Boosting for transfer learning with multiple sources

Transcription

1 Boostng for transfer learnng wth multple sources Y Yao Ganfranco Doretto Vsualzaton and Computer Vson Lab, GE Global Research, Nskayuna, NY 239 yaoy@gecom doretto@researchgecom Abstract Transfer learnng allows leveragng the knowledge of source domans, avalable a pror, to help tranng a classfer for a target doman, where the avalable data s scarce The effectveness of the transfer s affected by the relatonshp between source and target Rather than mprovng the learnng, brute force leveragng of a source poorly related to the target may decrease the classfer performance One strategy to reduce ths negatve transfer s to mport knowledge from multple sources to ncrease the chance of fndng one source closely related to the target Ths work extends the boostng framework for transferrng knowledge from multple sources Two new algorthms, MultSource- TrAdaBoost, and TaskTrAdaBoost, are ntroduced, analyzed, and appled for object category recognton and specfc object detecton The experments demonstrate ther mproved performance by greatly reducng the negatve transfer as the number of sources ncreases TaskTrAdaBoost s a fast algorthm enablng rapd retranng over new targets Introducton A common assumpton of tradtonal machne learnng algorthms s that the probablty dstrbutons of the tranng and testng data are the same Under such an assumpton, when presented wth a new set of data wth a dfferent dstrbuton, tranng samples need to be collected for learnng new classfers Let us consder a classc computer vson problem, such as object category recognton, whch s known to requre a large number of tranng samples to ensure good generalzaton [] When tasked wth the problem of recognzng a new object category, new tranng data has to be collected and labeled so as to represent the new dstrbuton However, one would save tme f he/she could leverage useful nformaton from exstng annotated data and/or classfers of old object categores In addton, dfferent reasons may mpede easy access to new data, and only a small number of samples may be avalable Tranng a new classfer under such condtons would dramatcally ncrease the rsk of overfttng the new data, leadng to poor generalzaton It would be more effcent f one could regularze the learnng n ths scenaro by explotng the knowledge prevously accumulated from smlar problems Transfer learnng [6, 22] represents a famly of algorthms that relaxes the dentcal dstrbuton assumpton of the tradtonal machne learnng approach As the name suggests, transfer learnng algorthms leverage and transfer nformatve knowledge from old data domans (sources) to a new data doman (target) The transferred knowledge helps mprovng the learnng n the target doman when the tranng samples are scarce Among the works n ths area TrAdaBoost [4] s becomng a popular boostng based algorthm that s most closely related to our work In general, the ablty to transfer knowledge from a source to a target depends on how they are related The stronger the relatonshp, the more usable wll be the prevous knowledge On the other hand, brute force transferrng n case of weak relatonshps may lead to performance deteroraton of the resultng classfer Ths s known as negatve transfer In order to avod ths effect one would have to answer the queston when to transfer Lmted work has been done n ths area [6] One strategy to decrease the rsk for negatve transfer s to mport knowledge not from one, but from multple sources In ths way, the chance to borrow benefcal knowledge closely related to the target doman sgnfcantly ncreases From another pont of vew, ths mples that answerng the queston of when to transfer becomes less mportant TrAdaBoost reles only on one source, and therefore s ntrnscally vulnerable to negatve transfer Ths work formally states the problem of transfer learnng from multple sources to mprove the tranng of a target classfer (Secton 3) Two boostng based approaches addressng ths problem are proposed The frst one, called MultSource- TrAdaBoost, extends the TrAdaBoost framework for handlng multple sources (Secton 4) The second one, called Task- TrAdaBoost, ntroduces a tranng process wth two phases (Secton 5) One s dedcated to the summarzaton of the knowledge from multple sources The other one s devoted to transferrng knowledge to the target, and has a very low tme complexty, whch enables rapd retranng when presented wth a new target The theoretcal performance of

