MULTI-SPECTRAL IMAGE AALYSIS BASED O DYAMICAL EVOLUTIOARY PROJECTIO PURSUIT YU Changhu a, MEG Lngku a, YI Yaohua b, a School of Remoe Sensng Informaon Engneerng, Wuhan Unversy, 39#,Luoyu Road, Wuhan,Chna,430079, yuchhus@263.ne b Dep. of Prnng and Packng, Wuhan Unversy, 39#,Luoyu Road, Wuhan,Chna,430079. WG VII /6 KEY WORDS: mul-specral mage, projecon pursu, dynamcal evoluonary algorhm ABSTRACT: Prncpal componen analyss (PCA s usually used for compressng nformaon n mulvarae daa ses by compung orhogonal projecons ha mamze he amoun of daa varance. PCA s effecve f he mulvarae daa se s a vecor wh Gaussan dsrbuon. Bu mul-specral mages daa ses are no probably submed o such Gaussan dsrbuon. The paper proposes a mehod based on Projecon Pursu o fnd a se of projecons ha are neresng, n he sense ha hey devae from Gaussan dsrbuon. Also a dynamcal evoluonary algorhm was developed n order o fnd he opmal projecon nde. The effecveness of hs mehod s demonsraed hrough smulaed daa and mul-specral mage daa. 1. ITRODUCTIO Remoe sensng s an ndspensable ool n many scenfc dscplnes. I s one of he major ools n monorng our earh envronmen n a cos-effecve way. As a fully new echnque, mul-specral & hyper-specral remoe sensng has specal characers such as narrow bands, mul channels and negrang of mage and specral compared o radonal remoe sensng. Imagng specral remoe sensng, whch negrae he echnques of magng and specraly, can ge mass mul-specral & hyper-specral mages abou earh resources and envronmen. Compared o radonal remoe sensng, Mul-specral and Hyper-specral remoe sensng mage could provde more nformaon. So new algorhms and sofware are requred o processng and eracng he nformaon n hyper-specral remoe sensng. Prncpal componen analyss (PCA s usually used for compressng nformaon n mulvarae daa ses by compung orhogonal projecons ha mamze he amoun of daa varance. PCA s effecve f he mulvarae daa se s a vecor wh Gaussan dsrbuon. Bu mul-specral mages daa ses are no probably submed o such Gaussan dsrbuon. Ths paper presens an algorhm based on Projecon Pursu o fnd a se of projecons ha are neresng, n he sense ha hey devae from Gaussan dsrbuon. In mul-specral & hyper-specral magery analyss applcaons, he general used mehod o processng hgh-dmenson daa s he Eploraory Daa Analyss (EDA. Whle as a new mehod for analyss mulvarae daa projecon pursu s aracng more and more aenons. 2.1 Tle 2. PROJECTIO PURSUIT Projecon Pursu s appled o eplore he poenal srucures and characers of he mul-dmenson daa hrough projecng he hgh dmensonal daa se no a low dmensonal daa space whle reanng he nformaon of neres. Projecon Pursu was frs presened by Kruskal n 70h of 20 cenury. He found he cluserng srucure and seled he classfcaon problem of fossl hrough projecon hgh dmenson daa no low dmenson space. Then Fredman and Tukey presened a new projecon nde whch combned he wholly cluserng srucures and local cluserng o carry ou he classfcaon problems. They coned he concep of projecon pursu formally. The kernel dea of projecon pursu s o projec a hgh dmenson daa se no a low dmenson space whle remndng he nformaon neres. The fness of he projecon was evaluaed by desgnng a projecon nde. So projecon pursu means o search he opmal projecon nde o ge he mamum projecon. In naure s a problem of mamum opmzaon. Projecon pursu s dfferen from PCA n ha can help us o fnd he neresng lnear projecon. From he pon of projecon pursu, PCA s jus a specal case of projecon y m n = w T m m pursu. Le he daa se s, we can ge, n whch w s he projecon vecor and s he correspondng projecon value. If made he mamum varance he projecon nde, and he columns of w are perpendcular o each oher. Then he projecon ransform becomes he PCA ransform. The core of projecon pursu s o fnd an approprae projecon nde. Ths paper use nformaon dvergence as he projecon nde. y
Gven wo connuous probably dsrbuons and, he relave enropy f ( g( f ( g( d = f ( f g g( log d g( of wh respec o can be defned as (. ( 1 And her absolue nformaon dvergence can be calculaed by he follow formul. ( 2 j ( f, g = d( f g + d( g f j ( f, g = j( g, f j( f, g 0 f = g g( Then we ge ha and. When he dvergence wll be zero. If le subms o Gaussan dsrbuon, hen we can calculae he dvergence of f ( relave o Gaussan dsrbuon. To do hs, we mus evaluae he f (. Bu he general used mehod Parzen Wndows s very dffcul. A smple and effecve mehod s appromae he connuous quany f ( and g( wh he dscree counerpars p and q respecvely. Then her relave enropy can wre as p D( p q ( 3 p = p log q q p and n whch and denoe he h componens of he separaely. The absolue nformaon dvergence becomes, = ( ( ( 4 J ( p q D p q + D q p The projecon nde can be calculaed as he follows: (1 Quanzed he sandard normal dsrbuon no n - dmenonal vecor by selecng he sep lengh Δ. (2 Sandardze he projecon daa usng he _ ( / σ formula. (3 Accordng o Δ calculang he hsogram p from he sandardzed daa and normalze p o le = 1. p (4 Calculang he probably of Gaussan dsrbuon by he formula ( + 1 Δ 2 / 2 q = 1/ 2π e d, = n / 2 ~ n / 2. Δ (5 Combne formula (3 and (4 o compue he projecon nde. q Δ = 1 In hs paper le and he dscree range be [ 10σ,10σ ] o fnd he daa pons ha dfferen from normal dsrbuon by searchng he projecon nde whch can mamum he projecon vecors. 