnng ablty. Zhang et al. [7] proposed a hybrd lnear dsrmnant analyss based support vetor mahne method for lassfaton of sx knds of ar ontamnants, and aheved the best auray. For those readers of nterest, some exellent revews n mahne olfaton

2 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Y enter X d 3 enter lass lass oure doman enter ew subspae enter enter d X 3 enter arget doman lass enter lass enter Classfer/Deson Fg.. hemat dagram of the proposed CDL method; after a subspae projeton, the soure doman and target doman of dfferent spae dstrbuton le n a latent subspae wth good dstrbuton onssteny (the enters of both domans beome very lose and drft s removed; n ths latent subspae, the lassfaton of two lasses s suessfully aheved. Formally, the upper oordnate system denotes the raw data ponts of soure doman and target doman n three dmensons. We use the word enter to represent the mean of the features. From the upper fgure, we an see that the dfferene between the mean of soure doman and the mean of target doman s large n eah dmenson. After a subspae projeton n the below fgure, we an see that the values of and beome smaller, whh demonstrate that the dstrbuton dfferene beomes small, and both domans of dfferent spae dstrbuton le n a latent ommon subspae wth good dstrbuton onssteny. and E-nose that have desrbed pattern lassfaton and sgnal proessng methods an be referred to as [8,9]. By revewng these researh fndngs desrbed above, we an observe a ommon property, that s, all these works tend to study hghly effent and effetve odor reognton algorthms n a sngle E-nose system. hs an be reognzed to be method drven. It s useful to reveal some better algorthms for mprovng the odor reognton performane of an E-nose. However, n real applaton senaros, multple E-nose systems of the same type would be developed for odor deteton and reognton. An essental ssue that we should pay attenton to s that although multple systems are of the same type, the well-traned reognton algorthm based on one system annot be easly adapted to another system. An explt reason s the nternal output dfferenes (e.g., sgnal shft between gas sensor arrays n multple systems. Another reason s the slow nstrumental agng of sensors (e.g., sgnal drft when exposed to ar for a long tme. It s just the hallengng Y d X aspet of mahne olfaton lamed at the begnnng of ths seton. he undesred result aused by ths ssue s that the obtaned mahne learnng algorthm based on E-nose system A annot be transferred to another E-nose system B of the same type. herefore, the dverse applaton of E-noses s serously restrted. hs s exatly what we are payng attenton to and amng to solve n ths paper. In terms of the non-transferrable restrton of E-nose n odor reognton, we propose a novel transferrng odor reognton framework, whh targets at odor reognton aross systems. pefally, the dagram of the proposed odor reognton framework s desrbed n Fg., whh nludes two parts: model tranng phase on system A (defned as master and model testng phase on system B (defned as slave. o effetvely address ths ssue, nspred by transfer learnng [] and doman adaptaton [] n mahne learnng ommunty, eah system s treated as a doman. hus, the master E-nose system s vewed as soure doman and other slave systems are vewed as target domans n ths paper. From the vewpont of doman dstrbuton (.e., data dstrbuton, the data dstrbuton between soure doman (master system and target doman (slave system s dfferent. hat s, the data n soure and target doman le n dfferent feature spaes. herefore, we propose a ross-doman dsrmnatve subspae learnng (abbrevated as CDL method, by pursut of a ommon (shared subspae of both doman data, suh that the data from dfferent domans le n the same (ommon subspae. hen, wth the proposed CDL method, we are able to aheve transferrng odor reognton aross multple systems (.e., aross domans. pefally, the merts of the proposed CDL method are three-fold: he am of the proposed CDL s to learn a ommon subspae (projeted by a transformaton suh that the soure and target domans share smlar feature dstrbuton. Consderng that our fnal task s lassfaton, and the lassfaton apablty should be augmented n the learned subspae. hus, n CDL, a dsrmnatve mehansm on the soure doman data s ntegrated, by mnmzng the ntra-lass satter matrx and smultaneously maxmzng the nter-lass satter matrx. hat s, the lass separablty of the soure doman data n the subspae an be further guaranteed wth the dsrmnatve learnng mehansm. o preserve the struture of the target doman data n the learned subspae and avod the target data dstorton, a data fdelty onstrant s mposed n CDL. Wth ths onstrant, muh avalable nformaton n the target doman we are nterested (e.g., drft knowledge s effetvely preserved. o learn a ommon subspae of soure and target data, we propose a soure to target doman dstane mnmzaton term n the learned subspae, suh that the doman dstrbuton onssteny an be mproved. Further, onsderng that the doman dstrbuton s feature-spef, that s, dfferent feature dmenson may have dfferent dstrbuton dsrepany degree, we further propose a novel and effetve mn-path feature weghted doman dstane representaton. he weghts measure the degree of feature msmath between soure and target doman. A larger

