ONE-AGAINST-ALL REMOTE SENSING IMAGE CLASSIFICATION USING SUPPORT VECTOR MACHINE

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1 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN ONE-AGAINST-ALL REMOTE SENSING IMAGE CLASSIFICATION USING SUPPORT VECTOR MACHINE Ouwa Okwuash, PhD Departmet of Geoformatcs & Surveyg, Uversty of Uyo, Ngera Dubem Isaac Ikedash, PhD Departmet of Buldg, Uversty of Uyo, Ngera Abstract Ths research presets a ew method of extedg a bary support vector mache algorthm to a mult-class remote sesg mage task usg a oe-agast-all techque A Ladsat mage s used for the expermet The lad use classes of terest are: developed, udeveloped ad water The spectral bads are extracted ArcGIS whle MATLAB programmg software s used for the modellg The selecto of support vector mache kerel fuctos ad parameters are based o the k-fold cross-valdato The tal classfcato result yelds four lad use classes: developed, udeveloped, water ad uclassfed; whle the fal classfcato result s resolved to three lad use classes: developed, udeveloped ad water For the fal result, the Kappa statstc was obtaed for teratos; the hghest Kappa statstc s obtaed at the 9th terato whle the least Kappa statstc s obtaed at the th terato The tal result yelds a Kappa value of 7787 whch dcates a substatal agreemet wth the groud truth data; whle the fal mage yelds a Kappa value of 867 whch dcates a almost perfect agreemet wth the groud truth data Keywords: Remote sesg, Oe-agast-all, Image classfcato, Satellte mage, Support vector mache Itroducto Remote Sesg (RS mage classfcato tasks are typcally multclass problems, mplemeted wth mult-class classfers Recetly bary classfers have bee appled to RS problems otably by ether Oe-agast- All (AA or Oe-Agast-Oe (A techque A maor dsadvatage of these techques s the uclassfcato of some pxels Several methods of extedg bary classfers to mult-class tasks have bee proposed past lteratures (Moutraks et al, Ths work therefore presets a robust 34

2 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN method of modellg a AA classfcato based o Support Vector Mache (SVM (Cortes ad Vapk, 995 SVM s trscally a cotemporary bary mache learg algorthm that has bee appled extesvely several dscples However, applcatos of bary classfcato are very lmted especally RS lad cover classfcato where most of the classfcato problems volve more tha two classes (Melga ad Bruzzoe, 4 I ths expermet, a AA techque wll be used to exted the bary SVM classfer to a mult-class task Ths AA techque s called a wertakes-all classfcato For a N class classfcato, N bary classfers are created Each classfer s traed to dscrmate oe class from the remag N- classes (Melga ad Bruzzoe, 4 The algorthms used for classfyg RS mages ca ether be supervsed or usupervsed Notable covetoal usupervsed techques clude kmeas ad fuzzy c-meas whle the supervsed clude K earest eghbour, maxmum lkelhood classfer ad Gaussa mxture model SVM mplemeted ths work s a supervsed techque Support vector mache For a SVM lear case, a bary problem that belogs to classes - ad + respectvely ca be classfed usg a lear hyperplae To separate these two sets of obects, a few trag samples must be chose Assumg that the trag set has -trag samples, that s, x, y,( x, y,,( x, y N (, where x R s a N dmesoal vector that belogs to oe of classes y {, + } The stated bary classfcato problem ca be separated usg a lear decso fucto (Vapk,, f ( x = w x + b ( N where w R s a vector that determes the oretato of the desred hyperplae requred for the separato, ad b R s called the bas The optmal hyperplae eeded to separate the two obects s, y ( w x + b ( The soluto to ths problem ca be foud by solvg the followg costraed optmzato problem (or prmal problem (Vapk,, mmse, w w + C ξ (3 = subect to: y ( w x + b ξ, ξ >, ad for =,, ; where C, < C <, s called the pealty value; whle ξ are the slack varables The 35

