Automated method for scoring breast tissue microarray spots using Quadrature mirror filters and Support vector machines

Transcription

1 Automated method for scorng breast tssue mcroarray spots usng Quadrature mrror flters and Support vector machnes Trang Km Le Abstract Tssue mcroarray (TMA) technque s one of the wdely used methods n treatment for breast cancer patents durng the past decade. Ths technology has shown postve results n the dagnoss, detecton and treatment of breast cancer. TMA spots can be classfed nto four man grades n whch a grade of 0 ndcates the spot s negatve for the dsease, and a grade of 3 s strongly postve. Ths score classfcaton s done by pathologst and n a large scale of mage data ths work becomes tme consumng, subectve and prone to approxmate errors. The obectve of ths study s to fnd a way to classfy the TMA spot mages nto four score types automatcally and evaluate algorthm for automatc, quanttatve analyss of TMA mages to help pathologst save tme and analyze the mages accurately. Ths paper explores a method of automated scorng spots usng densty approxmaton of color and features clusters n the feature space, these texton hstograms were then classfed usng multclass support vector machnes. The features used n ths paper were generated by usng Orthogonal quadratc mrror flters (QMF), characterzed every spot by a texton hstogram of nearest cluster center. The scorng performance was assessed usng TMA spots from Stanford Tssue Mcroarray Database. The average accuracy of four classes over 50 leave-half-out experments was around 65% to 67% wth nearly balanced data, was around 58% to 60% wth sgnfcant mbalanced data. The use of QMF feature of Coflet 4 wavelet, the accuracy could be reach 80.4% for score 0; 46.78% for score ; 64. % for score and 7% for score 3. Keywords-tssue mcroarray; texton hstogram; quadrature mrror flter; multclass support vector machnes I. ITRODUCTIO Tssue mcroarrays (TMA) are produced by combnng hundreds of spots or specmens of tssue onto a sngle slde for smultaneous analyss by pathologst, the nformaton contaned n each TMA spot of a TMA array has an mportant role n treatment plannng for breast cancer patents. Fg. and Fg. are examples of TMA spots. TMA spots could be classfed nto four types as to the man type of tssue that t contaned, whch are tumour, normal, stroma and fat as prevous work of Amaral [4]. TMA spots could also be classfed nto four classes of scorng or gradng, the scorng keys range from a grade of 0 to a grade of 3, n whch score 0 (.e. a grade of 0) ndcates negatve for dsease, score ndcates equvocal or un-nterpretable, score ndcates postve and score 3 s strongly postve []. Scorng breast TMA spots s tme consumng, subectve and prone to approxmate errors n a large scale of mage data. Therefore, there s a motvaton for the development of automated methods of gradng or scorng TMA mage data. Appearances of the TMA spots even n the same category or n the same type are very dfferent because the spatal orentaton and arrangements of sub-cellular compartments change greatly [5]. Ths suggested the use of texton hstogram could gve a better use n tranng data and help teach the system to deal wth test data. Texton hstogram s one of the effcent features to estmate the structural, orentaton or regularty dfferences of dverse regons n an mage. Several approaches for texton hstogram analyss have been proposed by researchers durng the last decades. The classfcaton usng texton hstogram s commonly dvded nto two man stages, whch are feature extracton and classfcaton. In feature extracton, flterng based approach has shown a relatvely hgh accuracy for a large scale of mage data n multclass classfcaton. Some technques of ths approach have been used nclude Gabor flterng, mult-channel flterng, wavelet decomposton, Gaussan and Laplacan of Gaussan