3 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 weght denotes a hgher feature msmath degree. Wth above haratersts of the proposed CDL, a ommon (shared, dsrmnatve, and robust subspae projeted by an be aheved. Further, the transferrng odor reognton aross domans (aross multple systems an be mproved wth the proposed CDL approah. Vsually, the shemat dagram of the proposed CDL s shown n Fg., from whh we an see that the ultmate goal s to aheve transferrng odor reognton (lassfaton n the learned new subspae. he learnng proess of s ompleted by jontly modelng on the soure doman and target doman, based on three key haratersts (merts: dsrmnatve learnng on soure doman, data fdelty on target doman and mn-path feature weghted doman dstane. he remander of ths paper s as follows. eton II presents the related works of shft albraton, drft orreton and subspae learnng. eton III desrbes the proposed ross-doman dsrmnatve subspae learnng (CDL approah nludng the model formulaton, optmzaton and lassfaton. he experments and results have been dsussed n eton IV. Fnally, eton V onludes ths paper. II. RELAED WORK A. hft Calbraton (Reprodublty he sgnal shft n E-nose s an nherent problem, whh results from the reprodublty of gas sensors []. Brefly, when two dental E-nose systems are exposed to the same ondtons, ther outputs are not the same. One reason s that the system s related to the physal ondton suh as temperature, humdty and pressure. Researhers have proposed dfferent methods to albrate the sgnal shft, suh as global affne transformaton based on robust weghted least square (GA-RWL [], the wndowed peewse dret standardzaton (WD [3], partal least square regresson (L [4], and unvarate dret standardzaton [5]. hese methods are suessful n shft albraton. However, the albraton model onstruton depends on the data amount, and thus the albraton beomes task spef. hat s, for dfferent odor reognton, the re-albraton should be onduted and also the generalty s too weak. Addtonally, the albraton s dretly shown n sgnal magntude, and ndependent of the subsequent learnng algorthm. B. Drft Correton (Agng Drft, that s supposed to be some slow, ontnuous and unertan effet, s affetng the lassfaton performane of an E-nose. ensor drft effet s aused by many objetve fators suh as agng, posonng, and the flutuatons of the ambent envronmental varables (e.g., humdty, temperature [5]. As a result, the nstrument responds dfferently to a onstant onentraton of some ontamnant at dfferent ambent ondtons. Drft s one thought to be an ll-posed problem due to ts very rregular haratersts. Although researhers have proposed several methods to orret drft [6-3], the results are stll unsatsfatory when both drft and shft happen. ore mportantly, these methods were proposed for drft ompensaton ndependent of shft. Our proposed work ams to solve more omplex transferrng odor reognton aross multple systems (.e., drft plus shft. pefally, Yan and Zhang [6] proposed an autoenoder method for tme-varyng drft orreton. Bg data should be used for tranng a deep model. artnell et al. proposed an artfal mmune system based adaptve lassfer for drft mtgaton [7], however the lassfer has no knowledge transfer ablty. Vergara et al. proposed a lassfer ensemble model for drft ompensaton, n whh multple Vs wth weghted ensemble are used [8]. he ensemble method an mprove the lassfer robustness, but t laks transfer ablty aross systems. Zhang et al. [9] proposed a doman adaptaton extreme learnng mahne based transfer learnng method for drft ompensaton, whh ams at proposng a robust lassfer but laks feature representaton ablty. adlla et al. [3] proposed an orthogonal sgnal orreton method for reognzng and removng the drft omponents, whh mposes a strong assumpton about the data property (e.g., orthogonalty. D Carlo et al. [3] proposed to orret drft evolutonarly by learnng a transformaton wth respet to the best pattern reognton auray, n whh overfttng s easly aused due to the lak of neessary onstrant on the transformaton. C. ubspae Learnng ubspae learnng ams at learnng a low-dmensonal subspae. everal popular subspae methods nlude prnpal omponent analyss (CA [3], lnear dsrmnant analyss (LDA [33], manfold learnng based loalty preservng projetons (L [34], and margnal fsher analyss (FA [35]. pefally, CA, as an unsupervsed method, ams at preservng the maxmum varane (energy of the raw data. LDA s a supervsed dmenson reduton method, whh targets maxmzng the between-lass satter matrx trae and mnmzng the wthn-lass satter matrx trae, suh the lnear separablty s mproved n the dsrmnatve subspae. L s an unsupervsed dmenson reduton tehnque wth manfold assumpton and graph embeddng, whh preserves the loal affnty struture n low dmensonal embeddng. FA s reognzed to be a omprehensve verson of LDA and L, whh ntegrates the ntra-lass ompatness and the graph embeddng. hese subspae learnng methods are applable to sngle doman senaros, but annot be adapted to the transferrng odor reognton senaro aross domans. herefore, ross-doman subspae learnng model s desred for the proposed transferrng senaro. III. CRO-DOAI DICRIIAIVE UBACE LEARIG A. otatons In ths paper, the soure and target doman are defned by subsrpt and, respetvely. he tranng data of soure and target doman s denoted as [ ] and [ ], respetvely, where D s the dmensonalty, and are the number of tranng samples n soure and target domans. [ ] denotes the labels wth respet to the soure data. Let