3 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN optmsato problem or dual form derved by solvg equato 3 ca be expressed as, maxmse: α α α y y ( x x = = = subect to: α y =, ad, α C, for =,, (Vapk, The = resultg decso fucto for the lear case ca be gve as, f ( x = sg yα ( x x + b (5 = where x are the trag samples; y are the target labels of the trag samples (such that, y {, + } ; are the Lagraga multplers; b s kow as the bas; whle x deotes the test set (Vapk, α For the olear case, the optmsato problem ca be wrtte as, maxmse: α α α y y K( x, x (6 = = = subect to: α y =, ad, α C, for =,, Whle the resultg = decso fucto ca be gve as, f ( x = sg yα ( x, x + b (7 = Gve two arbtrary support vectors x A class A ad x B class B, the bas ca be evaluated as, b = yα ( K( x A, x + K( xb, x (8 = The kerel K x, x ca be ay of the followg commo kerel ( fuctos: the lear kerel x x, polyomal kerel x ( x + d (4 ad Radal x x Bass Fucto (RBF kerel K ( x, x = exp γ (Gu, 998 A mult-class problem The formulato of a AA techque s such that, a data pot wll be classfed uder a certa class f ad oly f that class accepts t ad all the other classes reect t Usg a smulated mult-spectral satellte remote 36

4 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN sesg mage (where: =water, =udeveloped, ad 3=developed (Table, wth a matrx sze of 5 x 5, that cossts of three smulated spectral bads (Tables -4; we ted to classfy the three classes (water, udeveloped ad developed cotaed the mage All the three spectral bads Tables -4 cota hypothetcal dgtal umbers Table Actual mage Table 3 Bad Table Bad Table 4 Bad Table 5 Trag data Water Bad (, = Bad (, = 73 Bad 3 (, = 36 Water Bad (, = 8 Bad (, = 75 Bad 3 (, = 33 Udeveloped Bad (,5 = 6 Bad (,5 = 3 Bad 3 (,5 = 66 Udeveloped Bad (,4 = 7 Bad (,4 = 4 Bad 3 (,4 = 67 Developed Bad (3, = 4 Bad (3, = 8 Bad 3 (3, = 9 Developed Bad (4, = 43 Bad (4, = 8 Bad 3 (4, = 96 To classfy the mage gve Table, a trag set was radomly selected The trag data (sx pxels cosst of elemets from the three classes (Table 5 For modellg coveece let the remag etee pxels that were ot used for trag the classfer (Table 6 represet the test set Covetoally the sze of the test set s usually smaller tha that of the trag set mache learg But for the purpose of llustrato, let the remag etee pxels serve as the test set As metoed the precedg secto, the AA techque s prmarly kow as a wer-takesall classfcato N bary SVM classfers must be costructed for a N class classfcato; N beg the umber of classes volved Each classfer s traed to dscrmate oe class from the remag N classes A label s assged to a class f ad oly f that class accepts t, ad every other class reects t If ths s ot the case the pxel s left uclassfed Three classfers were requred for the classfcato (Table 7 From Table 7, 37

5 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN Classfer : Water (+ versus All (-, Classfer : Developed (+ versus All (-, ad Classfer 3: Udeveloped (+ versus All (- The modellg was mplemeted MATLAB usg the polyomal kerel of degree, d= The pealty value was, C= The trag ad test results were preseted Table 7 Table 6 Test data Bad (, = Bad (, = 78 Bad 3 (, = 3 Bad (4, = 47 Bad (4, = 86 Bad 3 (4, = 97 Bad (5, = 46 Bad (5, = 88 Bad 3 (5, = 9 Bad (, = Bad (, = 7 Bad 3 (, = 38 Bad (3, = 4 Bad (3, = 9 Bad 3 (3, = 93 Bad (5, = 45 Bad (5, = 84 Bad 3 (5, = 98 Bad (,3 = 4 Bad (,3 = 7 Bad 3 (,3 = 34 Bad (,3 = 9 Bad (,3 = 8 Bad 3 (,3 = 3 Bad (3,3 = 7 Bad (3,3 = 76 Bad 3 (3,3 = 39 Bad (4,3 = Bad (4,3 = Bad 3 (4,3 = 6 Bad (5,3 = 5 Bad (5,3 = 83 Bad 3 (5,3 = 99 Bad (,4 = Bad (,4 = 74 Bad 3 (,4 = 37 Bad (3,4 = 6 Bad (3,4 = 6 Bad 3 (3,4 = 68 Bad (4,4 = 9 Bad (4,4 = 9 Bad 3 (4,4 = 65 Bad (5,4 = 3 Bad (5,4 = 5 Bad 3 (5,4 = 66 Bad (,5 = Bad (,5 = Bad 3 (,5 = 63 Bad (3,5 = 4 Bad (3,5 = 8 Bad 3 (3,5 = 6 Bad (4,5 = 3 Bad (4,5 = 7 Bad 3 (4,5 = 6 Bad (5,5 = 5 Bad (5,5 = Bad 3 (5,5 = 64 Table 7 Trag ad test results (trag result: CLASSIFIER CLASSIFIER b & α ; test result: (x CLASSIFIER 3 f Water (+ versus All (- ( b = 374 Developed (+ versus All (- ( b = 84e 4 Udeveloped (+ versus All (- ( b = 39 α f (x α f (x α f (x *e *e *e *e *e *e *e *e *e

