Supervised Fuzzy Hyperline Segment Neural Network for Rotation Invariant Handwritten Character Recognition

Transcription

1 Supervsed Fuzzy Hyperlne Segment Neural Network for Rotaton Invarant Handwrtten Caracter Recognton U.V. KULKARNI, T.R. SONTAKKE, and G.D. RANDALE Electroncs and Computer Scence & Engneerng Department S.G.G.S. College of Engneerng & Tecnology Vsnupur, Nanded , (M.S.) INDIA Abstract: - In ts paper fuzzy yperlne segment neural network (FHLSNN) s proposed for recognton of andwrtten caracters. Te paper descrbes te arctecture, learnng algortm and an example tat demonstrates te qualtes of FHLSNN algortm. Te FHLSNN utlses fuzzy sets as pattern classes n wc eac fuzzy set s an unon of fuzzy set yperlne segments. Te fuzzy set yperlne segment s an n-dmensonal yperlne segment defned by two end ponts wt correspondng membersp functon. Te andwrtten caracters can be n arbtrary locaton, scale and orentaton. After moment normalzaton rotaton nvarant rng-data feature vectors are extracted from caracters. Fnally, FHLSNN algortm s used to classfy te rng-data vectors by ts strong ablty of dscrmnatng ll-defned caracter classes. Te performance of FHLSNN algortm s compared wt fuzzy neural network proposed by Kwan and Ca, wc s modfed to work under supervsed envronment and fuzzy mn-max neural network proposed by Patrck Smpson. Te FHLSNN algortm s found to be superor wt respect to te tranng tme, recall tme per pattern and te generalzaton. After te FHLSNN as been traned by one tousand patterns, t recognzes all te learned patterns wt 100% recognton rate. It also recognzes te patterns tat are not used durng tranng wt 99.5% recognton rate. Hence, one of te mportant features of FHLSNN algortm s tat t gves extremely good generalzaton even wt lnear moment normalzaton. Key-words: - Hyperlne segment, Fuzzy set, Neural network, Fuzzy neural network, Rng-data, Handwrtten caracter recognton 1 Introducton Artfcal neural network (ANN) s a massvely parallel structure composed of many processng elements connected to eac oter troug wegts [1]. On te oter and, fuzzy logc provdes a matematcal strengt to capture te uncertantes assocated wt uman cogntve process suc as tnkng and reasonng. It also provdes a matematcal morpology to emulate certan perceptual and lngustc attrbutes assocated wt uman cognton []. Artfcal neural networks offer exctng advantages suc as learnng, adaptaton, fault tolerance, parallelsm and generalzaton, wereas fuzzy teory provdes a matematcal morpology under cogntve uncertantes. Incorporatng concepts of fuzzy logc nto te ANN gves brt to fuzzy neural network [3]. Te fuzzy neural networks ave become very popular and wdely beng used n te pattern recognton applcatons. Many papers are reported on studes of nvarant pattern recognton but only few researcers lke Yuceer and Oflazer; Fukusma; Hussan and Kabuka; Kotanzad and Lu focused on nvarant recognton of andwrtten caracters. [4]-[7]. Kwan and Ca ave proposed four layer feedforward fuzzy neural network (FNN) wt unsupervsed learnng algortm, wc s used for caracter recognton [8]. Patrck Smpson proposed supervsed learnng neural network classfer named as fuzzy mn-max neural network (FMN) tat utlzes fuzzy sets as pattern classes [9]. He as also proposed unsupervsed fuzzy mn-max clusterng neural network n wc clusters are mplemented as fuzzy sets usng a membersp functon wt a yperbox core [10]. Cn and Tseng used supervsed FMN for nvarant recognton of andwrtten Cnese caracters and sown tat te FMN s superor to oter two tradtonal statstcal classfers [11]. Te proposed supervsed learnng neural network classfer utlzes fuzzy sets as pattern classes and eac fuzzy set s an unon of fuzzy set yperlne segments. Te yperlne segment s a fuzzy set defned by two end ponts wt membersp functon. Te two end ponts of fuzzy yperlne segments are determned by FHLSNN algortm. Ts algortm can learn ll-defned nonlnear class boundares n a sngle pass for te tranng data, and t s also sutable for on-lne adaptaton. In ts paper te lnear moment normalzaton s used to normalze andwrtten caracters to get scale and translaton nvarance. Te non-lnear normalzaton proposed by Yamade s preferred for andwrtten caracters because of ter rregulartes and partal

