Experimental Analysis on Character Recognition using Singular Value Decomposition and Random Projection

Transcription

1 Expermental Analyss on Character Recognton usng Sngular Value Decomposton and Random Projecton Manjusha K. 1, Anand Kumar M. 2, Soman K. P. 3 Centre for Excellence n Computatonal Engneerng and Networkng, Amrta Vshwa Vdyapeetham Amrta School of Engneerng, Combatore, Inda 1 manjushagecpkd@gmal.com 2 m_anandkumar@cb.amrta.edu 3 kp_soman@amrta.edu Abstract Character recognton, a specfc problem n the area of pattern recognton s a sub-process n most of the Optcal Character Recognton (OCR) systems. Sngular Value Decomposton (SVD) s one of the promsng and effcent dmensonalty reducton methods, whch s already appled and proved n the area of character recognton. Random Projecton (RP) s a recently evolved dmenson reducton algorthm whch can scale wth large dataset. In ths paper, we have appled SVD and RP as feature extracton technque for character recognton and expermented wth k-nearest Neghbor (k-nn) and Support Vector Machne (SVM) classfers. Our experments are conducted on MNIST handwrtten dgt database and Malayalam character mage database. On both databases SVD features could acheve lower msclassfcaton rate than RP based features. SVD features wth SVM classfer usng RBF kernel could acheve a msclassfcaton rate of 2.53% on MNIST database and 2.87% on Malayalam character mage database. Keyword-Character Recognton, Sngular Value Decomposton, Random Projecton, Pattern Recognton, Support Vector Machne, Dmensonalty Reducton I. INTRODUCTION Character recognton research dates back to 1950 s. It s the process of dentfyng the character or symbol represented by the gven mage. It comprses of feature extracton followed by classfcaton process. Feature extracton n the context of character recognton s mappng the segmented character mage to a real valued vector whch can better descrbe the character on that mage. Features extracted from character mages of dfferent classes should have a good separatng boundary to acheve good accuracy n character classfcaton. Thus the feature extracton algorthm used character recognton can greatly nfluence the accuracy of whole character recognton process. Sometmes the dfferent feature extracton algorthms can be combned together to acheve a hgher accuracy n character classfcaton. To deal wth hgh dmensonal feature vector, an effcent dmenson reducton technque would be desrable. The best way to reduce the dmenson of data s to project the data vector to a reasonably low-dmensonal orthogonal subspace that can capture most of the varatons present n the hgh dmensonal data. The amount of dstorton n data and the computatonal complexty are the two evaluaton parameters for dmenson reducton algorthms [1]. SVD s one of the most wdely used dmenson reducton method whch s a matrx factorzaton technque, whch breaks the data matrx nto smple and meanngful peces. It has been appled n several data processng applcatons successfully [15][16][17]. It can transform the data matrx from hgher to lower dmenson wthout much nformaton loss. SVD s appled to the character mage data set and the egenvectors assocated wth the most sgnfcant prncpal components are retaned for classfcaton. The dsadvantage of SVD s that t becomes computatonally expensve as the data dmenson ncreases. Random Projecton (RP) s recently emerged smple, powerful computatonally effcent dmenson reducton technque [6]. RP s based on random matrx to project data to lower dmensonal subspace whose columns have unt length. Another advantage of RP over SVD s that t s data ndependent. The random drectons we are choosng does not depend upon the dataset we are usng. RP have strong theoretcal backgrounds [2] and successfully appled n dfferent machne learnng applcatons [4][5][6][8]. Our paper s a comparatve study between SVD and RP on character recognton process. After feature extracton, the feature vector s mapped to a class label or membershp scores wth the help of machne learnng algorthms. Dfferent supervsed classfcaton algorthms can be used wth character recognton. k-nearest Neghbor (k-nn) and Support Vector Machne (SVM) algorthms are used for our expermental purpose. k-nn fnds k closest neghbors of gven feature vector from the tranng samples and decdes the fnal class label whle SVM creates hyper plane whch maxmally separates dfferent classes, and s used for classfyng the new test feature vector [18]. Instead of applyng the dmensonalty reducton on mage ISSN : Vol 7 No 4 Aug-Sep