6 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN From Table 7, the trag results were furshed by b ad α, whle the test result was furshed by f (x Scores wth f ( x > were assged, whle scores wth f ( x < were assged The results from the three bary classfers were preseted Tables 8, 9 ad The followg MATLAB pseudo codes were appled to the outcome of the three classfers to derve the result of the fal mage (Table : WATER = (WATER_ALL== & (DEV_ALL==; DEVELOPED = (DEV_ALL== & (UNDEV_ALL==; UNDEVELOPED = (UNDEV_ALL= & (WATER_ALL==; RESULT = WATER + 3* DEVELOPED + * UNDEVELOPED From Table, 6 pxels were correctly classfed whle 3 pxels were left uclassfed (the zeros Table were the uclassfed pxels The resultg classfcato soluto usg the AA SVM model (Table was compared wth the orgal dgtal mage gve Table ; the classfcato accuracy was 6 9 = 84% The cofuso matrx gve Table was derved based o a cell-by-cell comparso of the actual (Table ad predcted mage (Table The classfcato overall accuracy (computed from Table = sum of dagoal elemets sum of all elemets the matrx Therefore, overall accuracy = 5 = 84% Table 8 Result for Water versus All Table Result for Udeveloped versus All Table Cofuso matrx for the classfcato Table 9 Result for Developed versus All Table Predcted mage Referece data Water Udeveloped Developed Uclassfed Predcted data Water 7 Udeveloped 8 Developed 6 Uclassfed 39

7 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN If If If Resolvg the classes of pxels resultg from AA classfcato The result of the AA classfcato s regarded as a tetatve classfcato result For example, a three class problem wth lad uses such as developed, udeveloped ad water wll yeld four classes after the AA classfcato I order words, the fourth class represets the uclassfed pxels The fal classes of all the pxels (based o desgated lad use classes are obtaed by employg frst the followg equato, p t+ ( α ( wk t t t [ h ( α * ( h ( α *( γ ] ( + exp{ A* + } = Q B k k t+ where: p ( α ( wk = the probablty that pxel α belogs to class wk of the t-th terato t h ( α ( wk = the Moore eghbourhood fucto of pxel α that belogs to class wk of the t-th terato t γ = s a uform radom varable wth the rage ad of the t-th terato Q = s a coeffcet w k = w, w, w3,, wm classes A & B = costats By employg equato 9, each pxel wll yeld k umber of probablty values, where k represets lad use classes Equato represets trasto rules that decde the evetual class of a pxel The probablty equato 9 s calculated teratvely t + t + t + t + ( p ( α > p ( α & & ( p ( α > p ( α w ( m t + t + t + t + ( p ( α > p ( α & & ( p ( α > p ( α the the class _ class _ Wth equato, the calculated probablty of a pxel of terest that belogs to a gve class must be greater tha the calculated probablty of the rest t + classes computed t + for that gve pxel, t + for that t + class to w the class allocato p ( α ( w for pthat gve pxel p p the class m > ( α & & ( α ( wm > ( α w _ ( m Case study The research case study s based o a multspectral Ladsat 7 ETM satellte mage of Porrua, New Zealad, acqured 6 (Fgure The Ladsat mage cossts of seve spectral bads The orgal satellte data ( m m (9 ( 3