2 these two algorthms, and ther dynamc behavor, are dscussed n relaton to AdaBoost (Secton 6) The algorthms are general, and have the potental for sgnfcantly mprovng the performance of several computer vson applcatons The approaches are deployed and evaluated wthn the context of object category recognton, and specfc object detecton (Secton 7) A thorough comparson aganst TrAdaBoost, and the baselne tradtonal machne learnng algorthm AdaBoost, s also provded 2 Related work Transfer learnng has been deployed over a wde varety of applcatons, such as sgn language recognton [7], text classfcaton [25], WF localzaton [2], and adaptve updatng of land-cover maps [3] The approaches to transfer learnng are categorzed based on the means used for mportng knowledge from source to target, and can be based on nstance-transfer [4, ], feature-representaton-transfer [7, 24], parameter-transfer [8, 2, 9], and relatonalknowledge-transfer For more detals we refer the reader to the followng surveys: [6, 22] In the nstance-transfer approach samples from the source are drectly appled for tranng the target classfer TrAdaBoost [4] falls nto ths category, as well as MultSourceTrAdaBoost, the frst proposed approach In featurerepresentaton-transfer the focus s to fnd a representaton of the feature space that mnmzes the dfferences between source and target Parameter-transfer approaches assume that the target could share parameters wth a related source TaskTrAdaBoost, the second proposed method, falls nto ths category Relatonal-knowledge-transfer assumes that data wthn the source s correlated and the goal s to export ths correlaton to the target [6] In addton to these approaches, [7] appled the sparse prototype representaton to transductve transfer learnng, where no labeled data n the target doman s avalable [5] presented a learnng method where hgh-level semantc attrbutes, descrbng shape and color, are exploted to transfer knowledge from multple sources to the target Support vector machnes (SVM) have been modfed for transfer learnng In [27] an SVM s derved by adjustng exstng classfers accordng to the target data [4] derved more adaptable decson boundares by tranng a target SVM wth the help of weghted support vectors learned from multple sources [6] performed vdeo concept detecton by learnng an SVM where the kernel s derved by mnmzng the dstrbuton msmatch between the labeled source data and the unlabeled target data Although SVM-based transfer learnng has been extended to leverage knowledge from more than one source, to the best of the knowledge of the authors, ths s the frst work that extends boostng-based transfer learnng to multple sources Some related work has extended boostng for mult-task learnng [26] and on-lne ncremental learnng [2] In ths context, [2] presented a mult-class boostng-based classfcaton framework that jontly selects weak classfers shared among dfferent tasks In contrast, here the nterested s n boostng a sngle target classfer by leveragng the (nstance-based, or parameter-based) knowledge transferrable from multple sources Also, [2] assumes a comparable number of tranng samples for every task In contrast, the proposed method focuses on scenaros where target tranng samples are scarce 3 Problem statement In ths secton we ntroduce some notaton and defne the type of transfer learnng problem we ntend to approach Formally, a doman D s made of a feature space X, and a margnal probablty dstrbuton P (X), where X = {x,, x n }, and x X A task T s made of a label space Y = {+, }, and a boolean functon f : X Y Learnng the task T for the doman D, n tradtonal machne learnng, amounts to estmatng a classfer functon ˆf : X Y, from the gven tranng data D = {(x, y ),, (x n, y n ) x X, y Y}, that best approxmates f, accordng to certan crtera Let us now ndcate wth D T = (X, PT (X)) a target doman for whch we would lke to learn the target task T T = (Y, ft ), from the target tranng data D T = {(x T, y T ),, (x T n T, yn T T )} Let us also ndcate wth D S = (X, PS (X)) a source doman, and wth T S = (Y, fs ) a source task, for whch we have avalable the source tranng data D S = {(x S, y S ),, (x S n S, yn S S )} Improvng the learnng of the target classfer functon ˆf T : X Y by explotng the knowledge of the source task T S, n the source doman D S, s a so-called nductve transfer learnng problem [6, 22] Performng nductve transfer learnng, as opposed to tradtonal machne learnng, should be advantageous n the cases when the sze of the target tranng data D T, s very small n absolute terms, and also relatve to the sze of the source tranng data D S, e n T n S In fact, under such condtons, tradtonal machne learnng would suffer from serous overfttng problems From here comes the dea of attemptng to regularze the learnng problem by transferrng knowledge from a source doman, where resources have already been allocated to collect abundant tranng data for learnng the source task The TrAdaBoost algorthm [4] has become a popular boostng-based soluton for ths case of the nductve transfer learnng problem The source and target domans and tasks may dffer ether because ther margnal probablty dstrbutons dffer (P T P S ), or ther boolean functons dffer (f T f S ), or both dffer TrAdaBoost provdes a framework for automatcally dscoverng whch part of knowledge s specfc for the source doman or task, and whch part may be common between source and target domans or tasks, and provdes a way to attempt to transfer ths knowledge from the source