2 tself, t can be appled on features extracted from the mage. Wavelet and Radon transform can produce robust feature descrptors [19][20]. Wth wavelet transform, the mage can be decomposed nto four sub-mages wth the hgh- and low-pass flters. Radon transform represents the drectonal features n the mage [20]. Besdes transform doman features, structural features can also produce good feature descrptors. Our experments are conducted on MNIST hand wrtten dgt database and Malayalam character mage database. The challenges n terms of recognton for Malayalam Language scrpt, the offcal language of Kerala are the smlarty among character symbol shapes and large number of characters present n the scrpt. Malayalam language have a large number of character symbols representng, vowels, consonants, halfconsonants (known as chllu), vowel modfers and conjunct characters (formed from consonantconsonant/vowel combnaton). Scrpt revson and nonstandard font desgn are other man challenges n Malayalam character recognton [12]. Neeba and Jawahar [21] conducted an emprcal study on dfferent pattern classfcaton schemes for Malayalam language scrpt and observed that SVM outperforms other classfcaton approaches on Malayalam character recognton. But the performance of SVM degraded wth the ncrease n number of classes. Neural Network classfers wth wavelet features on Malayalam character recognton [22] could acheve an accuracy of 92%. SVD have appled on 90 classes of Malayalam Language [14] for dmensonalty reducton and then classfed the features n lower dmenson usng k-nearest Neghbor (k-nn) algorthm wth an accuracy of 94%. In ths paper, we are applyng the technque descrbed n [14] for creatng SVD based features. RP features are created usng the algorthm mentoned n Secton 3. The performance of both the features are evaluated usng k-nn and SVM classfers on Malayalam character mage database and MNIST hand wrtten dgt mage database. Secton 2 and 3 descrbes about the techncal detals about SVD and RP respectvely. Secton 4 s about the classfcaton algorthms used n our experments. Secton 5 represents our detaled experments and results. Secton 6 s the concluson and summary of our work wth SVD and RP on character recognton. II. SINGULAR VALUE DECOMPOSITION (SVD) SVD represents or transforms the data n the matrx to those axes n whch varaton among the data s maxmum whle keepng the total varaton among data same. It s bascally a matrx factorzaton method, whch factorzes any rectangular matrx A of sze m n to three matrces U, V and S. U s an m m, orthogonal matrx and ts columns are egen vectors of AA T. V s an n n orthogonal matrx wth ts columns, egen vectors of A T A. S s an m n rectangular dagonal matrx wth postve real values on ts dagonal and the dagonal values are decreasngly ordered [25]. The basc SVD process can be alternatvely descrbed as: If the rank of A s n, then U = (u 1 u 2 u 3. u n ), V = (v 1 v 2 v 3 v n ) and S = dag (s 1, s 2, s 3, s n ). A can be represented as n (1) n A= suv (1) = 1 T In the summaton gven n (1), even f we dscard the last few terms t can approxmate A. In last few terms actually nose s captured and those values don t contrbute to the nformaton contaned n A. Ths property s actually helpng for dmensonalty reducton and nose removal usng SVD. In our experments, we have created the SVD features of tranng and testng character mages usng the technque descrbed n [14]. The algorthm fnds the U, S and V factors of data matrx D usng SVD. The data matrx s created by appendng vectorzed form of all the character mages n tranng dataset. Then subset of V and S are multpled together to represent the reduced representaton of tranng mages. These are tranng features. The testng features are created by projectng each testng character mage vector to the subset of U. The subset of V, S and U are selected based on the number of sngular values we are consderng for the experment. The number of sngular values s the varyng parameter for our SVD based feature creaton process. III. RANDOM PROJECTIONS (RP) Random Projecton s acheved by projectng the d-dmensonal data on to k dmensonal space usng random matrx where k << d (k s very less than d). Let our data matrx s denoted by D of sze d N where, D denotes the feature data dmenson and N s the number of data observatons. Let R be the random matrx of sze k d. The columns of R are normalzed to get an approxmate orthonormal matrx. Then the random projecton P can be calculated as shown n equaton (2). P= RD (2) ISSN : Vol 7 No 4 Aug-Sep