flterng, etc. In prevous work of Amaral, dfferental nvarant flterng was used to extract features that are nvarant to rotaton and n classfcaton stage, generalzed lnear model (GLM), mult-layer perceptron (MLP) and Latent Drchlet Allocaton (LDAL) were used as classfers n whch dfferental nvarant features and MLP classfer acheved hgh results n classfcaton [4]. In ths work, the use of Quadrature mrror flters (QMF) for Wavelet transform s proposed for feature extracton stage together wth tunng parameter Support vector machnes (SVM) n classfcaton stage. The QMF flterng was chosen to use here based on the results of Randen and Husoy [] n a comparatve study on flterng for texture classfcaton, whch showed that QMF flters has hgh accuracy n recognzng texture. The study of Osowsk has confrmed that both MLP and SVM networks are well suted for classfcaton task, SVM approach has advantage n large datasets, the algorthm s usually qucker than MLP [8], thus n ths study SVM was chosen n the classfcaton stage. The next secton gves a descrpton of data and methods used for classfcaton followed by the expermental results n Secton III. A summary of observatons made from ths study and future work drectons n Secton IV. II. DATA AD METHOD A. Data The data used n ths study contaned color mages of breast tssue mcroarray spots orgnatng from the webste of 868

2 Stanford Tssue Mcroarray Database wth array block named TA- of a malgnant breast cancer patent [8]. Two experments were conducted to assess and analyze the performance of the method. The frst experment conssted of 56 TMA spots staned wth CATHEPSI-L, and the crtera of scorng were unspecfed. The second experment had 64 TMA spots staned wth HE, and crtera for scorng was based on stromal fbroblast. The results of these experments were then compared to the ground truth of scorng provded by the webste of Stanford Tssue Mcroarray Database [8]. Ground truth of experment obtaned on 9 June, 007 and ground truth of experment were results of scorng on July, 008. Fgure. Example of TMA spots staned wth CATHEPSI-L. Fg. shows an example of each type n experment and Fg. shows a spot characterstc of each type of score n experment, those TMA spots are hghly varable n appearance. In the next secton, step by step of the method of spot classfcaton ncludes feature extracton and multclass classfers are descrbed. B. Feature extracton Ths study proposes the uses of Orthogonal quadrature mrror flters (QMF) of Wavelet transforms whch had hgh accuracy n classfyng texture n the study of Randen and Husoy []. Wavelet transform and orthogonal QMF source code obtaned at [9]. ) Local features The TMA spot mages were frst converted nto grey scale and a et of local features was then calculated for each pxel of a spot by convolvng an mage wth orthogonal quadrature mrror flters (QMF) of Wavelet transforms usng crcular convoluton n the spatal doman method [3] n two dmensons of the mages. A et of local features of TMA spot ncluded red, green, blue color values of orgnal sze mage and QMF features whch used orthogonal quadrature mrror flters of Daubeches 8 (db8), Coflet 4 wavelet, Symmlet 4 wavelet and Beylkn wavelet transform. QMF are wdely used n sgnal processng, partcularly n dgtal audo applcaton, sub-band codng of speech, etc. The next part wll be a bref descrpton about these flters. ) QMF flters QMF flters lead to orthogonal flter banks wth frequency characterstcs symmetrc about /4 of samplng frequency. They are desgned to use n the process of makng orthogonal dscrete wavelet transform. The hgh and low pass flters n the forward or nverse transforms have mrror symmetry around π as n Fg 3 wth H0 (z) s low pass and H (z) s hgh pass. Fgure 3. Quadrature mrror flter (QMF). Fgure. Example of TMA spots staned wth HE. The hgh pass flter coeffcents are obtaned from an alternatng flp of the low pass flter coeffcents. Tme reverson of the flter coeffcents n the forward transform wll generate flter coeffcents n the nverse transform. Let x be a fnte energy sgnal, f for any x, y0 + y = x Then two flters F 0 and F are quadrature mrror flters (QMF). Defne y 0 s a decmated verson of the result of the process of the sgnal x fltered wth F 0 then x 0 = F 0 (x) and y 0 (n) = x 0 (n). 869