3 to the target The effectveness of any nductve transfer learnng method depends on the source doman and task, and on how they relate to the target doman and task It s reasonable to expect a transfer method to take advantage of strong relatonshps The most effectve transfer would occur when D T = D S, and T T = T S, whch reduces nductve transfer learnng to tradtonal machne learnng On the other hand, a weak relatonshp may cause the transfer method to not only be neffectve, but also to decrease the performance of the target task, when compared to tradtonal machne learnng performance Ths effect s known as negatve transfer In order to ncrease postve transfer, and avod the negatve, one can thnk of transferrng knowledge not from one but from multple sources In ths case the transfer learnng method could dentfy and take advantage of the source, among the ones that have been made avalable, that s found to be the most closely related to the target Or even better, t could take advantage of the best peces of knowledge, comng from varous avalable sources, that are found to be the most closely related to the target Therefore, n ths work we make the assumpton that N source domans D S,, D SN, wth source tasks T S,, T SN, and source tranng data D S,, D SN, are avalable, and would lke to explot them to mprove the learnng of the target classfer functon ˆf T : X Y Snce TrAdaBoost transfers knowledge only from one source, ts performance heavly reles on the relatonshp between source and target In Secton 4 we extend TrAda- Boost from handlng only one source to handlng multple sources, makng t much less vulnerable to negatve transfer In Secton 5 we further expand ths boostng-based approach by ntroducng a two-step learnng procedure that, gven the same sources, can transfer knowledge to a new target wth mnmal computatonal complexty 4 TrAdaBoost wth multple sources In ths secton we are gong to present an extenson of TrAdaBoost [4] to multple sources We recall that AdaBoost [] s a tradtonal machne learnng algorthm, whch assumes that the domans and tasks from where the tranng and testng data come from are the same (e there s no dstncton between source and target because D S = D T, and T S = T T ) AdaBoost at every teraton ncreases the accuracy of the selecton of the next weak classfer by carefully adjustng the weghts of the tranng nstances In partcular, t gves more mportance to msclassfed nstances because they are beleved to be the most nformatve for the next selecton TrAdaBoost assumes that there s abundant source tranng data to learn a classfer, but the target doman and task are dfferent from the source (D S D T, and T S T T ) Therefore, the TrAdaBoost learnng paradgm allows to ex- Algorthm : MultSourceTrAdaBoost Input: Source tranng data D S,, D SN, target tranng data D T, and the maxmum number of teratons M Output: Target classfer functon ) ˆf T : X Y Set α S = ( 2 ln + 2 ln n S M, where n S = k n S k 2 Intalze the weght vector (w S,, w S N, w T ), where w S k = (w S k,, ws k n Sk ), and w T = (w T,, wn T T ) to the desred dstrbuton for t to M do 3 Empty the set of canddate weak classfers, F 4 Normalze to the weght vector (w S,, w S N, w T ) for k to N do 5 Fnd the canddate weak classfer h k t : X Y that mnmzes the classfcaton error over the combned set D Sk DT, weghted accordng to (w S k, w T ) 6 Compute the error of h k t on D T : ɛ k t = j 7 F F (h k t, ɛk t ) w T j [yt j hk t (xt j )] wt 8 Fnd the weak classfer h t : X Y such that (h t, ɛ t) = arg mn (h,ɛ) F ɛ 9 Set α t = 2 ln ɛ t, where ɛ ɛ t < /2 t Update the weght vector w S k e α S h t (x S k w S k w T w T eα t h t (x T ) yt return ˆf T (x) = sgn ( t αtht(x)) ) y S k plot a small target tranng data set D T, n conjuncton wth the source tranng data set D S, for drvng the boostng of a target classfer ˆf T The target tranng nstances drve the selecton of a week classfer n the same way as AdaBoost does On the other hand, at every teraton the source tranng nstances are gven less mportance when they are msclassfed Ths s because they are beleved to be the most dssmlar to the target nstances, and therefore ther mpact to the next weak classfer selecton should be weakened We now extend TrAdaBoost to the case where abundant tranng data s avalable from multple sources, each of whch s dfferent from the target (D Sk D T, and T Sk T T ) The strategy for assgnng the mportance to the source and target tranng nstances remans the same as explaned above However, we no longer have to fnd a week classfer by leveragng only one source, and a mechansm has been ntroduced such that every weak classfer s selected from the source that appears to be the most closely related to the target, at the current teraton Clearly, ths approach greatly reduces the effects of negatve transfer caused by the mposton to transfer knowledge from a sngle source, potentally loosely related to the target More precsely, at every teraton each source, ndependently from the others,