4 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 represents a bass transformaton that would map the soure and target data from the raw spae to a new lower-dmensonal subspae. he symbol and denotes the Frobenus norm and l -norm, respetvely. ( denotes the trae operator and ( denotes the transpose operator. hroughout ths paper, matrx s wrtten n aptal bold fae, vetor s shown n lower bold fae, and varable s wrtten n tals. B. roblem Formulaton As llustrated n Fg., we am to learn a bass transformaton that maps the orgnal spae of soure data and target data to a new subspae,.e., and, suh that the feature dstrbuton between the mapped soure and target data [ ] and [ ] beomes smlar. herefore, t s ratonal to have an dea that the mean dstrbuton dsrepany between Y and Y an be mnmzed. Consderng that the dsrepany between domans s feature-spef (sensor-spef, that s, the dsrepany of eah feature dmenson between domans may be dfferent n real applaton, we propose a mn-path feature spef doman dstane (D to exatly desrbe the dstrbuton dsrepany by mposng dfferent weghts on eah mn-path feature ombnaton. hen, after doman adaptaton, the D s expeted to be mnmzed. pefally, the proposed D mnmzaton s formulated as follows. mn j j k w μ μ mn w y y ( k where denotes the sze of mn-path features, w denotes the weght of the -th mn-path, and denote the soure and target doman enter of the -th mn-path after doman adaptaton. denotes the projeted soure data sample j under the -th mn-path and represents the projeted target data sample k under the -th mn-path. As an be seen from the D mnmzaton, the weght w s expeted to be larger f the -th mn-path has smaller dstrbuton dsrepany. herefore, w s omputed as follows. w j k u j j j u j j u u u k k u u where w s alulated based on between-enter dstane whh an reflet the drft or dsrepany degree, and <w <. and represent the enters of the -th mn-path of soure and target data, respetvely. hey an be omputed as j x j u ( u (3 k u x (4 k where denotes the j-th soure data sample under the -th mn-path and represents the k-th target data sample under the -th mn-path. Aordng to the subspae projeton, the new representaton of soure and target data of the -th mn-path n the lower-dmensonal subspae an be formulated as Y Y,,,, x,, x y,, y,,,, x,, x y,, y X (5 X (6 j herefore, we have y x and y x. By substtutng Eqs.(5 and (6 nto Eq.(, the mnmzaton problem Eq.( an be reformulated as mn w j j x j k he narrowed mean dstrbuton dsrepany between soure and target doman after usng the learned projeton an be guaranteed by mnmzng (7. However, the dsrmnatve property among multple lasses annot be expltly shown. hat s, the separablty of multple odors n the soure doman s not effetvely desrbed. herefore, n the proposed CDL model, we would also lke to desgn a dsrmnatve term that tends to mnmze the trae of the ntra-lass satter matrx and smultaneously maxmze the trae of the nter-lass satter matrx of the soure data, suh that the ntra-lass ompatness and nter-lass separablty an be mproved. As a result, the lassfaton benefts from dsrmnaton beomes easer n the learned lnear subspae. pefally, we am to maxmze the rato between the nter-lass and the ntra-lass satter as follows, r max r b w max r r C r max C r, u, C C j x k μ μμ μ y μ y μ u uu u xclass yclass,, where μ and μ u.,,, x u x u,, j, herefore, the dsrmnatve term (8 an be further smplfed as B (7 (8 r max (9 r where and an be omputed as follows B C W u, uu, u (

5 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Algorthm. he proposed CDL Input: oure data, target data,,, d, and the mn-path sze ; roedure:. Compute the enter of the -th (=,, mn-path va (3;. Compute the enter of the -th (=,, mn-path va (4; 3. Compute the nter-lass satter matrx va (; 4. Compute the ntra-lass satter matrx va (; 5. Compute the weght w of the -th mn-path (=,, va (; 6. Compute the matrx R and Q va (5; 7. olve the egenvalue deomposton problem (; 8. Compute the optmal subspae, - va (; Output: he bass transformaton (.e., subspae projeton. W C x u, x u, ( xclass where u represents the enter of soure data and u, represents the enter of lass of soure data n the raw spae. Further, to guarantee that the projeton does not dstort the data of target doman, muh avalable nformaton should be preserved n struture under the ross-doman subspae representaton. herefore, for target data, t s ratonal to maxmze the followng term, maxr X X maxr X X ( It means that by addng Eq. ( as a onstrant n the model, the varane (energy of the target data n the new subspae an also be maxmzed. herefore, muh avalable nformaton n target doman an be preserved wthout dstortng the data. For learnng a robust ross-doman subspae, three unts suh as Eq.