3. DYAMICAL EVOLUTIOARY ALGORITHM Ths paper proposes a dynamcal evoluonary algorhm (DEA based on he heory of dynamcs evolvemen sysem o searchng he approprae projecon nde. The algorhm can be mplemened by he follow four man seps (1 selec he code scheme, (2 decde he selecon sraegy, (3 defne he parameer and varan o conrol he algorhm, (4 deermne he mehod and he sop rule. Through he above four process, he evoluonary algorhm can found he opmal projecon. q (1 Code scheme For radonal bnary process he mehod may be smple bu f needs hgher quanze precson he srng lengh by bnary codng wll be eremely longer. Then he me of codng and decodng of chromosome and soluon wll occupy los of compung me. Because he column vecor of projecon vecor w s un vecor ha s each componen has he value [ 1,1] beween. We can apply a codng scheme ha s assgned a space of double bye for each componen of column [ 1,1]. vecor. The value of he double bye s a real number of So he sep lengh of each real number s 2/65536=0.00003. Epermens show ha he above precson sasfed he praccal condon. Then one column can be represened by m such double bye of sze. Such a srng can be called one chromosome and he correspondence projecon racng value of some projecon nde of hs vecor s he adapve value of he chromosome. (2 Selecon sraegy The problem of projecon racng can be smplfed as a mamum problem: ma f ( w w s 0, j s.. w w j =, j = 1,2,..., m 1, = j,..., 1, 2 le be he parcles and hey composed a dynamc sysem. Ther funcon values are f (, f ( 2,..., f ( 1. Dfferen from radonal generc algorhm he erave sep n DEA s called me. The momenum of a parcle a he me s defned as p(, = f (, f ( 1, f, where denoes he funcon value of he a he me. ( The acvy of parcle a me s defned as a (, a( 1, + 1 = If a me he parcle s seleced hen he acvy wll be changed as he above formula, oherwse f keeps unchanged. Inroducon he above wo quanes we defne he selecon operaor n DEA as: slc (, = p( + a(, Assgn a wegh coeffcen λ (0,1 accordng o he mporance of he above quanes. Then he above formula changed o : slc(, = λ p( + (1 λ a(, In hs algorhm, we sor he slc(, ( = 1,2,..., from small o large and can slc(. From hese preparaons, we can descrbe denoe by he DEA as follows. (A Inalze a dynamc evoluonary sysem,, 0
Γ = (, 2,..., a. Random generae ; 1 b. Calculae he funcon values of parcles n Γ,and se p (, = 0, a(, = 0, Γ ; c. Save he bes parcle and s funcon value; d. Calculae and sor. slc( (B Perform Ieraon Repea: +1 parcles from he forefron of slc ( 1 ; (a ; (b selec (c Implemen cross and varaon operaor on parcles; (d Modfy he funcon values, momena and acves of he parcles; (e Save he bes parcle and s funcon value; (f Modfy and sor slc( ; Unl: {soppng creron} The selecon sraegy of DEA s ha he smaller varaons of funcon value beween wo generaons and he fewer seleced of a parcle, he more possble s seleced. Ths ensures every parcle can be seleced wh enough long me. Tha s he selecon sraegy drves all parcles movng jus lke molecules move all he me and everywhere. Tha s he reason why we called he algorhm he dynamcal evoluonary algorhm. (3 Selec he conrol parameer The selecon of parameer has mporan effec on he convergence and convergence pace. The parameers nclude nercross probably pc, dfferenaon probably pm and he populaon sze ec. Inercross s he key process n GA. The reasonable of nercross probably selecon s val o opmal resul and opmal effcency. All of he par of he parcles can parcpae n he nercross ha means le or. The parcle number s deermned p = 1.0 < 1. 