4 Algorthm 2: Phase-I of TaskTrAdaBoost Input: Source tranng data D S,, D SN, the maxmum number of teratons M, and the regularzng threshold γ Output: Set of canddate weak classfers H Empty the set of canddate weak classfers, H for k to N do 2 Intalze the weght vector w S k = (w S k,, ws k n Sk ), to the desred dstrbuton for t to M do 3 Normalze to the weght vector w S k 4 Fnd the canddate weak classfer h k t : X Y that mnmzes the classfcaton error over the set D Sk, weghted accordng to w S k 5 Compute the error ɛ j ws k j 6 α ɛ ln, where ɛ < /2 2 ɛ f α > γ then 7 H H h k t 8 Update the weghts w S k return H w S k [y S k j e αys k h k t (xs k j )] h k t (xs k ) combnes ts tranng data wth the target tranng data to propose a canddate weak classfer The fnal weak classfer s then chosen from the source that mnmzes the target classfcaton error A detaled descrpton of the proposed extenson s gven n Algorthm, and s called MultSourceTrAdaBoost, where N source tranng data sets are gven as nput, and M week classfers are extracted to compose ˆf T As t can be seen from lne, the weghtng update of the source tranng nstances s the same as n TrAdaBoost, and the weghtng update of the target tranng nstances s the same as n Ada- Boost At every teraton the nner loop computes: (a) N canddate week classfers from N dfferent tranng data sets, {D Sk DT }; (b) how each weak classfer relates to the target tranng data by computng the classfcaton error Lne 8 then selects the weak classfer correspondng to the source that mnmzes the target classfcaton error Fnally, when N = the algorthm reduces to TrAdaBoost 5 Boostng for transferrng source tasks Fgure (a) depcts the conceptualzaton of nductve transfer learnng, whch s ntended as the explotaton of the knowledge from dfferent sources to mprove the learnng of a classfer that s meant to work n a target doman, to address the target task that was defned on t MultSource- TrAdaBoost s one partcular mplementaton of ths concept More precsely, t tres to dentfy whch tranng nstances, comng from the varous source domans, can be reused, together wth the target tranng nstances, to boost the target classfer Fgure (b) depcts ths stuaton, whch s typcally referred to as an nstance-transfer approach Another way of mplementng nductve transfer learnng s by admttng that the target classfer model wll share some parameters wth the most closely related sources Therefore, Algorthm 3: Phase-II of TaskTrAdaBoost Input: Target tranng data D T, the set of canddate weak classfers H, and the maxmum number of teratons M Output: Target classfer functon ˆf T : X Y Intalze the weght vector w T = (w T,, w T n T ), to the desred dstrbuton for t to M do 2 Normalze to the weght vector w T 3 Empty the current weak classfer set F foreach h H do 4 Compute the error of h on D T ɛ j f ɛ > /2 then 5 h h 6 Update ɛ va () 7 F F (h, ɛ) wj T [yt j h(xt j )] () 8 Fnd the weak classfer h t : X Y such that (h t, ɛ t) = arg mn (h,ɛ) F ɛ 9 H H \ h t Set α t = 2 ln ɛ t ɛ t Update the weghts w T w T e α ty T hk t (xt ) return ˆf T (x) = sgn ( t αtht(x)) ths parameter-transfer approach tres to dentfy whch parameters, comng from varous sources, can be reused, together wth the target tranng data, to mprove the target classfer learnng In ths secton we ntroduce an nductve transfer learnng framework made of two phases Phase-I deploys tradtonal machne learnng to extract sutable parameters that summarze the knowledge from the sources Phase-II s a parameter-transfer approach for boostng the target classfer ˆfT More precsely, phase-i extracts the parameters that consttute the models of the source task classfers ˆf S,, ˆf SN Therefore, the source tasks are descrbed explctly, and not mplctly through the labeled source tranng data For ths reason, ths nstance of parameter-transfer approach can be thought of as a task-transfer approach, where sub-tasks, comng from the varous source tasks, can be reused, together wth the target tranng nstances, to boost the target classfer, because they are beleved to be closely related to the target task The sub-tasks wll be represented under the form of weak classfers Fgure (c) depcts ths stuaton A detaled descrpton of the proposed approach, whch s called TaskTrAdaBoost, s gven n Algorthm 2 for phase- I, and n Algorthm 3 for phase-ii Phase-I s nothng but AdaBoost run for each of the source tranng data The output H s a collecton of all the canddate weak classfers that are beng computed, and that are the most dscrmnatve In fact, we constran the coeffcent α to be greater