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Europea Scetfc Joural September 4

the layer propertes tool ad vsualsed MATLAB (Fgure Before mportg the data to MATLAB, they were frst coverted from raster

processg MATLAB I MATLAB the fal study area was extracted from the orgal satellte mage All the seve bads were used for

three classes to be classfed are water, developed ad udeveloped cells The stratfed radom samplg was used to select the

Bass Fucto ad the lear kerels were expermet The polyomal kerel furshed the best accuracy The selecto of d ad C was doe

together to tra the SVM whle the remag oe dataset was held to test the accuracy of the expermet The accuracy estmato was

8 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN were frst revewd ArcGIS software ad all seve bads were extracted usg the layer propertes tool ad vsualsed MATLAB (Fgure Before mportg the data to MATLAB, they were frst coverted from raster to ASCII data usg the ArcGIS coverso tool MATLAB caot read raster fles; hece the data must be ASCII format for oward processg MATLAB I MATLAB the fal study area was extracted from the orgal satellte mage All the seve bads were used for the classfcato expermet Bad Bad Bad 3 Bad 4 Bad 5 Bad 6 Bad 7 Satellte mage Fgure Ladsat mage ad ts extracted bads -7 The three classes to be classfed are water, developed ad udeveloped cells The stratfed radom samplg was used to select the trag data The expermet was mplemeted wth a polyomal kerel of degree d = 3 ad pealty value C = (Fgure The polyomal, Radal Bass Fucto ad the lear kerels were expermet The polyomal kerel furshed the best accuracy The selecto of d ad C was doe usg the k-fold cross-valdato process where k = (Bhardwa et al, 5 At each expermet, e datasets (k-datasets were put together to tra the SVM whle the remag oe dataset was held to test the accuracy of the expermet The accuracy estmato was based o Kappa statstc expressed from equatos -3 The expermet was repeated te folds utl all the datasets were used for both trag ad testg (Fgure 3

9 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN Kappa 8348 Kappa Degree & Gamma C Degree Gamma Polyomal RBF Lear Fgure Cross-valdato results for: (a Degree ad Gamma (b C Results I the expermet, each lad use class was dvdually classfed agast the rest classes; that s three classfers were desged The tetatve result preseted Fgure 3 was obtaed by combg all the three classfers Fgure 3 was vsualsed ArcGIS, by covertg the ASCII data from MATLAB to raster data ArcGIS usg the coverso tool Fgure 3 Ital result 3

Europea Scetfc Joural September 4 edto vol, No7 ISSN: 857 788 (Prt e - ISSN 857-743 Fgure 3 cotas four lad use classes: water, developed ad udeveloped Sce the classes of the pxels Fgure 3 are

10 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN Fgure 3 cotas four lad use classes: water, developed ad udeveloped Sce the classes of the pxels Fgure 3 are tetatve, equatos 9 ad were employed to obta the fal result Fgure 4 Sce the calculated probabltes were determed stochastcally (equato 9, each level of terato was ru tmes to compute the mea Kappa statstc at the 95% cofdece level The fal class of each pxel Fgure 3, was resolved to three classes usg equatos 9 ad Fgure 4 Fal result The Kappa statstc was used to evaluate the accuracy of the classfcato The Kappa statstc ca be expressed mathematcally as, Po Pc K = Pc ( where, m m Po = P = = N = ( ad, m m Pc = P + P+ = + + = N =, (3 (Ma ad Redmod, 995; Lo ad Yeug, 7, where, P o = proporto agreemet observed P = proporto agreemet expected by chace c 33