(7, Eq.(9 and Eq.( have been formulated n the proposed CDL model. In summary, the model has the followng three haratersts: As formulated n Eq. (7, the mn-path feature spef doman dstane s mnmzed, suh that the proposed model an effetvely handle the feature-spef dstrbuton dsrepany. From the vewpont of eletron nose, the drft s sensor-spef. herefore, t an be treated ndvdually or n mn-path as shown n our model. As formulated n Eq. (9, the dsrmnatve property (.e., separablty an be well desrbed, suh that n the learned subspae, dfferent lasses of the soure doman an be easly lassfed. he objetve of ross-doman subspae learnng s to mprove the probablty dstrbuton onssteny (.e., doman adaptaton, suh that the fnal lassfer an be adapted to both domans. ote that the ultmate goal of the proposed model s for lassfaton. As formulated n the onstrant of Eq. (, whh s motvated by prnpal omponent analyss (CA, t s easy to observe that the struture of the target doman data an be well preserved, suh that the target data would not be dstorted after subspae projeton,. After a detaled desrpton of the three unts n the proposed CDL model, by norporatng the Eq. (7, Eq. (9 and Eq. ( together, a omplete CDL model s formulated as follows max r W r r X X B w (3 j k x x j k where λ and λ represent the regularzaton (trade-off oeffents. From the CDL model (3, we observe that t an be further smplfed n formulaton for easer solvng. By substtutng (3 and (4 nto (3, the proposed CDL model (3 s reformulated as max r max max max r B r X X W w u u r B X X r W w u u u u r r B X X r W w u u u u r r B X X r W w u u u u (4 As an be seen from (4, the CDL model s solvng a rato maxmzaton problem, whh s non-onvex. Addtonally, there wll be a group of solutons. herefore, n optmzaton, we have mposed an equalty onstrant, suh that the solvng s transformed nto an effent egenvalue deomposton problem. he solver s desrbed n the followng seton. C. odel Optmzaton he optmal soluton to (4 s equvalent to solvng the Egenvalue problem shown n the followng heorem. heorem: An optmal soluton to (4 s gven by hosen as the matrx whose olumns are the egenvetors v, v,,v d, orrespondng to the frst d largest egenvalues ρ, ρ,,ρ d of the followng generalzed egenvalue deomposton problem: Q Rv ρv where ρ denotes the egenvalues, Q and R are represented as follows R Q B W X w X u u u u (5 he proof of heorem s shown n Appendx A. For easy followng the proposed CDL model n mplementaton, the algorthm s summarzed n Algorthm. D. Classfaton he proposed CDL s used to learn a ross-doman dsrmnatve subspae for doman adaptaton. After projetng the data from soure and target domans, the lassfer s learned on the projeted soure data (master system, and the fnal task s for aurate lassfaton

6 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Algorthm. Classfaton Input: oure data, target data, soure label, and the subspae projeton. roedure:. Compute the projeted soure data ;. Compute the projeted target data ; 3. V lassfer tranng on * + by solvng (6; 4. Classfaton of by usng (7; Output: the lassfaton results of target data. of multple knds of odors n target data (slave system. For lassfer tranng, support vetor mahne (V s used n ths paper. For easer followng, the brefs of V are smply provded as follows. Gven a tranng set of data ponts * +, where the label * +. Aordng to the strutural rsk mnmzaton prnple, V ams at solvng the followng rsk bound mnmzaton problem wth nequalty onstrant. s. t., y mn w C, w, (6 w x b where ( s a lnear/nonlnear mappng funton, w and b are the parameters of lassfer hyper-plane, C denotes the penalty oeffent, and ξ denotes predton error. Generally, for optmzaton, the raw problem (6 of V an be transformed nto ts dual formulaton wth equalty onstrant by usng Lagrange multpler method. After solvng Eq.(6, n lassfaton, the goal of V s to onstrut the followng deson funton sgn α y x, x b f x (7 where ( s a kernel funton. ( ( ( for lnear V and ( ( for nonlnear Gaussan V. In ths paper, Gaussan kernel funton s used due to ts generalzaton and better performane n experments. he odor lassfaton algorthm based on V s summarzed n Algorthm. E. Remark he proposed CDL model s a ross-doman subspae learnng method, and the learned subspae nludes three mportant aspets: dsrmnatve property of soure data, data fdelty of target data, and mn-path feature doman dstane mnmzaton. he task of CDL s to learn a ommon subspae for soure and target domans and aheve doman adaptaton. In modelng, the labels of soure doman are supposed to be avalable, whle the labels of target doman are unavalable or very few labels are avalable. Also, the mn-path feature s desgned by onsderng that the doman dfferene may be dfferent wth respet to dfferent features. When the mn-path sze =, all features ontrbute the same to the dstrbuton nonssteny between