5 Learnng System Transfer Learnng Instance Transfer Learnng System Task Transfer Learnng System (a) (b) (c) Fgure Transfer learnng approaches (a) Inductve transfer learnng (b) Instance-transfer based approach (MultSourceTrAdaBoost) (c) Parameter-transfer based approach (TaskTrAdaBoost) than a gven regularzng threshold γ We do so because we are not nterested n transferrng parameters that may lead the target classfer to overfttng the data Phase-II s agan an AdaBoost loop over the target tranng data D T However, at every teraton, from H t s pcked the weak classfer wth the lowest classfcaton error on the target tranng data, ensurng the transfer of the knowledge that s more closely related to the target task Moreover, the update of the weghts of the target tranng nstances drves the search for the transfer of the next sub-task that s needed the most for boostng the target classfer 6 Algorthm comparsons Decson boundares Fgure 2 shows a data dstrbuton, and a sketch of how varous learnng algorthms would attempt to separate the nstances Squares are negatve samples Crosses are postve samples from one source, D S Crcles are postve samples from another source, D S2 Orange stars, and orange crosses are postve tranng and testng nstances n the target doman, respectvely Fgure 2(a) shows that a tradtonal machne learnng algorthm, such as AdaBoost, would overft the target tranng data wth decson boundares unable to guarantee good generalzaton Fgure 2(b) shows the decson boundares obtaned by TrAdaBoost when D S and D S2 are used jontly, whch means that the sources are seen as one In ths case there s no overfttng Fgure 2(c) shows how MultSource- TrAdaBoost mproves the decson boundares Each source separately combnes wth the target, vrtually producng the dashed boundares on the left On the rght, the boundary parts more closely related to the target are transferred to produce tghter target decson boundares Fnally, Fgure 2(d) shows how TaskTrAdaBoost would behave Phase-I learns the dashed boundares between S, and everythng else, as well as the dashed boundares between S 2, and everythng else At every teraton phase-ii grabs the most useful peces of the dashed boundares to buld the tght target decson boundares Performance analyss The convergence propertes of MultSourceTrAdaBoost can be nherted drectly from TrAda- Boost [4], whereas for TaskTrAdaBoost they can be nherted drectly from AdaBoost [, 8] Moreover, because the condton of ɛ t < 5 s satsfed n both algorthms, the predcton error ɛ over the target tranng data D T s bounded by ɛ 2 M M t= ɛt ( ɛ t ), and the upper bound of the assocated generalzaton error s gven by ɛ + O( Md V C /n T ), where d V C s the VC-dmenson of the weak classfer model [23] We now make an observaton regardng how the cardnalty H, of the set of canddate weak classfers H, affects the performance of TaskTrAdaBoost If H s of the same order of magntude of M, the offerng of weak classfers may be too lmtng Therefore, the probablty to chose weak classfers wth hgher classfcaton error ɛ t ncreases, leadng to a hgher predcton error ɛ On the other hand, an overly rch H ( H very bg), would very much ncrease the probablty to choose weak classfers wth low classfcaton error, leadng to a low predcton error However, the VC-dmenson d V C would ncrease as well, leadng to a hgher rsk for overfttng, as well as poorer generalzaton Ths s the reason for nsertng the regularzng threshold γ n phase-i, whch allows to strke a balance between predcton and generalzaton performance The set H plays also another role n TaskTrAdaBoost More precsely, the fact that t lmts the freedom n pckng the weak classfers leads to a greater predcton error, n comparson wth MultSourceTrAdaBoost On the other hand, n the generalzaton error ths effect s compensated because ths reduced freedom also leads to a smaller VCdmenson d V C, and therefore a lower upper bound Fnally, snce we have n T << n S, the convergence rate of TaskTrAdaBoost has a reduced upper bound [, 4], compared to MultSourceTrAdaBoost, whch means that t requres fewer teratons 7 Expermental results The performance of the proposed methods are nvestgated based on two applcatons: object category recognton and specfc object detecton In object category recognton, t s assumed that we are gven a small number of tranng samples of a target object category, and abundant tranng samples of other source object categores When presented wth a test sample, we verfy whether t belongs to the target object category As for specfc object detecton, t s assumed that we are gven a small number of tranng samples of a target object, and abundant tranng samples of other source objects of the same category and of other categores (background) When presented wth a test mage, we want to verfy whether t contans the target object, and where t s located n the mage We use AdaBoost and TrAdaBoost as the baselne methods for performance comparson All the