3 The dmenson of P wll be of k*n. Here we can see that the data dmenson s reduced from d to k. The RP can also be consdered as a lnear transformaton n whch the bass s changed to random vectors. The whole process s of order O(dkN). Random projecton reles on the result that; n hgh dmensonal space, there s large number of almost orthogonal than orthogonal drectons [2]. As the dmenson ncreases, the random matrx vectors wll be almost orthogonal and the matrx R T R wll be approxmate dentty matrx. Random projecton preserves the par-wse dstances between the data vectors even n the reduced low dmenson whle SVD does not gve guarantee about ths. The nner product between the two data vectors are dstorted by random mappng s almost zero on the average and ts varance s at most the nverse of the reduced dmenson f the random matrx s chosen from normal dstrbuton wth zero mean and varance equals to one [1]. Apart from nner product, Eucldean measure can be utlzed to fnd the smlarty between data vectors. Johnson-Lndenstrauss lemma [3] states that the data dmenson can be reduced to k > log(d)/ε such that dstances between the ponts are approxmately preserved (.e., not dstorted more than a factor of 1± ε, for any 0 < ε < 1). But some prevous studes [1] suggests that the lower bound for k s not tght and even lower k values gves good results. Random projecton algorthm for feature extracton can be summarzed as follows 1. Generate random matrx, R of sze k d 2. Normalze the columns of R 3. Fnd the random projecton result P = RD The 3 rd step can be parallelzed f the number of data samples we are takng s very large. Each column of D can be taken and fnd the projecton vector. In RP, the feature sze s dependent the parameter k, the row sze of random matrx R. Feature sze ncreases wth ncrease n k. IV. FEATURE CLASSIFICATION After mappng the character mages from mage space to feature space, the feature vector has to be mapped or classfed to one of the predefned character classes. Supervsed and unsupervsed machne learnng algorthms can be appled for feature classfcaton purpose. In ths paper, we have used two supervsed machne learnng algorthms for classfyng the feature vector, k-nearest Neghbor (k-nn) and Support Vector Machne. A. K-Nearest Neghbor Classfer k-nn s one of the smple machne learnng technque, whch can be used for both classfcaton and regresson. In k-nn, no explct tranng phase s needed, t usually store all the features extracted from the tranng mages along wth ther class labels. Durng testng phase, t labels the new nstances (features extracted from the testng mages) wth that class whch s most common among the k tranng feature neghbors calculated wth the help of smlarty measurng technques. In k-nn, two parameters can be vared; k value and the smlarty measurng technque for calculatng dstance. Cross valdaton approach can be used for estmatng k value for whch k-nn gves good accuracy on the dataset. Dfferent dstance functons can be used for calculatng smlarty between testng feature and tranng features. In our experments, we have used Eucldean dstance as the dstance functon. B. Support Vector Machne SVM classfer s bascally a bnary (two-class) classfer based on the use of dscrmnant functons, whch represents a surface that separates the observatons so that the observatons from the two classes le on the opposte sdes of the surface. Consder labeled tranng dataset (x, y ) ; = 1,... n; y {-1, 1}, x R d where n s the total number of samples n tranng set, d s the dmensonalty of each sample. Suppose we have a hyperplane that separates the postve from the negatve samples. The ponts x whch le on the hyperplane satsfy wx + b = 0, where w s normal to the hyperplane and b s the offset [26]. For the lnearly separable case, SVM fnds a separatng hyperplane wth largest margn; the pont where the tranng data satsfy the followng constrants. wx. + b 1, for y = + 1 wx. + b 1, for y = 1 Identfcaton of the optmal hyperplane for separaton nvolves maxmzaton of an approprate objectve functon,.e, solvng the followng quadratc optmzaton problem n (3) durng tranng an SVM. ISSN : Vol 7 No 4 Aug-Sep