3 Smlarly for y, we have x = F (x) and y (n) = x (n). If F 0 s a Coflet scalng flter and F s QMF of F 0, then the transfer functons F 0 (z) and F (z) of the flters F 0 and F wll satsfy the followng frequency condton: F0 ( z) + F ( z) = For nstance, n ths study, wth Coflet 4 wavelet: Coflet4 = [ e e e e e e e -6 ]; Then, orthogonal QMF of Coflet 4 wavelet wll be: QMF(Coflet4) = [ e e e e e e e -4 0]. After that ths orgnal orthogonal QMF wll be shfted rght one unt before applyng crcular convoluton. Thus the flter used to convolve wth the mages s: FlterUsed = [ e e e e e e e -4 ] Fgure 4. QMF Coflet 4 wavelet. Fg. 4 shows a check for frequency condton whch s necessary for orthogonalty. The next part descrbes texton hstogram extracton whch wll be used as an nput for classfcaton stage. 3) Global features. Frstly, local feature ets were computed for all spots n tranng and test set and only a proporton of these local features were used for calculatng texton hstogram and for classfcaton. Therefore, each spot wll be assocated wth a proporton of ts local feature et. Then the means and varances of tranng spots were calculated, these values were used to normalze sample ets of all spots to zero means and unt varances. From tranng spots, a proporton of normalzed sample ets were randomly sub-sampled to put nto K-means unsupervsed clusterng. After beng traned wth K-means, centers of a number of clusters n mult-dmensonal normalzed local feature space were created and saved to compute hstogram of texton frequences for all spots. The obtaned set of cluster centers could be called a texton dctonary. ormalzed sample ets of all spots were then put nto a K-nearest-neghbor classfcaton to put each et to the nearest texton n dctonary (nearest cluster centers). Based on these textons, hstograms of all spots were computed. C. Classfcaton wth SVM The classfers can be dvded nto two man types: dscrmnatve approach and generatve approach. The former s traned by dscrmnant functons only for classfcaton purposes. If t s a class n a set of classes {T, T,..., T C } and x s a test sample, dscrmnatve methods drectly estmate P(t x) from the data (or a classfcaton functon t=f(x)). The latter approach frst estmates the ont probablty densty functon p(x,t) from the data p(x,t) = Σp(x t)*p(t) and then classfes by computng p(t x) usng Bayes rule. In ths work, support vector machnes (SVMs), whch are a dscrmnatve method, were used wth Heavy Tal Radal Basc Functon (HT RBF) kernel. The reason SVMs were chosen here s because they are n wdespread use and have rather hgh successful results n bonformatcs tasks. SVMs exhbt very compettve classfcaton performance, are robust n hgh dmensons and gve condtons for learnng algorthms to generalse well. Moreover, they have wde applcablty not only for hgh dmensonal vector data, but also for structured data such as strngs (proten and DA sequences), graph (molecules and proten nteracton networks), tme seres (tme seres of mcroarray data), and sets, trees, etc. The dscusson below based on the reference [] and [3]. ) SVM model: Decson functons of SVMs can be expressed as n (). f(x) = w T.Φ(x) + b () where x stands for nput vector, x R D, w s a normal vector of hyperplane n feature space whch s produced from the mappng from orgnal space to hgher dmensonal space: Φ(x): R D R H (H > D, Φ(x) can be lnear or non-lnear) and b s the devaton from the orgn. At frst, SVM s desgned for a bnary classfer, therefore the sgn of f(x) would ndcate vector x belong to class + or class -. Gven a sample dataset {(x,y ),..., (x, y )}wth x R D and y {±}, the goal of SVM classfer method s to fnd a hyperplane that maxmzes the margn between two classes, e.g. the dstance from ths hyperplane to the nearest data pont on each sde s maxmzed as n Fg