6 (a) (b) (c) (d) Fgure 2 Decson boundares Representaton of the decson boundares between the postve and negatve samples n the target doman, as computed by AdaBoost (a), TrAdaBoost (b), MultSourceTrAdaBoost (c), and TaskTrAdaBoost (d) Orange crosses and stars represent the target postve samples Dashed lnes represent canddate decson boundares Sold lnes are the learned boundares algorthms use a lnear SVM as the basc learner to buld a weak classfer For every experment, we provde the recever operatng characterstc (ROC) curve of the classfer output for performance comparson We also compute the area under the ROC curve A ROC as a quanttatve performance evaluaton 7 Object category recognton Data sets For object category recognton, we have used the Caltech 256 data set [3], whch contans 256 object categores Among them, we have used the 36 categores that have more than samples We have also used the background data set, collected va the Google mage search engne, along wth the remanng categores as our augmented background data set Expermental setup The bag-of-words method [9] s used to map mages nto the feature space for classfcaton We desgnate the target category and randomly draw the postve samples that form the target data The number of postve samples for tranng n + T, s lmted from to 5, for testng s 5 We treat the remanng categores as the repostory from whch to draw postve samples for the source data We vary the number of source categores, or domans, N, from to to nvestgate the performance of the classfers wth respect to the varablty of the domans The number of postve samples for one source of data s The negatve samples of both source and target data are randomly drawn from the augmented background data set The number of negatve tranng samples n the target data s gven by 5n + T The number of negatve testng samples n the target data s 25 The number of negatve tranng samples n the source data s 5 For each target object category, the performance of the classfer s evaluated over 2 random combnatons of N source object categores Gven the target and source categores, the performance of the classfer s obtaned by averagng over 2 trals of experments The overall performance of the classfer s averaged over 2 target categores Results Fgure 3 compares AdaBoost, TrAdaBoost, MultSourceTrAdaBoost, and TaskTrAdaBoost based on the area under the ROC wth dfferent number of postve target tranng samples (n + T {, 5, 5, 5}) and source domans (N {, 2, 3, 5}) Fgure 3(a) assumes N = 3 and shows the behavor of the algorthms as n + T ncreases Snce Ada- Boost does not transfer any knowledge from the source, ts performance heavly depends on n + T For a very small n + T t performs slghtly better than chance, accordng to the A ROC TrAdaBoost combnes the three sources nto one and mproves upon AdaBoost due to the transfer learnng mechansm By ncorporatng the ablty to transfer knowledge from multple ndvdual domans, MultSource- TrAdaBoost and TaskTrAdaBoost demonstrate a sgnfcant mprovement n recognton accuracy, even for a very small n + T In addton, the performance of AdaBoost and TrAda- Boost strongly depends on the selecton of source domans and target postve samples, as revealed by the standard devaton of A ROC On the other hand, a much smaller standard devaton s observed from both of the proposed algorthms As expected, the performance gaps among all the approaches dwndle as n + T ncreases They show a sgnfcant decrease when n + T = 5, for the gven dataset wth a lmted amount of postve testng samples Fgure 3(b) assumes that N = It shows that Mult- SourceTrAdaBoost reduces to TrAdaBoost and therefore they have the same performance Moreover, t shows that Task- TrAdaBoost outperforms MultSourceTrAdaBoost when n + T s very small, and underperforms t for a larger n + T These are the effects of a low VC-dmenson offered by TaskTrAda- Boost, whch s leveragng only one source When n + T s very small t helps avodng overfttng more than other approaches When n + T ncreases t lmts the ablty to buld the desred decson boundares Fgure 3(c) assumes n + T =, and shows that as the number of source domans ncreases, the A ROC of MultSourceTrAdaBoost and TaskTrAdaBoost ncreases, and the correspondng standard devatons decrease, ndcatng an mproved performance n both accuracy and consstency TrAdaBoost s ncapable of explorng the decson boundares separatng multple source domans, resultng n a mantaned performance regardless of the number of source domans Wth N = 3 and n + T =, MultSourceTrAdaBoost and TaskTrAdaBoost have an A ROC of 966 ± 47 and 972 ± 43, respectvely, n comparson wth an A ROC of 848 ± from TrAdaBoost Tme complexty Wth C h and C w we ndcate the tme complexty to compute a weak classfer, and update the weght of one tranng nstance The tme complexty of AdaBoost s approxmately C h O(M) + C w O(Mn T ), the tme complexty of TrAdaBoost s C h O(M)+C w O(Mn S ),