11 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN = the total umber of correctly classfed pots by class alog the dagoal of the error matrx N = the total umber of pots checked (sampled P = the proporto of correctly classfed sample pots by class at the dagoal of the error matrx (e / N P + = the margal dstrbuto of the sample data ( / N + where + s the row sum by class P + = the margal dstrbuto of the referece data( + / N where + s the colum sum of class m = the total umber of classes The Kappa estmate of the classfcato was obtaed by a cell-by-cell comparso betwee the classfed ad the groud truth data The mea Kappa estmates for twety teratos were preseted Fgure Mea Kappa Fgure 5 Mea Kappa statstc for twety teratos 8 The hghest Kappa result was obtaed at the 9th terato; whle the lowest Kappa 8 result was obtaed at the th terato (Fgure 5 The tal result (Fgure 3 yelded a Kappa value of 7787 computed from the 8 cofuso matrx gve Table Number of teratos Table 3 Cofuso matrx for the tal result Groud truth data Developed Udeveloped Water Uclassfed Predcted data Developed Udeveloped Water Uclassfed

12 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN Usg the terpretato Table 5 (Lads & Koch 977, ths result however dcates a substatal agreemet betwee the groud truth ad the predcted data (Table 5 The cofuso matrx for the fal result (Table 4 dcates substatal mprovemet the amout of correctly classfed pxels, by comparg the cofuso matrx of the tal result wth that of the fal result Table 4 Cofuso matrx for the fal result Groud truth data Developed Udeveloped Water Uclassfed Predcted data Developed Udeveloped Water Uclassfed The off-dagoal elemets were the correctly classfed pxels The fal mage yelded a Kappa value of 867 Usg the terpretato Table 5 (Lads & Koch 977, ths result dcates a almost perfect agreemet betwee the groud truth ad the predcted data Ths work showed the possblty of obtag accurate classfcato result usg bary classfers, doe smply by ehacg the kow classcal algorthm Table 5 Iterpretato of Kappa statstc KAPPA INTERPRETATION < No agreemet Slght agreemet 4 Far agreemet 4 6 Moderate agreemet 6 8 Substatal agreemet 8 Almost perfect agreemet Cocluso Ths work elucdated how a bary classfer ca be exteded to mult-class task by applyg a ew techque that resolved the classes of uclassfed pxels resultg from the AA classfcato bascally by employg pxel eghbourhood ad stochastcty Ths ew techque mproved the calculated Kappa statstc from 7787 to 867 Refereces: Bhardwa, N, Laglos, R, Zhao, G ad Lu, H Kerel-based mache learg protocol for Predctg DNA- dg protes Nuclec Acds Research, 33: , 5 35

13 Europea Scetfc Joural September 4 edto vol, No7 ISSN: (Prt e - ISSN Cortes, C ad Vapk, V Support vector etworks Mache learg, :73-97, 995 Gu, S Support vector maches for classfcato ad regresso Techcal Report, ISIS Southampto, Eglad: Departmet of Electrocs ad Computer Scece, Uversty of Southampto, 998 Lads, J R ad Koch, G G The measuremet of observer agreemet for categorcal data Bometrcs, 33:59 74, 977 Lo, C P Ad Yeug, A K W (Eds Cocepts ad techques of geographc formato systems (d ed Upper Saddle Rver, New Jersey: Pearso Pretce Hall, 7 Ma, Z Ad Redmod, R L Tau coeffcets for accuracy assessmet of classfcato of remote sesg data Photogrammetrc Egeerg ad Remote Sesg, 6: , 995 Melga, F ad Bruzzoe, L Classfcato of Hyperspectral Remote Sesg Images wth Support Vector Maches IEEE Trasactos o Geoscece ad Remote Sesg, 4:778-79, 4 Moutraks, G, Im, J ad Ogole, C Support vector maches remote sesg: A revew ISPRS Joural of Photogrammetry ad Remote Sesg, 66:47 59, Vapk, V N The ature of statstcal learg theory New York: Sprger- Verlag, 36

Stochastic GIS cellular automata for land use change simulation: application of a kernel based model

Stochastic GIS cellular automata for land use change simulation: application of a kernel based model Stochastc GIS cellular automata for lad use chage smulato: applcato of a kerel based model O. Okwuash, J. McCoche, P. Nwlo 3, E. Eyo 4 School of Geography, Evromet, ad Earth Sceces, Vctora Uversty of Wellgto,