Proceedngs of the 2009 IEEE Internatona Conference on Systems Man and Cybernetcs San Antono TX USA - October 2009 Mutspectra Remote Sensng Image Cassfcaton Agorthm Based on Rough Set Theory Yng Wang Xaoyun Lu Zhensong Wang Wufan Chen Schoo of Automaton Engneerng Unversty of Eectronc Scence and Technoogy of Chna Chengdu Schuan Provnce Chna gfwy_0@63com Abstract Rough set theory s a reatvey new mathematca too to dea wth mprecse ncompete and nconsstent data A method of mutspectra mage cassfcaton usng rough set theory s proposed Frst to decrease computatona tme and compexty band reducton of mutspectra mage usng attrbute reduct concept n rough set theory and nformaton entropy s performed Then mxture mode nta parameters of remote sensng mage are mapped from crude casses whch are generated usng equvaent reaton Fnay mage custer s obtaned unsupervsed wth Gaussan mxture mode whose parameters are refned by Expectaton Maxmzaton agorthm The proposed method s performed on a mutspectra mage and the expermenta resuts show the feasbty and effectveness of the agorthm by means of comparson and anayss Keywords rough set attrbute reducton mutspectra mage cassfcaton I INTRODUCTION Wth the fast deveopment of spata dgta mage processng and computer technoogy remote sense technoogy has made great progress The appearance of mutspectra and hyperspectra technoogy s the focus of deveopment of remote sense technoogy n 2st century Because of the arge dmenson of mutspectra remote sensng mage correaton and data redundancy among bands; how to obtan effectve reducton of mut-spectrum s the mportant probem to decrease computatona compexty Remote sense technoogy forms mages for spata obects of earth surface usng satete sensor thus the remote sensng data had the characterstc of compcacy and uncertanty the genera mathematca statstc method can not dea wth the uncertanty effectvey Pawak ntroduced rough set theory n the eary 980s [] as a too for representng and reasonng about mprecse or uncertan nformaton It s one of the most chaengng areas of modern computer appcatons nowadays Rough set theory s an effectve too to anayze remote sense mage There are many teratures about mage cassfcaton based on rough set theory home and abroad but a of them are amost used for gray or coor mages Dr Pa used rough set to make reducton of mutspectra mage [2] but there s a probem n dscretzaton of the feature space whch performed by gray-eve threshods of the ndvdua band mages for they do not exst n such mage wth snge-peak hstogram In ths paper we focus on mutspectra mage dmenson reducton unsupervsed and mage cassfcaton wth statstca means The expermenta resut of band reducton s compared wth common bands seecton methods whch overcome the dsadvantage of changng mage characterstc [3] and the resut of mage custer s shown n secton V II ROUGH SET THEORY We present some premnares of rough-set theory that are reevant to ths paper Detas have been ncey characterzed n [4] and [5] An nformaton system s S ( U A F) where U { x x2 x n } s a nonempty fnte set caed the unverse and A{ a a2 a m } s a nonempty fnte set of attrbutes each eement a ( m) n A s one of the attrbutes F s a reatve set between U and A F { f : U V ( m)} V s the vaue doman of a ( m) Wth every subset of attrbutes B A one can easy assocate an equvaence reaton IB onu : IB {( x x ) f( x) f( x ) forevery a B} () Then I B I a ab A Attrbute Reduct One way to ncrease computaton effcency s to reduce the sze of data by reducng attrbutes Attrbutes that do not contrbute to the cassfcaton resuts can be omtted such that the ndscernbty reaton remans ntact and the attrbutes eft consttute reducts of the system ConsderU { x x2 x n } and A{ a a2 a m } n the nformaton system By the dscernbty matrx M( S ) of S means an n n matrx such that c { a A: f ( x ) f ( x )} (2) Ths research s supported by Natona Natura Scence Foundaton of Chna (No7087084) 978--4244-2794-9/09/$2500 2009 IEEE 4998