4 Fgure 5. A bnary support vector machne. b The value of parameter fnds out the offset of the w hyperplane from the orgn along normal vector w. The values of w and b are chosen so that they wll maxmse the margn, or the dstance between the parallel hyperplanes that are as far apart as possble. These hyperplanes could be expressed as n (): w T. Φ(x) + b = - and w T. Φ(x) + b = + () The dstance between these two hyperplanes s = w T w w, so we need to mnmse w. The followng constrant s added to avod data ponts from fallng nto the margn: w T. x + b + for x of the frst class, w T. x + b - for x of the second class, whch s equvalent to y [w T. Φ(x) + b], wth =,..., ; y {±}. ) Inseparable data: In case of such separatng hyperplane does not exst, a so called slack varable ξ s ntroduced such that T y[ w Φ( x ) + b] ξ, =,..., ξ 0, =,..., By addng some balance factors to avod over-fttng and accordng to the structural rsk mnmzaton prncple, the rsk bound s mnmzed. Therefore tranng SVM s to solve the followng problem: Subect to T mnj( w, ξ ) = w w + c ξ (3) y[ w T = Φ( x ) + b] ξ, =,..., ξ 0, =,..., where α 0, β 0 are the Lagrange multplers and c s the bound on the Lagrange multplers that loosen the condtons for classfcaton [0]. Instead of solvng problem (3), ts dual problem s solved whch s called a quadratc programmng optmsaton problem. By substtutng w by ts expresson, the quadratc programmng problem wll be acheved as n (4): maxq ( α ) = αα y y K( x, x) + α (4), = = where K(x,x ) = <Φ T (x ), Φ(x )> s called the kernel functon. If K(x, x ) s lnear, SVM s lnear, otherwse, f K(x, x ) s non-lnear, SVM s non-lnear. Solvng ths QP problem subect to constrans n (4), the hyperplane n the hgh dmensonal space and hence the classfer n the orgnal space wll be obtaned. The optmal pont wll be n the saddle pont of the Lagrange functon, then we obtan L = 0 w = Φ α y ( x ), w t= L = 0 = α y 0, w t= L = 0 0 α c, =,..., w Each tranng sample x wll correspond to a Lagrange α. After tranng, samples wth α > 0 are called supported vectors. From (5) and (), decson functon wll be: = T (5) f ( x) = α y Φ ( x ). Φ( x) + b (6) Suppose n (6), Φ T (x ). Φ(x ) = K(x, x ), e.g, dot product (scalar) n feature space (new space) equvalent to a kernel functon K of nput space (orgnal space). We do not need to calculate drectly Φ T (x ) and Φ(x ) but only need to know the result of Φ T (x ). Φ(x ) of (6) va functon K(x, x ). Therefore decson functon wll have the form of (7) f ( x) = α y K( x, x) + b (7) = Only support vectors contrbute to produce hyperplane, therefore one sample x wll be classfed by the decson functon n equaton (8) sv f ( x) = sgn( α yk( x, x) + b) (8) = where SV s number of support vectors 3) Kernel machne: The frst optmal hyperplane algorthm proposed by Vapnk was a lnear classfer. However, Boser, Guyon and Vapnk developed nonlnear classfers by applyng the kernel trck to maxmum-margn hyperplanes []. Every dot product s replaced wth a nonlnear kernel functon. The feature space wll be a Hlbert space of nfnte dmenson f the kernel used s a Gaussan radal bass functon. The nfnte dmenson does not spol the results because the maxmum margn classfers are well regularsed. 87