soure and target domans. In experments, dfferent values are dsussed, and dfferent number of labeled target data s also evaluated and explored. A. Expermental data IV. EXERIE In ths seton, three odor datasets, nludng soure doman dataset (, target doman dataset (, and target doman dataset (, are expermented. he three datasets are wth large knowledge shft (nstrumental related and drft (tme related. hese datasets are olleted by usng three eletron nose systems wth ompletely the same type of metal oxde sem-ondutor gas sensors, nludng G6, G6, GA and GB. An extra module for temperature and humdty sensng s also used. For eah observaton, the steady state response pont s extrated, and as a result, a 6-dmensonal feature vetor s formulated. Also, the soure dataset was olleted 5 years earler than target dataset and target dataset. hat s, shft and drft are mpled between soure dataset and target dataset, whle only shft s mpled between target dataset and target dataset. For eah dataset, sx knds of odors (ar ontamnants are nluded, suh as toluene (C 7 H 8, benzene (C 6 H 6, ammona (H 3, arbon monoxde (CO, ntrogen doxde (O, and formaldehyde (CH O. he detaled desrpton of the three datasets s shown n able I. he raw features of all samples aqured by usng master system, slave system and slave system are desrbed n Fg. 3(a, wth respet to eah lass. As an be seen from Fg. 3(a, sx knds of features (feature dmensonalty are nluded n eah E-nose system and the feature value (sensng value s normalzed nto (,. he sgnfant feature dstrbuton dfferene between soure and target domans for the same lass an be easly observed. Further, the mean feature for master, slave and slave omputed based on Fg. 3(a s shown n Fg. 3(b wth respet to eah lass. It s lear that the mean soure feature s dfferent from slave features for the same lass. o vsualze the satter ponts of the soure dataset (master, target dataset (slave and target dataset (slave n raw feature spae, CA s analyzed on the three datasets, respetvely. he satter ponts of the frst two prnpal omponents are shown n Fg. 4, from whh we observe that the data ponts from dfferent lasses are almost lustered. B. n-path Feature Combnaton As desrbed n the expermental data, 6 knds of features (.e., sx sensors are formed, whh s nomnated as f, f,,f 6, respetvely. In ths paper, dfferent mn-path sze s dsussed. pefally, the desrpton of the mn-path (feature ombnaton s shown n able II. In experments, dfferent values have been dsussed separately. ote that when =5, two ases of feature ombnaton are onsdered. From able II, t s lear that when =, t s a general problem. When =6, eah knd of feature s vewed to be one path, that s, the feature dmensonalty for eah path s. C. Expermental ettng In experments, aordng to the avalablty of the target data labels, two ross-doman settngs are expermented respetvely. he performane on target data s reported. Cross-doman settng : In CDL tranng, the labels of the target doman data are unavalable. hat s, the target labels are not used for model tranng and lassfer learnng and only the soure data and soure labels are used.

7 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 ABLE I DECRIIO OF EXERIEAL DAAE E-nose systems Dmensonalty oluene Benzene Ammona Carbon trogen monoxde doxde Formaldehyde otal oure doman arget doman arget doman Feature value ean feature.8. lass 4 6 Feature ndex lass Feature ndex lass.8 lass 3 lass 4.8 lass 5 lass (a Raw feature of all samples for master (soure, slave (target and slave (target lass lass 3 lass 4.8 lass 5 lass (b ean feature of all samples for master (soure, slave (target, and slave (target Fg. 3. Desrpton of features of the soure doman and target doman wth respet to dfferent lasses aster lave lave.4.. aster lass lass lass3 lass4 lass5 lass6.6.4 lave.4.3. lave C.8 C. C C C C Fg. 4. he prnple omponent analyss (CA results of the three datasets: soure doman (.e., master, target doman (.e., slave, and target doman (.e., slave. Class ~lass 6 orrespond the odors C 7 H 8, C 6 H 6, H 3, CO, O, and CH O. ABLE II DECRIIO OF FEAURE COBIAIO WIH DIFFERE II-ACH IZE Feature athes ath Feature=[f, f, f 3, f 4, f 5, f 6 ] ath ath Feature =[f, f ] Feature =[f 3, f 4, f 5, f 6 ] ath ath ath 3 Feature =[f, f ] Feature =[f 3, f 4 ] Feature 3=[f 5, f 6 ] ath ath ath 3 ath 4 Feature =[f, f ] Feature =[f 3 ] Feature 3=[f 4 ] Feature 4=[f 5, f 6 ] ath ath ath 3 ath 4 ath 5 Case Feature =[f, f ] Feature =[f 3 ] Feature 3=[f 4 ] Feature 4=[f 5 ] Feature 5=[f 6 ] Case Feature =[f ] Feature =[f ] Feature 3=[f 3 ] Feature 4=[f 4 ] Feature 5=[f 5, f 6 ] ath ath ath 3 ath 4 ath 5 ath 6 Feature =[f ] Feature =[f ] Feature 3=[f 3 ] Feature 4=[f 4 ] Feature 5=[f 5 ] Feature 6=[f 6 ]