4 Maxmze 1 α n n n j j j = 1 2 = 1 j= 1 subject to α 0 n = 1 αα yyk( x, x) α y = 0; = 1,2,... n where α are the Lagrangan multplers correspondng to each of the tranng data ponts x. The functon K s the kernel functon. It s defned as K(x, y) = Φ(x). Φ(y), where ø maps the data ponts n d dmensons to a hgher dmensonal space [26]. Kernels used n our experments are lnear, polynomal and radal bass functon (RBF). 1. Lnear Kernel : K x, y = x y (Φ s dentty no mappng) ( ) T 2. Polynomal Kernel : ( ) ( T d T, ) or ( 1 ) K x y = x y + x y (d represents degree) 3. Radal Bass Functon (RBF) Kernel : 2 K( x, y) = exp γ x y (γ represents kernel bandwdth) The result of the tranng phase n SVM s the dentfcaton of a set of labeled support vectors and a set of coeffcents α. Support vectors are the samples near the decson boundary and most dffcult to classfy. The decson of test sample x s made from (4). n y = sgn( α y K( x, x)) (4) = 1 For extendng bnary SVM to mult class classfcaton problem, there are two approaches: - Drect and Indrect [26]. In ndrect approach several bnary SVM are constructed and are combned together to fnd fnal target class (one-aganst-one). In drect approach all the classes are consdered n a sngle optmzaton formulaton (one-aganst-rest). In our experments we have used one-aganst-one approach n multclass SVM based classfcaton. V. EXPERIMENTAL RESULTS Experments are conducted on our Malayalam character s mage database and MNIST hand wrtten dgt database [24]. Malayalam character mage database s bult from scanned document mages of Malayalam language story books and magaznes. The mage database ncludes the consonants, vowels, vowel modfers (datrcs), conjunct characters of Malayalam language scrpt. In total 135 character classes are consdered. 75% character mages of each character classes s taken as tranng mages and the rest 25% as testng mages. MNIST hand wrtten dgt database contans totally 60,000 tranng samples and 10,000 testng samples. MATLAB tool s used as expermental platform for conductng our trals. Msclassfcaton rate s consdered as the evaluaton measure to decde the performance of technques used n our experments. Msclassfcaton rate s found by calculatng the percentage of testng samples classfed ncorrectly among total number of test samples. For the frst experment, SVD features extracted from character mages n Malayalam character mage database s frst tested wth k-nn classfer. SVD features for dfferent number of sngular values are extracted and are classfed wth dfferent k values (k=1,2, 9) n k-nn classfer. Msclassfcaton rate obtaned for features of dfferent numbers of sngular values are analyzed and the range of sngular values for whch lowest msclassfcaton rate obtaned s found out. The result obtaned s lsted n TABLE. I. The lowest msclassfcaton rate s obtaned for k=1 when the number of sngular values s n the range For all other k values tll 9, the lowest msclassfcatons occurred on the range of A graph s drawn n between the lowest msclassfcatons and dfferent k values n k-nn classfer, and s shown n Fg.1. d (3) ISSN : Vol 7 No 4 Aug-Sep

5 TABLE I. LOWEST MISCLASSIFICATION RATE OBTAINED FOR K-NN CLASSIFIER FOR SVD FEATURES ON MALAYALAM CHARACTER IMAGE DATABASE k Lowest Msclassfcaton Varaton (%) Range of Number of Sngular Values Fg. 1. Vsual representaton of the msclassfcaton rate varaton obtaned for the range of sngular values lsted on TABLE I n k-nn classfer for dfferent k values on Malayalam character mage database. Among dfferent k values n k-nn, 1-NN s gettng lowest msclassfcaton rate. Then, the same SVD features are tested wth SVM classfer. For testng wth SVM multclass classfer we have used LbSVM tool [23]. Durng tranng process, Lnear, Polynomal and Radal Bass Functon (RBF) kernels n SVM classfer are appled and tested wth the features. The msclassfcaton rate obtaned for SVD features created by consderng dfferent