5 Below are some common kernels: Polynomal (homogeneous): k ( x, x ) = ( x. x ) Polynomal (nhomogeneous): k ( x, x ) = ( x. x + ) Gaussan Radal Bass Functon: k( x, x ) = exp( γ x d x for γ>0 (sometmes usng γ = / σ ) Heavy taled Radal Bass Functon (HT RBF): k a a b p x x (, ) exp x x =, wth a, b. The kernel s related to the transform Φ T (x ) by the equatons K(x, x ) = Φ T (x ). Φ(x ). The value w s also n the transformed space, wth w = = α y Φ( x ) D. Multclass SVM The goal of multclass SVM s to assgn labels to nstances by usng support vector machnes, where the labels are drawn from a fnte set of more than two elements. The approach for dong so s to reduce the sngle multclass problem nto multple bnary classfcaton problems [4]. The orgnal mult-class SVM s converted to bnary problems: bnary classfers are bult whch dstngush between one of the labels to the rest of labels (one-versus-all approach) or between every par of classes (one-versus-one approach). Ths s dvde and conquer method, whch decomposes the multclass problem nto several bnary sub-problems, and bulds a standard SVM for each. ) One-vs-all approach Classfcaton of new nstances s done by a wnner-takes-all strategy [5], n whch the classfer wth the hghest output functon assgned to the class. One SVM s bult per class, f C s the number of classes, there wll be C classfers. These classfers are traned to dstngush the samples n a sngle class from the samples n all remanng classes. ) One-vs-one approach One SVM s bult for each par of classes, f C s the number of classes then there wll be C*(C-)/ classfers. Classfcaton s done by a "Max Wns" votng strategy [4], n whch every classfer assgns the nstance to one of the two classes, then the vote for the assgned class wll be ncreased by one, and the class wth the most value of vote determnes the nstance classfcaton. In ths work, the SVM and kernel methods Matlab Toolbox of S. Canu, Y. Grandvalet, V. Gugue and A.Rakotomamony was used [5]. Heavy taled RBF (HT RBF) kernels of the form a a b p x x x k(, x ) = exp, a, b, are evaluated on the classfcaton of mages extracted from the Corel Stock Photo collecton and shown to out-performed tradtonal polynomal ) d and Gaussan RBF kernel [3], based on ths result, ths study only uses heavy taled RBF kernels n experments. III. EXPERIMETS AD RESULTS There were two data sets, one dedcated to calculate texton usng k-means algorthm, whch was called dataset, and the remanng data set, whch was called dataset, was used to compute hstograms of texton base on texton dctonary of dataset. Fnally these texton hstograms of dataset were used to tran and test classfers. A. Experment Experment contaned 56 TMA spots staned wth CATHEPSI-L, and crtera for scorng was unspecfed and the ground truth obtaned on 9 June, 007 [8]. These TMA spots were then dvded nto two datasets. Dataset contaned 4 TMA spots of all scores, whch was used to compute a texton dctonary of 73 centres, based on a random sample of,000,000 normalsed ets over all the nvolved spots (equvalent to.73% of all ets n dataset). Dataset nvolved 4 spots (66 for score 0; 46 for score ; 56 for score and 46 for score 3) and only one wavelet feature was used at a tme, so that a et contaned 4 local features: the R, G, B colour values and one wavelet transform feature. The dataset was randomly dvded nto two halves of 07 spots each, sutable for runnng leave-half-out experments. These experments were based on the process of randomsng tranng spots and test spots of dataset. Each dctonary was used along wth a nearest-neghbour classfer to obtan a texton hstogram of all 4 spots n dataset, based on a random sample of at most 90,000 normalsed ets per spot (specally, 4.5% of each spot s ets). Hstograms of texton frequences of 07 tranng spots were used to tran the SVM classfers. Then hstograms of texton frequences of 07 testng spots were classfed by SVM wth both approaches: one-vs-all and one-vs-one to compare the outcomes. ) Parameter tunng There are many ways proposed for tunng SVM parameters by researchers. The smplest way could be used s assgn values for parameters, value of one specfc