A dscernbty functon f S s a functon of m Booean varabes a a2 am correspondng to the attrbutes a a2 am respectvey and defned as foows: f ( a a a ) { ( c ): n c } (3) S 2 m Where ( c ) s the dsuncton of a varabes a wth a c { a a a } s a reduct n S f and ony f a a a 2 p 2 p dsunctve norma form) of s a prme mpcant (consttuent of the f S A decson system S ( U A F d) s smar wth an nformaton system where A caed condton attrbutes d s decson attrbute V s the vaue doman of d d B Descrpton of Attrbutes Dscretzaton Based on Rough Set Theory Decson system S ( U A F d) V s the vaue doman of attrbute a For a A on V [ b t] R any cuts set {( a )( 2) ( c a c a ck)} s defned as the foowng partton: P {[ c0 c)[ c c2) [ ck ck ]} where b c0< c< < ck t V [ c0 c) [ c c2) [ ck ck ] Therefore any set P P defnes a new decson tabe P P P P P S ( U A F d) where A { a : f ( x) f ( x) [ c c ]} for x U {0 k} The orgna system S has been repaced by a new one after dscretzaton [5] III GAUSSIAN MIXTURE MODEL AND EM ALGORITHM Statstca methods are wdey used n unsupervsed pxe cassfcaton framework because of ther capabty of handng uncertantes arsng from both measurement error and the presence of mxed pxes [2] The Gaussan mxture mode approxmates the data dstrbuton by fttng g component densty functons p 2 g to a dataset D For x D the mxture mode probabty densty functon evauated at x s g p( x) p ( x; ) T g x x exp ( ) ( ) (4) 2 n/2 (2 ) /2 The weghts denote the fracton of data ponts beongng to mode and they sum to one g The functons p ( x; ) 2 g are the component densty functons modeng the ponts of the th custer represents the specfc parameters used to compute the vaue of p [6] The Expectaton Maxmzaton (EM) agorthm s an effectve and popuar technque for estmatng the mxture mode parameters It teratvey refnes an nta custer mode to better ft the data and termnates at a souton that s ocay optma for the underyng custerng crteron An advantage of EM s that t s capabe for handng uncertantes due to mxed pxes but one dsadvantage s that the convergence speed and souton of EM agorthm depend strongy on nta condton Dr Pa ntazed the mxture mode parameters usng equvaence cass whch parttoned by equvaence reaton n rough set [2] IV PROPOSED ALGORITHM FOR BAND REDUCTION OF MULTISPECTRAL IMAGE Remote sensng mages can be anayzed usng rough set theory However snce the vaue domans of attrbutes are too wde to decrease computatona tme the attrbutes dscretzaton process of mutspectra mage s requred In terature [2] Dr Pa used gray-eve threshod for dscretzaton of 4-band mutspectra mages whch s not sutabe for mage wth snge peak hstogram A Attrbutes Dscretzaton of Remote Sensng Image Dfferent requrements of attrbute dscretzaton n rough set are needed n dfferent appcaton feds In ths paper we choose nformaton entropy to dscretze the spectra vector of mutspectra mage whch keeps the compatbty of decson tabe Documents about dscrete threshod n rough set theory one may refer to [7] and [8] Decson system S ( U A F d) subset X U ts cardnaty s X the number of exampes wth decson attrbute are k ( 2 ) Informaton entropy of subset X s: H ( X) p og 2 p p k/ X (5) Obvousy H( X) 0 the smaer the H ( X ) s the ower the chaos s Ths property ensures that the agorthm can not change the compatbty of decson tabe For any a A fnte attrbute vaues are sorted as: b v0< v< < vm t the canddate cuts set can be chosen as c ( v v)/2( 2 m) (6) For breakpont c n a exampes whch decson attrbute vaue be ( 2 ) the number of exampes beonged to X whch attrbute a s vaue ower than c X X s b ( c ) otherwse t ( c ) Then we have: X X X X b ( c ) b ( c ) t ( c ) t ( c ) (7) Obvousy breakpont c dvded X nto two parts X and b X t 4999