0 c by he nercross probably. The new generaed parcles whch corporae pars of chromosomes from faher and anoher par of chromosome from maher maybe nferor o her paren and wll be elmnaed or hey maybe ecellen han her paren for nher he fne genes. In any case he new parcle wll be fall no he possble soluon areas. Generally speakng he nercross probably should selec bgger. Daa shows he value should be 0.6~1.0. In hs paper he nercross probably s 0.65. probably s rangng from several n a housand o several n a hundred. Ths paper we defne he as 0.01. Consderng he selecon of populaon sze, f he sze s small we can rean he dversy of genes and f s oo large he me of erave compue wll ncrease and canno ge he good searchng effcency. Moreover he populaon sze s respec o he problem space. Volumes of daa ell us f he sze be conrolled n 40~120 hen he resul wll good. So hs paper he sze s 80. (4 Soreron In he DEA we can use dynamc o ge wo sorerons. The frs one s when = 1 p(, < ε he evolvemen wll over. In whch ε s a gven posve consan. The nuve eplanaon of hs creron s ha f all he parcles canno be mproved he evolvemen wll be sopped. From he pon of sascs when all of he molecule ehaus s energy hen he sysem wll aan a low energy sae. In fac he lef of he formula equals o he energy norm defned a sascs. The second soreron s when ma p( > M he process sopped. Where Γ M s a gven large posve consan. In here M s only on heory and n pracce he M s hard o found. The frs Sop creron was used n hs paper 4. EXPERIMET AD COCLUSIO 4.1 Smulaed Daa Epermens To demonsrae our approach we consruced a non-gaussan daa se. Generang 1000 en-dmensonal sample whch has zero-mean. The varance of he en-dmensonal feaure are geomercally decreased wh he value s 1, 1/2, 1/4,1/8,,1/512. In whch 1 % (enof he sample were regenerae by Gaussan random generaor n he hrd and fourh feaures. Because here are lle relave varance ess n he daa feaures. The PCA canno fnd he unnormal 10 pons. Whereas usng he mehod of dvergence nde we can deec he unnormal pons. Fgure 1 s he resul of PCA and fgure 2 denoes he resul of dvergence nde. Dfferenaon probably s also an mporan parameer. If he s oo small hen he dfferenae ably of he un wll no enough and resul n all he populaon evaluaed o a unary un model. Ths model may correspond o a local eremum and no a global eremum. However f he s oo large hen he un wll dfferenae frequenly and lead o he machng mproved slowly and lower convergence pace. A opmal dfferenaon probably can ge he opmzaon populaon and model and no fall no a local eremum. Daa shows he approprae Dfferenaon
Fgure2. Resul of Dynamcal Evoluonary Projecon Pursu Fgure 1. Resul of Prncpal Componen Analyss Fgure1 s scaer pon of he PCA o smulae daa. (a he frs and he second componen. (b he hrd and he fourh componen. Fgure 2 s he scaer pon of dvergence nde o smulae daa. (a he frs and he second projecon. (bhe hrd and he fourh projecon. The frs and he second componen n fgure 1 show he non-gaussan dsrbuon of daa. Jus as we epeced he hrd and he fourh componen dsplayed he nformaon of he abnormal pons. Fgure 2 shows he mehod of projecon pursu. The dsrbuon of he abnormal pons of he frs and he second componen can be found eacly by usng convergence nde as he projecon nde. 4.2 Mul-specral Image Daa Epermens The 7-band ETM+ daa used n he epermens s maged n he June weny-nnh 2000.I s a sub-scene of 100*100 pels eraced from HEKOU own. Only 6 bands (ncludng vsble and nfrared bands were chosen, ha s band 1~5 and 7. Is space resoluon s 30meer. Fgure3 s he compose color mage by R-3 G-4 B-2 Fgure3. ETM+ mul-specral mage daa Fgure4 shows he frs hree prncpal componen mages and fgure5 s he frs hree projecon mages afer Dynamcal Evoluonary Projecon Pursu (DEPP by dvergence nde.
Mul-specral Image Daa Epermens show ha he proposed DEPP mehod provdes an effecve means for fndng he anomaly srucure characer from mul-dmensons daase. REFERECES Cheng Png, L Guoyng. 1986. Projecon Pursu - a ew Sascal Mehod. Applcaon of probably sasc 2(3: pp.8-12. (1 (2 A.Ifarragaerr and C.-I.Chang 2000. Mulspecral and hyperspecral mage Analyss wh projecon pursu. IEEE Trans.Geosc. Remoe Sensng. vol.38 pp.2529-2538. S.-S.Chang and C.-I.Chang 2001. Unsupervsed Targe Deecon n Hyperspecral Images Usng Projecon Pursu, IEEE Trans,Geosc Renoe Sensng. vol.39,pp.1380-1391. (3 Fgure4. The fore hree Componen mages from PCA L YuanXang, Zou XuFen, Kang Lshan and Zbgnew Mchalewcz. 2003. A ew Dynamcal Evoluonary Algorhm Based on Sascal Mechancs, J.Compu. Sc & Technol, vol.18 pp.361-368. ( 1 ( 2 Componen/Projecon Table1. Ma Ma q PCA ( 3 Fgure5. The fore hree Projecon mage from DEPP Ma q DEPP 1 0.090679 1.359902 2 0.158729 0.762566 3 0.227217 0.213851 4 0.064051 0.104878 5 0.029244 0.085720 6 0.006726 0.079304 q Values for he PCA and DEPP Table 1 s he dvergence value of he each prncpal componen mage and projecon mage. I can be concluded ha he dvergence value afer PCA processng s much more small han ha afer DEPP processng from able.1. Smulaed Daa and