sngular values usng dfferent kernels on SVM classfer are shown n Fg 2. RBF kernel s performng better than lnear and polynomal kernels. Average msclassfcaton rate of 2.87% s obtaned wth RBF kernel on SVM multclass classfer for number of sngular values n the range From Fg. 2 t s obvous that for small number of sngular values, the msclassfcaton rate s hgh; up on ncreasng the number of sngular values the msclassfcaton rate tends to decrease. On Malayalam character mage database the SVD - SVM combnaton performs better than SVD - k-nn combnaton. In experments mentoned above, we have used vectorzed form of character mages for applyng SVD. Instead of usng mage vector drectly, a pre-processng can be appled to character mages to extract features. After pre-processng, SVD can be appled on those extracted features. We have used Wavelet Transform, Radon Transform and Projecton Profle features on Malayalam character mage database for pre-processng. Wavelet transform features are extracted by fndng the approxmaton co-effcent after applyng wavelet decomposton usng haar wavelets on the character mages. Radon transform computes the lne ntegrals from multple sources along parallel paths, n a certan drecton; n our experments angle s vared n between 0 and 180 degree. Projecton profle features are computed by summng the pxel values n character mage horzontally and vertcally. The same SVD approach s appled for the extracted features wth SVM classfer and the msclassfcaton rate obtaned s tabulated n TABLE II. ISSN : Vol 7 No 4 Aug-Sep

6 TABLE II. SVD APPROACH WITH DIFFERENT PRE-PROCESSING METHODS ON MALAYALAM CHARACTER IMAGE DATABASE Feature Name Raw Image (wthout pre-processng) 2.81 Wavelet Transform 2.51 Radon Transform 4.5 Projecton Profle Least Msclassfcaton Rate Obtaned (%) Fg. 2. Graph shows the msclassfcaton rate on Malayalam character mage database, when SVD features from dfferent sngular values are classfed wth SVM classfer. Lnear, polynomal and radal bass functon based kernels nsde SVM are expermented. Fg. 3. a)graph shows the average msclassfcaton rate obtaned for the RP features classfed wth k-nn on Malayalam character mage database. The lowest msclassfcaton s for RP feature sze = 425 b) Msclassfcaton for dfferent k n k-nn classfer for RP feature sze 425. In our approach, SVD works on whole of the tranng dataset to generate ts factor matrces. As the number of mages n tranng set ncreases, applyng SVD becomes computatonally expensve. RP s another dmenson reducton algorthm whch scales wth growng data set. We have appled RP on Malayalam character mage database and tested wth k-nn and SVM classfers. The random matrx sze determnes the number of features n RP. In our experments wth RP on Malayalam character mage database, we have vared the RP feature sze from 50, 75,100 to 500. These RP features are classfed wth k-nn and SVM classfer. The msclassfcaton rate obtaned for dfferent RP feature sze on k-nn classfer s shown n Fg 3. From Fg 3, t s obvous that the msclassfcaton rate decreased wth the ncrease n RP feature sze ntally. When the RP feature sze crossed 425, the msclassfcaton rate s below 10% for all k n k-nn classfer. We have obtaned lowest msclassfcaton rate of 9% for RP feature sze 425 n 1-NN and 2-NN classfer. The RP features from Malayalam character mage database are classfed wth SVM classfer for dfferent kernels: lnear, polynomal and radal bass functon. The result obtaned s graphcally shown n Fg 4. RBF kernel performs better than the other two kernels on RP features. As the RP feature sze ncreased and t reaches 350, lnear kernel could ISSN : Vol 7 No 4 Aug-Sep

7 acheve almost the same result as that of RBF kernel. RP features of sze 350 could acheve a msclassfcaton rate of 4.21% wth SVM classfer usng RBF kernel. We have performed the same set of experments wth SVD and RP on MNIST handwrtten dgt database. In MNIST database each character mage s of sze All the mages nsde MNIST database are converted to bnary mages before applyng SVD and RP. On vectorzed form each bnarzed character mage represents a feature vector of sze 784. All the bnarzed tranng mage vectors are appended together to create the tranng data matrx. SVD features are extracted for dfferent numbers of sngular values from the