Experiments on Individual Classifiers and on Fusion of a Set of Classifiers

Transcription

1 Experimens on Individal Classifiers and on Fsion of a Se of Classifiers Clade Tremblay, 2 Cenre de Recherches Mahémaiqes Universié de Monréal CP 628 Scc Cenre-Ville, Monréal, QC, H3C 3J7, CANADA claderemblay@monrealca Pierre Valin 2 2 Lockheed Marin Canada 6 Royalmon avene Monréal, QC, H4P K6, CANADA pierrevalin@lmcocom Absrac In he las decades many classificaion mehods and fsers have been developed Considerable gains have been achieved in he classificaion performance by fsing and combining differen classifiers We experimen a new mehod for ship infrared imagery recogniion based on he fsion of individal resls in order o obain a more reliable decision [] To opimize he resls of every class of ship, we implemened individal classifiers sing Dempser-Shafer(DS) mehod for each class ie an individal classifier rerns if he ship belongs o he class or no We compare he resl of he DS classifier wih he resls of he individal classifier The improvemen recogniion varies beween 3% o 20% for a class We hen experimen a new mehod based on a fsion of a se of classifiers [2] The objecive of a good fser is o perform a leas as good as he bes classifier in any siaion For his prpose, we consider hree classifiers: DS classifier, Bayes classifier and neares neighbor classifier and one fser: feedforward neral nework fser We compare he resls of he bes classifier wih he resls of he fsion of a combinaion of classifiers The fser gives a performance eqal or sperior o he bes classifier Keywords: FLIR imagery, fsion of classifiers, Bayes classifier, DS classifier, k-neares neighbors classifier, neral neworks fser Inrodcion In image recogniion, several classifiers have been designed and implemened and heir performance is varied A solion o varios performances is o fse or combine differen classifiers in order o ge beer performance compared o he bes classifier decision and he has also demonsraed ha he performance of a fser can be garaneed o perform a leas as good as he bes classifier nder cerain condiions [3] Or work is closely relaed o Rao s work b in a more pracical way Firs, we compare he resl of he Dempser-Shafer (DS) classifier wih he resl of a fsion of individal DS classifiers We hen consider hree classifiers: DS classifier, Bayes classifier and neares neighbor classifier We compare he resls of he classifiers wih he resls of he fsion of wo or hree classifiers wih a neral nework fser 2 Daa Se and Feare Selecion Park and Sklansky [4] have developed an aomaed design of linear ree classifiers for ship recogniion We sed he same daa se and feares in or work The daa se is composed of 2545 forward looking infrared (FLIR) ship images Each ship image belongs o one of he eigh classes lised in Table For every image, he ship silhoee was hreshold manally Figre shows silhoees for he 8 classes of Table The feares sed are seven invarian momens given by H [5] These momens are invarian nder ranslaion, roaion and scale B hese momens deliver informaion primarily of he global shape of he objec and represen poorly he deails of he obje Hence, Park and Sklansky added as feares for parameers exraced by fiing an ao regressive model o one-dimensional seqence of he projeced image along he horizonal axis Recenly, Rao has demonsraed ha individal resls can be fsed in order o obain a more reliable 272

2 Class Class of ship Desroyer 2 Conainer 3 Civilian Freigher 4 Axiliary Oil Replenishmen 5 Landing Assal Tanker 6 Frigae 7 Criser 8 Desroyer wih Gided Missile Table : Ship classes 3 Classifiers and fser descripion 3 Bayes Classifier Bayes classifiers se a probabilisic approach o assign a class They compe he condiional probabiliies of differen classes given he vales of he aribes and hen predic he class wih he highes condiional probabiliy Desroyer Conainer Civilian Freigher Axiliary Oil Replenishmen Land Assal Tanker Criser Frigae Desroyer wih Gided Missile Figre : Images of he 8 classes of ships The qaliy of each image varies a lo The disance of he ship o he camera and he noise on he image affecs he performance of he classifier Figre 3 : Freqency graph for aribe Eqaion () represens he probabiliy of an objec belonging o in he class i (C i ) knowing he vale of aribe j (A j ), where i represens he nmber of classes i = {, 2,,m} and j he nmber of aribes = {,2,, N} P(C A ) = i j P(A C) j i P(C) i m P(A C)P(C) j i i i= >3000 Type Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 () We compe he probabiliy of an objec o be in he class i knowing he vale of aribe j for each aribe and sm hem N P(C)= s i P(C A) i j (2) j= Finally, we idenify he class of he objec X We choose he class wih he highes probabiliy X=Arg{max i m [ P(Ci)]} s (3) Figre 2: Civilian Freigher in broadside view 273