8 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 C.3 aster C aster lass lass lass3 lass4 lass5 lass C C 5 lave 5 lave 5 5 C.35 C C.5..3 C ask: ask: Fg. 5. he satter ponts of the frst two omponents by usng the proposed CDL method under ettng. he left denotes the task (.e., of soure doman target doman and the rght denotes the task (.e., of soure doman target doman. Class ~lass 6 orrespond the odors C 7 H 8, C 6 H 6, H 3, CO, O, and CH O, respetvely. ABLE III COARIO OF RECOGIIO ACCURACY O WO AK (EIG Cross-doman task V CA LDA L E CA D LFDA GFK GF A OC D GLW CDL oure doman target doman oure doman target doman ABLE IV RECOGIIO ACCURACY WIH DIFFERE -VALUE I HE ROOED CDL Cross-doman reognton task CDL CDL CDL CDL CDL CDL CDL (= (= (=3 (=4 (=5, ase (=5, ase (=6 oure doman target doman oure doman target doman Cross-doman settng : In lassfer tranng, partal labels of target doman an be used. pefally, for eah lass n the target doman, k labeled samples are used for lassfer learnng, and k=, 3, 5, 7, 9 s dsussed separately. he ompared methods follow the same setup. ranng and estng rotool: In experments, the soure doman data s fxed as tranng set for model tranng (CDL and lassfer learnng (V. A few target doman data s used as a valdaton set for the best regularzaton parameters tunng. he remanng target doman data s used for testng. ote that there s no overlap among tranng, valdaton and testng sets. D. Compared ethods o show the effetveness of the proposed method, we have hosen 4 mahne learnng based methods of four ategores. Frst, 3 baselne methods suh as support vetor mahne (V, prnpal omponent analyss (CA and lnear dsrmnant analyss (LDA are ompared. eond, 3 representatve albraton transfer methods n E-nose, suh as orthogonal sgnal orreton (OC [36], generalzed least squares weghtng (GLW [37] and dret standardzaton (D [38] are ompared. hrd, 5 sem-supervsed learnng methods

9 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 ABLE V COARIO OF RECOGIIO ACCURACY O EIG (AK : OURCE DOAI ARGE DOAI WIH DIFFERE O. OF LABELED ARGE DAA ER CLA o. of labeled target data per lass (k Average V CA LDA L E CA D LFDA GFK GF A OC D GLW CDL (= CDL (= CDL (= CDL (= CDL (=5, ase CDL (=5, ase CDL (= ABLE VI COARIO OF RECOGIIO ACCURACY O EIG (AK : OURCE DOAI ARGE DOAI WIH DIFFERE O. OF LABELED ARGE DAA ER CLA o. of labeled target data per lass (k Average V CA LDA L E CA D LFDA GFK GF A OC D GLW CDL (= CDL (= CDL (= CDL (= CDL (=5, ase CDL (=5, ase CDL (= based on manfold learnng, nludng loalty preservaton projeton (L [34], multdmensonal salng (D [39], neghborhood omponent analyss (CA [4], neghborhood preservng embeddng (E [4], and loal fsher dsrmnant analyss (LFDA [4] are explored and ompared. Fnally, 3 popular subspae transfer learnng methods suh as geodes flow kernel (GFK [43], samplng geodes flow (GF [44] and subspae algnment (A [45] are also explored and ompared. hese methods are losely related wth CDL. E. Results In ths seton, the expermental results on ross-doman settngs are reported to evaluate the proposed CDL method. ettng : Under the ross-doman settng, we frst observe the qualtatve result shown n Fg. 5 by plottng the satter ponts of the frst two omponents after subspae projeton. We an see that after ross-doman subspae projeton (.e., between soure doman and target doman, and between soure doman and target doman, the separablty among data ponts from dfferent lasses (represented as dfferent symbols s muh mproved n the learned ommon subspae ompared

10 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Auray (% lave umber of labeled target data (a oure doman (master arget doman (slave Auray (% Fg. 6. Odor reognton auray wth respet to dfferent number of labeled target data per lass for two ross-doman tasks: (a oure doman target doman and (b soure doman target doman lave umber of labeled target data (b oure doman (master arget doman (slave V CA LDA L E CA D GFK GF A OC D GLW CDL to Fg. 4 that s wthout ross-doman learnng. Further, the odor lassfaton auray of the target doman data has been reported n able III. We an learly observe that the proposed CDL method sgnfantly outperforms other methods. he reognton auray for two ross-doman tasks aheves 7.88%, whh s almost % mprovement n omparsons. ote that the result of CDL s obtaned when the mn-path sze =. he results wth dfferent -values are shown n able IV, from whh we observe that = shows better performane. he omparson results learly demonstrate the effetveness of the proposed CDL method n ross-doman lassfaton tasks. ote that, for ross-doman lassfaton task, the lassfer s traned on one doman, but tested on another doman. radtonal lassfaton mples that the dstrbuton between tranng data and testng data s the same or smlar. However, due to the doman dstrbuton dsrepany, ths assumpton s volated, suh that ross-doman learnng and lassfaton (.e. the proposed CDL s desred. In ths paper, the odor datasets aqured by usng dfferent eletron noses (master and slaves at dfferent tme nterval are reognzed as dfferent domans. ettng : Under the ross-doman settng, two tasks,.e., soure doman (master target doman (slave and the soure doman (master target doman (slave, are ompleted by usng the proposed method respetvely. Dfferent from ettng that only the soure data are used for lassfer tranng, n ettng, k labeled target data are also used as auxlary data of soure data for lassfer tranng. Consderng