factorzed tranng data matrx. The obtaned features are frst expermented wth k-nn classfer. The msclassfcaton rate obtaned for dfferent values of k n k-nn classfer s lsted n TABLE III. From TABLE III t s clear that wth for feature sze of range 32-38, the 5-NN classfer could acheve the lowest msclassfcaton rate of 3.24%. The results mply that the reduced dmenson n thrtes from the orgnal dmenson of 784 could capture most of the nformaton contaned n the tranng data matrx. The SVD features from MNIST database are appled on SVM classfer. The msclassfcaton rate obtaned for SVD features on dfferent kernels wth SVM classfer s shown n Fg 5. The RBF kernel outperforms the lnear and polynomal kernel on the SVD features from MNIST. An average msclassfcaton rate of 2.53% s obtaned wth RBF kernel n SVM classfer on feature sze on the range From Fg 5, t can be seen that the msclassfcaton rate s hgh for very small number of sngular values and s decreased wth the ncrease n number of sngular values and reached a mnmum range. Msclassfcaton Rate s slghtly ncreased when the feature sze s ncreased beyond 50 n both RBF and lnear kernel. It can be seen that the SVD - SVM combnaton could acheve a msclassfcaton rate lower than that of SVD - k-nn combnaton on MNIST database. The RP features extracted from hand wrtten dgt mages MNIST database are classfed wth k-nn and SVM classfer. The RP feature sze we have consdered from 50 to 500 and tested wth k-nn for dfferent k values. The result obtaned s lsted n TABLE IV. The sze of RP features ncreased, accuracy also ncreased n k-nn. 4-NN s gettng lowest msclassfcaton rate n majorty cases of dfferent RP feature szes. It can be seen that n hgher feature dmensons the dfference n msclassfcaton rate for dfferent k n k-nn classfer s very less. The lowest msclassfcaton rate s obtaned for 4-NN for RP feature sze of 450 and 475. The same RP features are tested wth SVM classfer wth lnear, polynomal and radal bass functon kernels and the results are lsted n TABLE IV. It can be concluded that RBF kernel performs better than lnear and polynomal kernels. The lowest msclassfcaton rate of 5.56% s obtaned n RP feature sze of 150 for SVM classfer wth RBF kernel. The results of RP features on k-nn and SVM classfers shows that there s not much dfference n the lowest msclassfcaton rate obtaned for both of the classfers. k-nn could acheve the lowest msclassfcaton rate of 5.98% for RP feature sze of 450 whle SVM could acheve 5.56% for RP feature sze of 150. k-nn could acheve almost comparable msclassfcaton rate as that of SVM classfer but n hgher dmenson of RP feature on MNIST database. Fg. 4. Graph of msclassfcaton rate Vs RP features, when classfed wth SVM on Malayalam character mage database ISSN : Vol 7 No 4 Aug-Sep

8 TABLE III. LOWEST MISCLASSIFICATION RATE OBTAINED FOR K-NN CLASSIFIER FOR SVD FEATURES ON MNIST DATABASE k Range of Number of Sngular Values for whch Lowest Msclassfcaton Rate obtaned Average Msclassfcaton Rate on the range (%) Fg. 5. Graph shows the msclassfcaton rate obtaned for SVD features usng SVM classfer wth lnear, polynomal and radal bass functon kernels on MNIST database ISSN : Vol 7 No 4 Aug-Sep

9 RP Feature Dmenson TABLE IV. MISCLASSIFICATION RATE OF RP FEATURES ON MNIST DATABASE RP+k-NN Msclassfcaton Rate (%) RP+SVM Msclassfcaton Rate (%) k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 Lnear Polynomal RBF VI. CONCLUSION Dmenson reducton algorthms play a great role n almost all machne learnng applcatons. We have tred to compare the performance of SVD and RP, two dmenson reducton technques wth the help of two classfcaton algorthms, k-nn and SVM on the context of character recognton. The experments are conducted on Malayalam character mage database (135 dfferent classes) and MNIST handwrtten dgt database. SVD features are gvng better accuracy wth SVM classfer than k-nn on both the databases. In case of RP features, on Malayalam character mage database RP SVM combnaton s performng better than RP k-nn combnaton. On MNIST database the performance of RP k-nn and RP SVM s almost same, except that k-nn performs well on hgh dmensons of RP feature. On comparng the performance of SVD and RP features, SVD domnates over RP on both the mage databases we have used