parameter wll be run n a range (called non-fxed parameter), values of the other were fxed (called fxed parameters) to compare the result to fnd the best value of the current non-fxed parameter. For example n ths study, tunng the parameters of multclass SVM one-vs-one classfer, the QMF feature of Coflet 4 wavelet was used. There are four parameters need to consder, namely c, and λ of SVM classfer, n whch c s the bound on the Lagrange multplers n (3) and (5), λ s the condtonng parameter for QP algorthm, and two parameters of heavy taled RBF kernel, namely a and b of the form a a b p x x x k(, x ) = exp wth a, b a) Frst tune a = 0., b =.5, c {000, 000, 3000, 4000, 5000} and λ {0 -, 0 -, 0-3, 0-4, 0-5 }. 87

6 There are 5 values of c and 5 values of λ n ths tune, thus there wll be 5x5 = 5 cases. 5 leave-half-out experments were conducted and the results showed that c = 000 and λ = 0 - had the best accuracy. b) Second tune c = 000, λ = 0 -, a [0....0], b [....0] 5 leave-half-out experments were performed and parameters havng values a = 0., b =.9 can be the best ones. c) Thrd tune c = 000, λ =0 -, a [ ], b = [ ] 5 leave-half-out experments were performed and the results showed that c=000, λ =0 -, a = 0., b =.98 or b =.99 have the best performance n classfcaton wth the average error rate usng b=.99 over four classes of scores was 33.7% and error rate usng b=.98 was 3.9%. d) Best parameters Tunng one-vs-all approach smlar to tunng one-vs-one approach. The best values of parameters found n ths study are: one-vs-one approach: c = 000, λ =0 -, a= 0., b =.98 or b =.99 one-vs-all approach: c = 000, λ =0 -, a = 0., b =.95 or b =.96 ) Leave half out experments usng QMF features of Coflet 4, Daubeches 8, Symmlet 4 and Berklyn wavelet 50 leave-half-out experments were performed (equal to 00 runs) to survey the outcome of one-vs-one, one-vs-all methods usng heavy taled RBF kernels wth parameters found n parameter tunng stage and the number of clusters of texton dctonary were kept at 73 clusters. Best parameters of tunng process and results are n Table I and Table II. TABLE I. RESULTS OF 50 LEAVE-HALF-OUT EXPERIMETS USIG OE- VS-OE MULTICLASS SVM CLASSIFIER Average Mn Max one-vs-one c = 000 λ =0 - Error Std error error Coflet 4 a = 0. b = Dau 8 a = 0. b = Symmlet 4 a = 0. b = Berklyn a = 0. b = TABLE II. RESULTS OF 50 LEAVE-HALF-OUT EXPERIMETS USIG OE- VS-ALL MULTICLASS SVM CLASSIFIER Average Mn Max one - vs - all c = 000 λ =0 - Error Std error error Coflet 4 a = 0. b = Daus 8 a = 0. b = Symmlet 4 a = 0. b = Berklyn a = 0. b = ) Confuson matrx of the best classfer n experment The confuson matrx of the best classfer found n experment s presented n Table III and Table IV. TABLE III. COFUSIO MATRIX OF 50 LEAVE HALF OUT EXPERIMETS USIG OE-VS-OE SVM AD QMF OF COIFLET 4 WAVELET TRASFORM Parameters of HT RBF kernel and SVM classfer: a = 0., b =.96, c = 000 and λ = 0 - Truth TABLE IV. COFUSIO MATRIX OF 50 LEAVE HALF OUT EXPERIMETS USIG OE-VS-OE SVM AD QMF OF COIFLET 4 WAVELET TRASFORM Truth Predct (%) Score 0 Score Score Score 3 Score Score Score Score Predct (%) Score 0 Score Score Score 3 Score Score Score Score Parameters of HT RBF kernel and SVM classfer: a = 0., b =.96, c = 000 and λ = 0 - Average accuracy = ( ) / (07*50*) = 67.08%. 4) Spots always msclassfed ) Score 0 - Predct ) Score - Predct 3) Score - Predct 0 4) Score - Predct 5) Score - Predct 6) Score - Predct 0 7) Score - Predct 3 8) Score - Predct 3 9) Score 3 - Predct 0, 0) Score 3 - Predct ) Score 3 - Predct ) Score 3 - Predct 3) Score 3 - Predct 4) Score - Predct 5) Score - Predct Fgure 6. Spots that always been msclassfed n 50 leave-half-out experments of 4 spots staned wth CATHEPSI-L. 873