7 A ROC Standard devaton AdaBoost TrAdaBoost MSTrAdaBoost TaskTrAdaBoost Number of postve tranng samples A ROC Standard devaton AdaBoost TrAdaBoost MSTrAdaBoost TaskTrAdaBoost Number of postve tranng samples (a) (b) (c) (d) Fgure 3 Performance comparson (a) Area under the ROC curve (A ROC), wth correspondng standard devaton (σ AROC ) aganst the number of postve target tranng samples n + T wth N = 3 sources; (b) AROC and σa aganst ROC n+ T wth N = ; (c) AROC and σ AROC aganst N wth n + T = (d) Processng tme aganst n+ T wth N = 2 (top), and aganst N wth n+ T = (bottom) MSTrAdaBoost represents MultSourceTrAdaBoost A ROC Standard devaton AdaBoost TrAdaBoost MSTrAdaBoost TaskTrAdaBoost Number of source domans Processng tme (s) Processng tme (s) AdaBoost TrAdaBoost MSTrAdaBoost TaskTrAdaBoost Number of postve tranng samples Number of source domans and the tme complexty of MultSourceTrAdaBoost s C h O(MN) + C w O(Mn S ), whch s roughly the same as that of phase-i of TaskTrAdaBoost, whereas phase-ii has a tme complexty of C w O(M H n T ) Therefore, snce we typcally have C h C w and H n T n S, the phase-ii of TaskTrAdaBoost s very fast and deployable when there s a strong need for rapd retranng over a new target doman Fgure 3(d) plots the recorded average tranng tme per experment tral aganst n + T and N of all the algorthms 72 Specfc object detecton Data sets For ths experment we have collected a data set made of two vdeo sequences of hghway traffc The frst one (Sequence A) ncludes vehcle mages from a fxed vew pont, whereas the second one (Sequence B) ncludes vehcle mages from dfferent vew ponts For each vdeo, we manually annotated the ground-truth vehcle locatons, and szes, by recordng rectangular regons of nterest (ROIs) around each vehcle movng along the hghway, resultng n a total of about 7 dfferent ROIs, correspondng to 4 dfferent vehcles The szes of the ROIs vary from about 3 2 to 2 4 pxels, dependng on the type of the vehcle and the vew ponts The average number of annotated ROIs per vehcle s approxmately and 4 for Sequence A and Sequence B, respectvely Expermental setup Consderng the small szes of the ROIs, n ths experment we have chosen the regon moment descrptor [5] for mappng mage ROIs onto the feature space We fx the number of source domans to N = 5 Postve samples are selected from the annotated ROIs and negatve samples are randomly cropped from the background For a target object, n + T vares from to 5, whereas the remanng postve samples are used for testng The overall ROC curves are obtaned by averagng the performances over 5 target vehcles The remanng expermental setup s the same as for the object category recognton The traned classfers have been deployed to perform specfc object detecton n vdeo by usng a multscale sldng wndow scheme, whch reveals poston and scale of the detected vehcle (see Fgure 5) Results Fgure 4 compares the performances among classfers based on ROC curves, and Table lsts the correspondng A ROC values For n + T = 5, all the classfers produce comparable performances As n + T decreases and becomes we observe sgnfcant performance gaps As expected, the proposed approaches can effectvely explot the decson boundares between multple sources and outperform TrAdaBoost The reduced tme complexty of the phase-ii of TaskTrAdaBoost makes t a good canddate for applcatons that need rapd retranng for the detecton of a new target object Fnally, Fgure 5 shows example frames wth the detecton of specfc vehcles usng Task- TrAdaBoost True postve rate AdaBoost n T AdaBoost n T + = TrAdaBoost n T TrAdaBoost n T + = MSTrAdaBoost n T MSTrAdaBoost n T + = TaskTrAdaBoost n T TaskTrAdaBoost n T + = False postve rate False postve rate (a) (b) Fgure 4 ROC curves (a) Sequence A and (b) Sequence B True postve rate AdaBoost n T AdaBoost n T + = TrAdaBoost n T TrAdaBoost n T + = MSTrAdaBoost n T MSTrAdaBoost n T + = TaskTrAdaBoost n T TaskTrAdaBoost n T + = 8 Conclusons Ths work extends the boostng framework for nductve transfer learnng when knowledge from multple sources s avalable to help tranng a target classfer Consderng multple sources drectly addresses the problem of negatve transfer because the chance to mport knowledge from a source related to the target ncreases sgnfcantly MultSourceTrAdaBoost, an nstance-transfer approach, and TaskTrAdaBoost, a parameter-transfer (or more specfcally a task-transfer) approach, are ntroduced They are appled to the problem of object category recognton and specfc object detecton when the target data avalable s scarce Compared to TrAdaBoost, an mpressve performance ncrease n terms of recognton and detecton rates s observed, even wth only one postve target tranng sample,