n our experments. But for applcatons, handlng massve data, the SVD approach we have used becomes computatonally expensve whle RP scales well. Our future work ncludes mprovng the performance of RP to make ts performance comparable to that of SVD and on makng SVD approach practcal for applcatons nvolvng growng datasets. REFERENCES [1] Ella Bngham and Hekk Mannla, Random projecton n dmensonalty reducton: Applcatons to mage and text data, n Proc. KDD'01, pp , [2] R. Hecht-Nelsen, Context vectors: general purpose approxmate meanng representatons self-organzed from raw data, n Computatonal Intellgence: Imtatng Lfe, IEEE Press, pp , [3] W. Johnson and J. Lndenstrauss, Extensons of lpschtz mappng nto a hlbert space, n Conf. on Modern Analyss and Probablty, vol. 26, pp , [4] S. Kask, Dmensonalty reducton by random mappng, n Proc. Int. Jont Conf. on Neural Networks, vol. 1, pp , [5] S. Dasgupta, Experments wth random projecton, n Proc. UAI '00, pp , [6] Tetsuya Takguch, Jeff Blmes, Marko Yosh and Yasuo Ark, Evaluaton of Random Projecton Based Feature Combnaton on Speech Recognton, n IEEE Internatonal Conf. on Acoustcs Speech and Sgnal Processng (ICASSP), pp , [7] Xaol Zhang Fern and Carla E. Brodley, Random Projecton for Hgh Dmensonal Data Clusterng: A Cluster Ensemble Approach, n Proc. of the 20th Internatonal Conference on Machne Learnng, pp , [8] Navn Goel, George Bebs, and Ara Nefan, Face Recognton Experments wth Random Projecton, n Proc. of the SPIE, vol. 5779, p , [9] Armn Eftekhar, Massoud Babae-Zadeh and Hamd Abrsham Moghaddam, Two-dmensonal random projecton, Sgnal Processng, vol. 91, pp , [10] Mchael B. Wakn and Rchard G. Baranuk, Random Projectons Of Sgnal Manfolds, n Proc. IEEE Internatonal Conf. on Acoustcs, Speech and Sgnal Processng, vol. 5, [11] Magnus Sahlgren, An Introducton to Random Indexng, n Methods and Applcatons of Semantc Indexng Workshop at the 7th Internatonal Conf. on Termnology and Knowledge Engneerng, [12] Setlur, Srrangaraj. Gude to OCR for Indc Scrpts. Edted by Venu Govndaraju. Sprnger London, [13] U. Pal and BB Chaudhur, Indan scrpt character recognton: A survey, n Pattern Recognton, Elsever vol. 37, no. 9, pp , ISSN : Vol 7 No 4 Aug-Sep

10 [14] S. Sachn Kumar, K. Manjusha and K. P. Soman, Novel SVD Based Character Recognton Approach for Malayalam Language Scrpt, Recent Advances n Intellgent Informatcs Advances n Intellgent Systems and Computng, vol. 235, pp , [15] Soren Holdt Jensen, Per Chrstan Hansen, Steffen Duus Hansen and John Aasted Sorensen, Reducton of Broad-Band Nose n Speech by Truncated QSVD, n IEEE Transactons on Speech and Audo Processng, vol.3, no.6, [16] Vladmr I. Gorodetsk,Leonard J. Popyack,Vladmr Samolov and Vctor A. Skormn, SVD-Based Approach to Transparent Embeddng Data nto Dgtal Images, n Proc. MMM-ACNS '01, pp , [17] W. Zhao, R. Chellappa and A. Krshnaswamy, Dscrmnant Analyss of Prncpal Components for Face Recognton, n Proc. FG '98, p. 336, [18] Mohamed Cheret, Nawwaf Kharma, Cheng-Ln Lu and Chng Y.Suen, Character Recognton Systems, A Gude for Students and Practtoners WILEY-INTERSCIENCE: John Wley & Sons, Inc., Hoboken, New Jersey, [19] Mallat, S., "A theory for multresoluton sgnal decomposton: the wavelet representaton," n IEEE Pattern Anal. and Machne Intell., vol. 11, no. 7, pp , [20] Dattatray V. Jadhav and Raghunath S. Holambe, Feature extracton usng Radon and wavelet transforms wth applcaton to face recognton, n Neurocomputng, vol.72, pp , [21] N. V. Neeba and C. V. Jawahar, Emprcal Evaluaton of Character Classcaton Schemes, n ICAPR, 7th Internatonal Conference on Advances n Pattern Recognton, 2009 [22] M. Abdul Rahman, M. S. Rajasree, OCR for Malayalam Scrpt Usng Neural Networks, ICUMT '09, Internatonal Conference on Ultra Modern Telecommuncatons & Workshops, [23] Chh-Chung Chang and Chh-Jen Ln, LIBSVM: a lbrary for support vector machnes, n ACM Transactons on Intellgent Systems and Technology, [24] LeCun Y. and Cortes C, 'MNIST handwrtten dgt database', (Accessed on: 10 Nov. 2014). [25] Kalman, D., A Sngularly Valuable Decomposton: The SVD of a Matrx n The College Mathematcs Journal, [26] Soman K. P., Loganathan R., and Ajay V. Machne learnng wth SVM and other kernel methods. PHI Learnng Pvt. Ltd ISSN : Vol 7 No 4 Aug-Sep