7 There are 5 spots that always msclassfed by SVM classfer wthn 50 leave-half-out experments, detals are n Fg. 6. B. Experment In experment, there are 64 TMA spots staned wth HE, and crtera for scorng was based on stromal fbroblast. The results of these experments were then compared to the ground truth of scorng provded on July, 008 [8]. Smlar to experment, there were datasets, dataset contaned 48 spots of all types, dataset contaned 0 spots (ncludng00 spots score 0, 6 spots score, 80 spots score and 4 spots score 3). Ths dataset are sgnfcant mbalanced n the number of spots among 4 types of scores. Smlar to experment, parameters of SVM classfers also tuned to choose the best combnaton. ) Leave half out experments usng QMF features of Coflet 4, Daubeches 8, Symmlet 4 and Berklyn wavelet TABLE V. RESULTS OF 50 LEAVE-HALF-OUT EXPERIMETS USIG OE- VS-OE MULTICLASS SVM CLASSIFIER Average Mn Max one - vs - one c = 000 λ =0 - error Std error Error Coflet 4 a = 0. b = Dau 8 a = 0. b = Symmle t4 a = 0. b = Berklyn a = 0. b = TABLE VI. RESULTS OF 50 LEAVE-HALF-OUT EXPERIMETS USIG OE- VS-ALL MULTICLASS SVM CLASSIFIER Average Mn Max one - vs - all c = 000 λ =0 - error Std error Error Coflet 4 a = 0. b = Dau 8 a = 0. b = Symmlet 4 a = 0. b = Berklyn a = 0. b = Table IV and Table V contan the average error, standard devaton, mnmum error, maxmum error of 50 leave-halfout experments together wth the best parameter settngs. ) Confuson matrx of the best classfer n experment Table VII and VIII show confuson matrx of ths experment, parameter settng s a = 0., b =.95, c = 000 and λ = 0 - TABLE VII. COFUSIO MATRIX OF 50 LEAVE HALF OUT EXPERIMETS USIG OE-VS-OE SVM AD QMF OF COIFLET 4 WAVELET TRASFORM Truth Predct (%) Score 0 Score Score Score 3 Score Score Score Score TABLE VIII. COFUSIO MATRIX OF 50 LEAVE HALF OUT EXPERIMETS USIG OE-VS-OE SVM AD QMF OF COIFLET 4 WAVELET TRASFORM Truth Predct (%) Score 0 Score Score Score 3 Score Score Score Score Accuracy=( ) / (0 * 50 * )=60.65% 3) Balanced dataset and m-balanced dataset TABLE IX. UMBER OF SPOTS I TWO EXPERIMETS Score 0 3 Experment nearly balanced Experment sgnfcant m-balanced In experment, four classes dd not have the same number of spots as n Table IX., the dataset s sgnfcant mbalancng. The score 0 type had 00 spots whle score 3 type only had 4 spots, ths made the classfers have dffcultes n classfyng spots belong to score 3, therefore most of the spots n ths type were ms-classfed as score. To explore how the number of spots affect the accuracy of that knd of spot, spots n score, score, score 3 were kept fxed at spots n dataset. Spots n score 0 wll be ncrease from spots to 4, 36, 48, 60, 7, 84 and 96 spots. Fg. 7 show the result of ths experment, the accuracy of the class ncreased from 4.67% to 94.48% when number of spots n ths class ncreased. Fgure 7. The accuracy rate s drectly proportonal to the number of spots IV. DISCUSSIOS AD COCLUSIOS Based on the qualtatve and quanttatve results of spot classfcaton and segmentaton as well as based on confuson matrces, standard devaton values, some conclusons are drawn. The outcomes depend on whch spots were n tranng set, whch spots were n test set. One-vs-one approach outperformed one-vs-all approach n ths study. The values of parameters of SVM classfers affect the classfcaton accuracy. The best parameter settngs found n ths study were c=000, λ = 0 -, a = 0., b =.96 or b =.95 for one-vs-one approach. These settngs together wth QMF feature of Coflet 4 could be seen the best classfer n ths work when 874