that the number of labeled target data s very lmted, k=, 3, 5, 7, 9 samples per lass (odor are randomly seleted from target doman for lassfer learnng. he reognton auray of the frst task (.e., soure doman target doman s reported n able V, from whh we an learly observe that the proposed CDL performs the best ross-doman reognton wth dfferent - value. artularly, when =, the best auray for eah k s aheved, whh s about 5% mprovement omparng to LDA based reognton result. mlarly, the reognton auray of the seond ross-doman task (.e., soure doman target doman s Auray (% OC GLW GFK A CA D V CA D GF LDA E L CDL ethods Fg. 7. Reognton auraes n sngle E-nose system by usng 4 methods. reported n able VI. From the results, we also observe the better performane of the proposed CDL method by omparng wth other methods. hese results demonstrate that the proposed method s very effetve n ross-doman lassfaton (.e., odor reognton n multple E-noses. he performane urves wth respet to dfferent number of labeled target data for two ross-doman lassfaton (transferrng odor reognton tasks are shown n Fg. 6. From the auray urves, we an observe that the proposed CDL method shows the best reognton results. Addtonally, the auray beomes hgher wth the nreasng of labeled target samples ontanng drft nformaton, that are used as auxlary data for tranng a more robust CDL model. herefore, the reognton performane and generalzaton ablty beome better by addng more target data nto the soure tranng data. However, n real applatons t s dffult to obtan muh labeled target data ponts, we have therefore dsussed very few labeled target data as shown n Fg. 6. he performane of the proposed method has been valdated n odor reognton aross multple E-nose systems. o show the performane of CDL n odor reognton based on a sngle E-nose system, we have onduted further exploraton. We selet 5% samples from the master system to tran a model usng CDL, and the remanng 5% samples are used for testng the model. he reognton auraes wth omparsons are desrbed n Fg. 7, from whh we an observe that the proposed CDL stll outperforms others. hs experment shows the double relablty of CDL method n not only multple E-noses, but sngle E-nose system.

11 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 lave lave ( =-6 ( =-4 ( =- ( = ( ( ( = ( ( = ( ( = ( ( log ( Fg. 8. erformane varaton urves wth respet to the logarthm of λ by frozen (λ =-6, -4, -,,, 4, and 6, respetvely. lave lave ( =-6 ( =-4 ( =- ( = ( log ( ( = log ( ( = log ( ( = ( log ( log ( Fg. 9. erformane varaton urves wth respet to the logarthm of λ by frozen (λ =-6, -4, -,,, 4, and 6, respetvely. F. Dsusson In ths paper, a mn-path onept s used n modelng. From the results shown n able IV, V and VI, we observe that a smaller value of performs better results. We note that when =, a sngle mn-path wth all sensors n mult-dmensonal data takes plae. hs an better show the feature dstrbuton dsrepany between systems. Unlke that =6, eah mn-path only ontans a sngle sensor, suh that the dstrbuton annot be well learned and algned based on a subspae projeton. he ross-senstvty among sensors may be lost and harmful to odor reognton. Addtonally, the proposed CDL model s a ross-doman learnng framework, whh an be used to handle heterogeneous data lassfaton problems. In E-nose, the well-traned lassfer based on master deve may not be adapted to the slave deves due to some nherent dfferenes. Also, n mage lassfaton, when the mage data s from dfferent domans (e.g., dfferent sensors of low and hgh resoluton, the lassfer traned wth hgh resoluton mages may not be adapted to the low resoluton mages. herefore, the proposed ross-doman learnng method an be expeted to solve suh knd of generalzed heterogeneous problem. G. arameter enstvty Analyss In the proposed CDL model, there are two parameters: the regularzaton oeffents λ and λ. o observe the performane varatons n tunng the two parameters, λ and λ are fne-tuned nreasngly aordng to, where * +. o show the performane wth respet to eah oeffent, one s tuned by frozen the other one. pefally, the performane varaton wth respet to λ by frozen λ s shown n Fg. 8, from whh we an see that a larger λ ontrbutes postve effet on reognton of target domans

12 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 (.e., slave and slave. mlarly, the performane varaton wth respet to λ by frozen λ s shown n Fg. 9. We an see that a smaller λ ontrbutes postve effet. Further, from the proposed CDL formulaton (4, we an see that λ s the oeffent of the mn-path feature based doman dstane term. ne a larger λ shows better reognton performane, t demonstrates that the proposed mn-path feature based doman dstane term s very helpful for ross-doman learnng. Addtonally, λ s the oeffent of the target data fdelty term, whh s used to redue data dstorton and preserve more useful nformaton n the learned subspae. ne a smaller λ shows better performane, t demonstrates that the proposed ross-doman subspae s useful and effetve wthout dstortng the target data too muh. Even that