H ( X ) p og p p b ( c )/ b ( c ) (8) H ( X ) q og q q t ( c )/ t ( c ) (9) X X b 2 X X t 2 c on X : So defne nformaton entropy for breakpont X Xb Xt H ( c) H( Xb) H( Xt) X X (0) The breakpont c U for whch H ( c ) s mnma among a the canddate breakponts s taken to be the best breakpont c parttonsu nto two setsu andu 2 Let c be the best break U pont wth H ( c ) and c 2 be the best breakpont wth U2 2 H ( c ) If U U2 2 H ( c ) H ( c ) () we parttonu otherwse we parttonu 2 The worse one s dvded Now we can get cuts set C usng (0) and () B Band Reduct Agorthm Based on Rough Set Theory Informaton entropy based dscretzaton does not change the compatbty of decson tabe but t has the mtaton that the decson tabe generated from remote sensng mage supervsed s needed whch not ony costs ots of tme but aso brngs human effect The proposed band reduct agorthm can obtan decson tabe and band reducton unsupervsed The bock dagram of band reduct agorthm s shown n Fg Agorthm steps are as foows: ) Map the mutspectra mage to an nformaton system and each band s an attrbute coumn 2) Dvde the unverse nto equvaence casses usng equa nterva dscretzaton and ndscernbty reaton then append dfferent cass abes as decson vaues to each equvaence cass 3) A decson tabe s conssted of the orgna nformaton system and the decson attrbute coumn appended whch s unsupervsed rather than supervsed sampng 4) Obtan canddate break ponts usng (6) for each attrbute of the decson tabe repeat (0) and () to get fna cuts set 5) Reduce the attrbutes accordng to dscernbty matrx (2) and dscernbty functon (3) now we get the fna band reduct V CLASSIFICATION OF MULTISPECTRAL IMAGE AND EXPERIMENTAL RESULTS After the band reduct n secton IV to obtan cassfcaton of mutspectra mage usng Gaussan mxture mode whch parameters are refned by EM agorthm Resuts are presented on 6-band TM mage whch sze s 263 275 Fg 2 shows each band gray mage of the mutspectra mage For the 6-band mutspectra mage the nformaton system s mapped and a sma part of the data s chosen as seen n Tabe I A the attrbutes are dscretzed usng equa nterva dscretzaton wth the wdth 30 Tabe II shows the data after (a) Band (b) Band 2 Mutspectra mage Each band s an attrbute coumn Informaton tabe (c) Band 3 (d) Band 4 Equa nterva dscretzaton Decson tabe Informaton entropy Break ponts Dscernbty functon Fgure Band reducton Bock dagram of band reduct agorthm (e) Band 5 Fgure 2 (f) Band 6 6-band remote sensng mage 5000
attrbute dscretzaton Dfferent cass abes are gven to each cass after dvded the nformaton tabe nto dfferent equvaent casses by means of ndscernbty reaton; append the cass abes to the nformaton tabe as decson attrbute as gven n Tabe III Now we change an nformaton system to a decson tabe whch s combned wth orgna mage data and the appended decson attrbute coumn whch s presented n Tabe IV Breakponts are obtaned from attrbutes dscretzaton usng nformaton entropy After dscretzaton we get the nformaton system Tabe V Then reduce attrbutes accordng to (2) and (3) here the reduct are bands {35} Fnay map the reduct to the nta parameters of Gaussan mxture mode and refne them to convergence usng EM agorthm and cassfy the mage accordng to Bayesan cassfcaton rue; for detas one may refer to [2] TABLE I ORIGINAL REMOTE SENSING DATA U Band Band 2 Band 3 Band 4 Band 5 Band 6 23 46 63 34 49 43 2 24 46 64 34 49 44 3 23 46 64 34 50 44 4 29 54 46 38 49 43 5 34 66 27 29 39 40 6 29 6 28 29 38 38 7 29 62 7 28 36 38 8 34 65 4 29 38 39 9 34 62 26 32 40 43 0 3 59 25 29 38 42 TABLE II EQUAL INTERVAL DISCRETIZATION DATA U Band Band 2 Band 3 Band 4 Band 5 Band 6 2 6 2 2 2 2 2 6 2 2 2 3 2 6 2 2 2 4 2 5 2 2 2 5 2 3 5 2 2 6 3 5 2 2 7 3 4 2 2 8 2 3 4 2 2 9 2 3 5 2 2 2 0 2 2 5 2 2 TABLE III DIFFERENT