8 consderng both average accuracy and confuson matrx (accuracy was 67.08% ±.49% over 50 leave-half-out experments, score0: 80.4%, score: 46.8%, score: 64% and score3: 7%). If the dataset s balanced or nearly balanced, the accuracy s better than the sgnfcant m-balanced dataset. In experment, the system has rather hgh performance n predctng score 0 and score 3. It s ambguous n classfyng score (/4 of the cases were msclassfed as score and /5 of the case were ms-predcted as score 0). Wth score, the result was better than n score, sometmes a spot was msclassfed wth score and score 3. In experment, because the dataset s sgnfcant m-balanced, there are 00 spots score 0 and 80 spots score, but only 4 spots score 3, ths made the system fal n recognzng spots of score 3, they were almost ms-classfed as score. And because the number of spots score also very few, some of spots of score and score 3 were ms-classfed as score 0 nstead of score. To overcome ths dsadvantage, the dataset should be balanced or nearly balanced. The ncreasng n number of spots for each class wll make the test results have better accuracy. The mprovement can be acheved n feature extracton or classfcaton. Prevous work of Amaral [4], dfferental nvarant to rotaton yelded very hgh result, ths suggest to the use of features whch are nvarant to can mprove the classfcaton accuracy. Those features could be the features n study of Amaral or rotaton nvarant Gabor features, or rotaton n varant usng Randon and wavelet transforms, etc. Condtonal random felds (CRF) outperformed SVM n many research areas [6] and tree-structured CRF outperformed CRF [7], thus the use of CRF or tree structured CRF mght mprove the performance. REFERECES [] T. Randen, J.H. Husoy, "Flterng for texture classfcaton: a comparatve study," IEEE Trans Pattern Anal. Mach. Intell, vol., no. 4, pp. 9 30, Apr [] R.J. Marnell, K. Montgomery, C.L. Lu,.H. Shah, W. Prapong, M. tzberg, Z.K. Zacharah, G. Sherlock, Y. atkunam, R.B. West, M.V.D. Rn, P.O. Brown, and C.A. Ball, "The Stanford Tssue Mcroarray Database", uclec Acds Research, 36Database ssue:d87- D877, Jan [3] S. Mallat, "Wavelet bases" n A Wavelet Tour of Sgnal Processng. The Sparse Way, 3rd ed., Academc Press, pp , Dec [4] T. Amaral, S. McKenna, K. Robertson and A. Thompson, Classfcaton of breast tssue mcroarray spots usng texton hstogram, Medcal Image Understandng and Analyss, pp , 008. [5] T.Amaral, "Analyss of breast tssue mcroarray spots," PhD. thess, Unversty of Dundee, UK, 00. [6] O. Chapelle, P. Haffner, and V. Vapnk, "Support vector machnes for hstogram-based mage classfcaton," IEEE Transactons on eural etworks, pp , 999. [7] S. Canu, Y. Grandvalet, V. Gugue and A. Rakotomamony, SVM and kernel methods matlab toolbox," Percepton Systeme Informaton, ISA de Rouen, Rouen, France, 005. [8] Stanford tssue mcroarray database [Onlne]. Avaable: [Accessed March 3, 0] [9] Wavelab 850 [Onlne]. Avalable: [Access March 0]. [0] J. Platt, "Fast Tranng of Support Vector Machnes Usng Sequental Mnmal Optmzaton" n Advences n Kernel Methods - Support Vector Learnng, MIT Press, pp , 999. [] B. E. Boser, I. M. Guyon, and V.. Vapnk, "A tranng algorthm for optmal margn classfers," D. Haussler, edtor, 5th Annual ACM Workshop on COLT, pp 44 5, Pttsburgh, PA, 99. [] V. Vapnk, " The nature of statstcal learnng theory," Sprnger-Verlag, ew York, 995. [3] C. Cortes, V. Vapnk, "Support-Vector etworks," Machne Learnng, 0, 995. [4] C. W. Hsu, C.J. Ln. "A Comparson of Methods for Multclass Support Vector Machne," IEEE Transactons on eural etworks, 00. [5] K. Duan, S. Sathya Keerth, "Whch s the Best Multclass SVM Method? Empercal Study," Proceedngs of the Sxth Internatonal Workshop on Multple Classfer Systems, 005. [6] D. L, K. Kpper-Schuler, G. Savova, "Condtonal Random Felds and Support Vector Machnes for Dsorder amed Entty Recognton n Clncal Texts," HLT Workshop on Current Trends n Bomedcal atural Language Processng; Oho, USA, 008. [7] J. Tang, M. Hong, J. L, B. Lang, "Tree-structured condtonal random felds for semantc annotaton," Internatonal Semantc Web Conference, 006. [8] S. Osowsk, K. Swek, and T. Markewcz, "MLP and SVM networks - a Comparatve study," Proceedngs of the 6th ordc Sgnal Processng Symposum, pp 37-40, Espoo (Fnland),