wthout the data fdelty term the proposed CDL may stll be effetve. V. COCLUIO In ths paper, we propose a ross-doman dsrmnatve subspae learnng (CDL model for handlng transferrng odor reognton tasks n multple E-nose systems, and approxmate atual applaton senaros. he proposed transferrng odor reognton onept denotes that the reognton model s learned on one odor dataset from master system A and tested on another odor dataset from slave system B of the same type as system A or another odor dataset stll from system A but aqured at dfferent tme. hree novel aspets are nluded n the proposed method. Frst, a model s formulated by mnmzng the ntra-lass ompatness and smultaneously maxmzng the nter-lass separablty based on soure doman. eond, the data fdelty term s mposed as onstrant n CDL based on target doman for avodng dstorton. hrd, a mn-path feature-spef doman dstane s proposed, suh that we an gve dfferent penalty oeffents n terms of drft degree (e.g., the further the dstane s, the more serous the drft s. In ths way, those mn-paths wth more serous drft wll be pad more attenton to. Essentally, the proposed method n ths paper s to address the ssue of sensor drft n E-nose. Formally, we regard the drft ssue as a ross-doman reognton problem that s ratonal and novel, suh that ross-doman learnng tehnques an be developed to solve the transferrng odor reognton problems. Dfferent from exstng subspae learnng methods suh as CA and LDA that an only work on sngle doman, the proposed ross-doman method ams at learnng a ommon subspae for onnetng soure and target domans. Experments on olfaton datasets of multple knds of odors by usng three E-nose systems (.e., one master and two slaves demonstrate the effetveness of the proposed method and the superorty n omparsons. AEDIX A ROOF OF HEORE roof: We an re-wrte (4 wth an equalty onstrant as follows maxr s. t. r maxr s. t. r B X X W R Q w u u u u (8 where R and Q are represented n Eq. (4, and denotes a postve onstant for equalty onstrant suh that the soluton an be normalzed for unqueness. By ntrodung Lagrange multpler ρ, the objetve funton of model (5 an be formulated as, r R r Q J (9 By omputng the partal dervatve of J(, ρ wth respet to, and let t be zero, there s Q J, R Q R ( where the optmal s the matrx whose olumns are the egenvetors v, v,,v d, orrespondng to the frst d largest egenvalues ρ, ρ,,ρ d of the followng generalzed egenvalue deomposton problem, Q Rv ρv ( where the optmal subspae projeton an be represented as v, v,, v d ( where d denotes the expeted dmensonalty of the new subspae. roof of the heorem s ompleted. AEDIX B DAA REROCEIG mooth flterng and the vetor standardzaton are used for preproessng and normalzaton, respetvely. In ths paper, the fltered sgnal vetor x of eah sensor an be alulated by x L l q,, q mnq,, q ql max L L ( L where =,...,n-l+,, - s a response sequene for one sensor, and the length of raw sgnal s n. he fltered sgnal sequene of eah sensor s ndated as, ( ( -. he wdth L of the smoothng flter wndow s set as n ths work. By subtratng the maxmum and mnmum values, the nose may be removed, whh s smlar to averagng flters funtoned essentally as a low-pass flter. For normalzaton, the steady-state pont n eah sensor sequene after flterng s seleted as the feature of eah observaton, and dvded by the maxmum value of all observatons.

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14 hs paper has been aepted for publaton n IEEE ransatons on Instrumentaton and easurement, 7 Le Zhang ( 4 reeved hs h.d degree n Cruts and ystems from the College of Communaton Engneerng, Chongqng Unversty, Chongqng, Chna, n 3. He was seleted as a Hong Kong holar n Chna n 3, and worked as a ost-dotoral Fellow wth he Hong Kong olytehn Unversty, Hong Kong, from 3 to 5. He s urrently a rofessor/dstngushed Researh Fellow wth Chongqng Unversty. He has authored more than 5 sentf papers n top journals, nludng the IEEE RAACIO O EURAL EWORK AD LEARIG YE, the IEEE RAACIO O IAGE ROCEIG, the IEEE RAACIO O ULIEDIA, the IEEE RAACIO O IRUEAIO AD EAUREE, the IEEE RAACIO O YE, A, AD CYBEREIC: YE, the IEEE EOR JOURAL, IFORAIO FUIO, EOR & ACUAOR B, and AALYICA CHIICA ACA. Hs urrent researh nterests nlude eletron olfaton, mahne learnng, pattern reognton, omputer vson and ntellgent systems. Dr. Zhang was a repent of Outstandng Revewer Award of ensor Revew Journal n 6, Outstandng Dotoral Dssertaton Award of Chongqng, Chna, n 5, Hong Kong holar Award n 4, Aademy Award for Youth Innovaton of Chongqng Unversty n 3 and the ew Aadem Researher Award for Dotoral Canddates from the nstry of Eduaton, Chna, n. Lu Yan reeved her Bahelor degree n Informaton Engneerng n 4 from Chengdu olytehn Unversty, Chna. ne eptember 4, she s urrently pursung a degree n Chongqng Unversty. Her researh nterests nlude eletron nose and ntellgent algorthm. nglng Deng reeved her Bahelor degree n Informaton ene and Engneerng n 5 from Lanzhou Unversty, Chna. ne eptember 5, she s urrently pursung a degree n Chongqng Unversty. Her researh nterests nlude mahne learnng and eletron nose.