8 Sequence A n + T = 5 n+ T = AdaBoost 976 ± ± 7 TrAdaBoost 979 ± ± 7 MultSourceTrAdaBoost 976 ± 3 99 ± 87 TaskTrAdaBoost 985 ± ± 68 Sequence B n + T = 5 n+ T = AdaBoost 94 ± ± 3 TrAdaBoost 896 ± ± 29 MultSourceTrAdaBoost 9 ± ± 8 TaskTrAdaBoost 922 ± ± 36 Table ROC area Area under the ROC curves, A ROC, and correspondng standard devatons (a) (c) (d) Fgure 5 Specfc object detecton Example frames wth specfc vehcles detected (a)-(b) Sequence A and (c)-(d) Sequence B Green and red boxes depct the ground-truth and detected ROIs, respectvely Gray boxes show a zoom-n vew of the detected ROIs showng the effectveness of both of the approaches n explotng multple sources, wth a slght advantage of Task- TrAdaBoost Moreover, as the number of sources ncreases, a dramatc decrease n performance varablty s observed, showng that the approaches tend to become ndependent of the source choces, and therefore they properly address the negatve transfer problem The framework s general, and applcable to help the learnng n a wde varety of computer vson problems Fnally, an mportant property of TaskTrAdaBoost s ts speed when t s presented wth a new target task to learn Ths aspect makes t a good canddate for applcatons where the source knowledge needs to be quckly reused, for nstance for the on-lne retranng for the detecton of a new specfc object References [] S Bckel, M Bruckner, and T Scheffer Dscrmnatve learnng for dfferng tranng and test dstrbutons In Int l Conf on Machne Learnng, 27 [2] E Bonlla, K M Cha, and C Wllams Mult-task gaussan process predcton In Annual Conf on Neural Informaton Processng Systems, pages 53 6, 28 (b) [3] L Bruzzone and M Marconcn Toward the automatc updatng of land-cover maps by a doman-adapton SVM classfer and a crcular valdaton strategy IEEE Trans on Geoscence and Remote Sensng, 47(4):8 22, Apr 29 [4] W Da, Q Yang, G Xue, and Y Yu Boostng for transfer learnng In Int l Conf on Machne Learnng, Corvalls, OR, 27 [5] G Doretto and Y Yao Regon Moments: Fast nvarant descrptors for detectng small mage structures In CVPR, 2 [6] L Duan, I W Tsang, D Xu, and S J Maybank Doman transfer SVM for vdeo concept detecton In CVPR, 29 [7] A Farhad, D Forsyth, and R Whte Transfer lernng n sgn language In CVPR, 27 [8] L Fe-Fe, R Fergus, and P Perona One-shot learnng of object categores IEEE TPAMI, 28(4):594 6, Apr 26 [9] L Fe-Fe and P Perona A Bayesan herarchcal model for learnng natural scene categores In CVPR, volume 2, pages , June 2 25, 25 [] R Fergus, P Perona, and A Zsserman Object class recognton by unsupervsed scale-nvarant learnng In CVPR, 23 [] Y Freund and R E Schapre A decson-theoretc generalzaton of on-lne learnng and an applcaton to boostng Journal of Computer and System Scence, 55:9 39, 997 [2] H Grabner and H Bschof On-lne boostng and vson In CVPR, pages , New York, NY, Jun 26 [3] G Grffn, A Holub, and P Perona Caltech-256 object category dataset Techncal Report 7694, Calforna Insttute of Technology, 27 [4] W Jang, E Zavesky, S-F Chang, and A Lou Cross-doman learnnng methods for hgh-level vsual concept classfcaton In ICIP, 28 [5] C H Lampert, H Ncksch, and S Harmelng Learnng to detect unseen object class by between-class attbute transfer In CVPR, pages , Mam Beach, FL, Jun 29 [6] S J Pan and Q Yang A survey on transfer learnng Techncal Report HKUST-CS8-8, Department of Computer Scence and Engneerng, Hong Kong Unversty of Scence and Technology, Hong Kong, Chna, Nov 28 [7] A Quatton, M Collns, and T Darrell Transfer learnng for mage classfcaton wth sparse prototype representaton In CVPR, 28 [8] R E Schapre A bref ntroducton to boostng In Int l Conf on Artfcal Intellgence, 999 [9] M Stark, M Goesele, and B Schele A shape-based object class model for knowledge transfer In ICCV, pages , Tokyo, Japan, Oct 29 [2] Z Sun, Y Chen, J Q, and J Lu Adaptve localzaton through transfer learnng n ndoor W-F envronment In Int l Conf on Machne Learnng and Applcatons, 28 [2] A Torralba, K P Murphy, and W T Freeman Sharng vsual features for multclass and multvew object detecton IEEE TPAMI, 29(5): , May 27 [22] L Torrey and J Shavlk Transfer learnng IGI Global, 29 [23] V N Vapnk Estmaton of Dependences Based on Emprcal Data Sprnger-Verlag, 982 [24] C Wang and S Mahadevan Manfold algnment usng procrustes analyss In Int l Conf on Machne Learnng, 28 [25] P Wang, C Domencon, and J Hu Usng wkpeda for coclusterng based cross-doman text classfcaton In IEEE Int l Conf on Data Mnng, 28 [26] X Wang, C Zhang, and Z Zhang Boosted mult-task learnng for face verfcaton wth applcatons to web mage and vdeo search In CVPR, 29 [27] J Yang, R Yan, and A G Hauptmann Cross-doman vdeo concept detecton usng adaptve SVMs In ACM Multmeda, 27