3 32 k-neares Neighbors Classifier The k-neares neighbor classifier finds he k neares neighbors based on a meric disance and rerns he class wih he greaes freqency We sed a disance weighed by he inverse of he iner-classes covariance marix: by: 2 T dγ ( x, x ) = ( x x ) Γ ( x x ) (4) where he iner-classes covariance marix is defined Γ= N i= T ( xi x) ( xi x) N and where x,, x N are N vecors, for which we know he re ideniy 33 DS Classifier DS heory of evidence is a good means of reasoning nder ncerainy A key aspec of his heory is is abiliy o combine evidences by sing he echniqe of orhogonal smmaion The DS heory reqires ha he proposiions perain o he se of all possible proposiions ha can be op This se is called he frame of discernmen denoed by θ whose elemens are mally exclsive The power se of θ is P(θ) P(θ) is he se of all he 2 θ sbses of θ Le A be an elemen of P(θ) A basic probabiliy assignmen is a fncion from P(θ) o [0, ] is defined by : m : P (?) [0, ] A (5) m(a) (6) There are hree fndamenal axioms abo he mass: m( φ ) = 0 (7) θ 2 ma ( i) = (8) i= m A K A m I A (9) I + ( n) ( ) ( i) I {,2, K, n} i I The probabiliy disribion of P(θ) can be esimaed by he mass fncion The precise probabiliy disribion of P(θ) may no be known exacly so bonds of probabiliy disribion are defined The lower probabiliy and pper probabiliy of a sbse A of P(θ) is denoed as belief measre Bel(A) and plasibiliy measre Pls(A), respecively They can be deermined from he mass fncion as follows: A 2 Bel( A) = ma ( i) (0) i= Pls( A) = Bel( A) () Generally, Bel(A) Pls(A), he re probabiliy of A is beween Bel(A) and Pls(A) The combined mass fncions of wo independen mass fncion m and m 2 is calclaed by sing DS s rle of combinaion, denoed by m m 2 : m m2 A ( ) = K B C= A m B m2 C ( ) ( ) K (2) = m( B) m2( C) (3) B C= where K is normalizaion consan, called conflic becase i measres he degree of conflic beween B and C Afer he combinaion, we rern he class wih he highes mass 34 Single fser The performance of fsion of classifiers has been demonsraed by analyical and experimenal resls The choice of a fser is very imporan becase a bad fser choice can resl in a performance worse han he wors classifier Figre 4 shows he concep of he fsion of he classifiers We choose he neral nework fser becase his fser is garaneed o give resls a leas as good as he bes classifier 274

4 Classifier Classifier N Fser 4 Experimens on individal classifiers 4 Resls of he DS Classifier We implemened a classifier sing he DS mehod We fsed seqenially he eleven aribes wih his mehod Table 2 shows he confsion marix: O p s O p s Figre 4: Single fser f r o m C l f r o m C l N x x 8 y y 2 y 8 inps Figre 5: Neral nework srcre where Cl i means classifier i hidden layers ops C C2 C3 C4 C5 C6 C7 C8 C C C C C C C C Table 2: DS Classifier confsion marix 42 Resls of Individal DS Classifiers To improve he resls of every class of ship, we implemened individal classifier sing he DS mehod for each class ie an individal classifier rerns if he ship belongs o he class X or no For every individal classifier, we chose a sbse of feares, which opimize he performance of he class Table 3 shows he percenage of correc classificaion of he DS mehod, of each individal DS We see ha individal DS classifier gives beer resls for all he classes han he DS classifier DS Classifier Individal DS class Class Class Class Class Class Class Class Class Toal Table 3: Classificaion (wih DS) and fsion resls 275

5 5 Experimens on a neral nework fser for a se of classifiers 5 Resls of Single Classifiers Training Tesing DS K-NN Bayes, K-NN, DS Bes single classifier Firs, we esed he daa se wih hree mehods of classificaion: DS and k-neares neighbor The classificaion resls of each mehod are lised in able 4 For he neares neighbor mehod, we sed k = 3 and he weighed disance by he inverse of he iner-classes covariance marix Table 5: Fsion resls of classifiers wih feedforward neral neworks Classificaion mehod 000 images 500 images Toal Training Tesing DS K-NN K- NN, DS Bayes Bes single classifier DS Neares neighbor Table 6: Fsion resls of classifiers wih feedforward neral neworks Table 4: Classificaion resls 52 Resls of he fsion of classifiers We hen fsed he resls of wo or hree classificaion mehods wih a feedforward neral nework fser Or neral nework fser has 6 or 24 inps (hese inps are he resls of seleced sbses of wo or hree classifiers) and has 8 ops, one for each class We sed he following parameers: 2 hidden layers, 50 nerons on he firs layer, 30 nerons on he second layer momenm = 05, maximal error = 000, epsilon = 0, nmber of maximal ieraions = 00 We rained he fser wih 000 daa and esed on 500 daa We also rained he fser wih 500 daa and esed on 000 daa From ables 5 and 6, we can see ha he fser gives performance eqal or sperior han he bes classifier 6 Conclsions The resls indicae ha individal classifiers can be a good choice In or pariclar case, he individals DS classifiers perform beer An advanage of his mehod is ha we se simple algorihms We see ha a feedforward neral nework is a good choice for a fser In or experimens, he performance of he fser was always a leas as good as he bes classifier Fsion of classifiers is a promising echniqe for image recogniion 7 Acknowledgemens FLIR images from he Unied Saes Naval Airfare Cener, China Lake, California was provided by Dr Jack Sklansky of he Universiy of California a Irvine 8 References [] J Kiler and F Roli Mliple Classifiers Sysems, volme 857 Springer-Verlag, Berlin,

6 [2] N S V Rao On Sample-Based Implemenaion of Decision Fsion Fncions, Workshop on Targe Tracking and Sensor Fsion, Monerey, CA, May 200 [3] N S V Rao On Design and Performance of Meafsers, Proceedings of he Workshop on Esimaion, Tracking and Fsion : A ribe o Yaakov Bar-Shalom, Monerey, CA, May 200 [4] Y Park and J Sklansky Aomaed Design of Linear Tree Classifiers, Paern Recogniion, Vol 23, No 2, pp393-42, 990 [5] M K H Visal Paern Recogniion by momen invarian, IRE Trans Inform Theory, IT-8, pp79-87, 962 [6] F Rhéame, A -L Josselme, D Grenier, E Bossé, and P Valin, New Iniial Basic Probabiliy Assignmens for Mliple Classifiers, in Conference 4729, Signal Processing, Sensor Fsion, and Targe Recogniion XI, SPIE Aerosense 2002, Orlando, USA, April , paper #35 277