CLASS LABELS APPENDED U Band Band 2 Band 3 Band 4 Band 5 Band 6 Cass abe 2 6 2 2 2 2 2 6 2 2 2 3 2 6 2 2 2 4 2 5 2 2 2 2 5 2 3 5 2 2 3 6 3 5 2 2 8 7 3 4 2 2 22 8 2 3 4 2 2 9 9 2 3 5 2 2 2 2 0 2 2 5 2 2 TABLE IV DECISION TABLE U Band Band 2 Band 3 Band 4 Band 5 Band 6 Cass abe 23 46 63 34 49 43 2 24 46 64 34 49 44 3 23 46 64 34 50 44 4 29 54 46 38 49 43 2 5 34 66 27 29 39 40 3 6 29 6 28 29 38 38 8 7 29 62 7 28 36 38 22 8 34 65 4 29 38 39 9 9 34 62 26 32 40 43 2 0 3 59 25 29 38 42 TABLE V INFORMATION ENTROPY DISCRETIZATION DATA U Band Band 2 Band 3 Band 4 Band 5 Band 6 3 4 5 3 2 4 4 5 3 3 2 2 4 3 5 7 2 4 3 5 2 4 5 3 6 7 3 8 4 9 4 2 0 2 The performance of the proposed band reduct method s compared wth the common band seecton means [3] as n Tabe VI - Tabe VIII The order of band seecton accordng to standard devaton s 3>4>2>5>>6 band3 w be chosen f ony one band s requested The order of Optmum Index Factor (OIF) wth bands combned s {235}>{234}> {35}> but the correaton of bands{35} s better than {234} So as we have seen the reduct bands { 3 5} obtaned form proposed approach s vad Fgs 3-6 are demonstrated the vadty and appcabty of the proposed method for mutspectra mage custer Fg 4-Fg 6 are cassfed mage of 6 custers usng dfferent methods Compared wth fase-coor mage n vsua effect mscassfcaton of the rver rght sde of the mage mxed wth ts rght and exsts n both Fg3 and Fg4 Therefore not a the bands are essenta to cassfy mage wth comparson above; choosng sutabe bands can not ony mprove accuracy of cassfcaton but aso decrease computatona tme and compexty TABLE VI STANDARD DEVIATION OF DIFFERENT BANDS Band 2 3 4 5 6 SD 7757 8508 204 9533 8279 3705 TABLE VII CORRELATION MATRIX OF DIFFERENT BANDS Band Band2 Band3 Band4 Band5 Band6 Band 0807 097 0428 052 0688 Band2 0056 0305 044 0463 Band3 00005 08 005 Band4 0822 0633 Band5 0387 Band6 500
TABLE VIII OPTIMUM INDEX FACTOR Bands 23 24 25 26 34 OIF 3572 6749 22256 02 624 Bands 35 36 45 46 56 OIF 7939 34703 8236 2006 6 Bands 234 235 236 245 246 OIF 086 894 58367 20699 5523 Bands 256 345 346 356 456 OIF 20624 4249 50055 59363 68 Fgure 6 Cassfcaton usng proposed method Fgure 3 Orgna fase-coor mage wth bands35 Fgure 4 Cassfcaton usng k-means method wth bands35 VI CONCLUSION AND DISCUSSION The content of ths paper s twofod Frst to decrease computatona tme band reduct s performed on mutspectra mage usng rough set and nformaton entropy Second mage cassfcaton s obtaned after band reducton Gaussan mxture mode and EM agorthm are consdered The agorthm desgned n ths paper can make bands reducton and mutspectra mage cassfcaton unsupervsed Expermenta resuts show that the proposed method dd have effectve and vad performance But there are st some mss custerng probems to be soved REFERENCES [] Z Pawak Rough sets Int J Inform Comput Sc vo no 5 pp 34-356 982 [2] S K Pa and P Mtra Mutspectra mage segmentaton usng the rough-set-ntazed EM agorthm IEEE Trans Geosc Remote Sensng vo 40 pp 2495-250 November 2002 [3] C Zhao W Chen and L Yang Research advances and anayss of hyperspectra remote sensng mage band seecton J Natura Sc Heongang Unvers vo 24 no 5 pp 592-602 October 2007 [4] W Zhang and G Qu Uncertan decson makng based on rough sets Beng: Tsnghua Unversty Press 2005 [5] S Hu Y He Rough decson makng theory and appcaton Beng: Behang Unversty Press 2006 [6] A R Webb Statstca Pattern Recognton (Second Edton) Beng: Pubshng House of Eectroncs Industry 2004 pp 27-40 [7] U M Fayyad and K B Iran On the handng of contnuous-vaued attrbutes n decson tree generaton Machne Learnng vo8 pp 87-02 992 [8] H Xe H Cheng and D Nu Dscretzaton of contnuous attrbutes n rough set theory based on nformaton entropy Chnese J Comput vo 28 no 9 pp 570-574 September 2005 Fgure 5 Cassfcaton usng k-means method wth 6 bands 5002