2 varaton n sape [1]. Te non-lnear normalzaton as better generalzaton ablty tan moment normalzaton. However, te non-lnear normalzaton lacks n rotaton nvarance, because te normalzed sapes of caracters vary n dfferent orentaton. Te metod of lnear normalzaton gves rotaton nvarance but lacks n generalzaton [11]. However, te proposed FHLSNN algortm wt lnear normalzaton gves extremely good generalzaton and rotaton nvarance. Followng ts ntroducton, secton s a problem formulaton n wc te selected problem and proposed arctecture wt ts learnng algortm s descrbed. Secton 3 gves problem soluton n wc te expermental results derved after mplementaton are tabulated n detal. In addton to ts one example of pattern classfcaton for two classes s also llustrated n te -dmensonal pattern space to compare FHLSNN wt FMN algortm. e 1 c 1 c c p d 1 d d p e e 3 e m r 1 r r n F C layer F D layer U F matrx layer E V and W matrces F R layer Problem Formulaton We ave selected te problem of rotaton nvarant andwrtten caracter recognton. Te database conssts of two tousand caracters. Ten numerals from two undred wrters are scanned and stored n BMP format. Te metod of moment normalzaton dscussed by Perantons and Lsboa s used to normalze te caracters to get translaton and scale nvarance [13]. Te rotaton nvarant rng-data features defned by Ueda and Nakamura and extended by Cu and Tseng are ten extracted from te normalzed caracters by settng rng wdt to two [14]. Te extracted rng-data vector s a 16-dmensonal feature vector. Tese feature vectors are ten scaled wtn te range [0,1], along eac dmenson so te pattern space of FHLSNN s a 16-dmensonal unt cube I n.e. n = 16. In te followng subsecton te arctecture and learnng algortm of FHLSNN s descrbed..1 Topology of te proposed FHLSNN Te arctecture of te FHLSNN conssts of four layers as sown n Fg.1. In ts arctecture frst, second, trd and fourt layer s denoted as F R, F E, F D, and F C, respectvely. Te F R layer accepts an nput pattern and conssts of n processng elements, one for eac dmenson of te pattern. Te F E layer conssts of m processng nodes tat are constructed durng tranng. Tere are two connectons from eac F R to F E node; one connecton represents one end pont for tat dmenson and te oter connecton represents anoter end pont of tat dmenson, for a partcular yperlne segment as sown n Fg.. One end pont of fuzzy yperlne segment s stored n matrx V and te oter end pont s stored n matrx W. Fg. 1: Four layer fuzzy yperlne segment neural network. Eac F E node represents yperlne segment fuzzy set and s caracterzed by te transfer functon. Let R = ( r1, r,..., r ) represents te t nput pattern, n V = ( v 1, v,..., v n ) s one end pont of te yperlne segment e, and W = ( w 1, w,..., w n ) s te oter end pont of e. Te transfer functon of t F E node s te yperlne segment membersp functon defned as e ( R, V, W ) = 1 f ( x, γ, l), ( 1) n wc x = l 1 + l, te dstances l1, l and l are defned as l n = = 1/ ( ), ( ) w r 1 1 l l n = = 1/ ( ), ( 3) v r 1 n = = 1 1/ ( ), ( 4) w v and f ( ) s a tree-parameter ramp tresold functon defned as ( x,, l) = 0 ( r r,...., r ) 1, f γ f x = l oterwse n

3 ( x, γ, l) f xγ = 1 f f 0 xγ 1 xγ > 1. Te fuzzy yperlne segment membersp functon returns gest membersp value equal to one f te pattern R falls on te yperlne segment oned by two end ponts V and W. Te membersp value s governed by te senstvty parameter γ wc regulates ow fast te membersp value decreases wen te dstance between R and e ncreases. For te gven nput pattern R, e 's output value s computed usng equaton (1). r Fg.: Te mplementaton of fuzzy yperlne segment Eac node of F C and F D layer represents a class. Te F D layer of FHLSNN gves soft decson and te output of kt F D node represents te degree to wc te nput pattern belongs to te class d k. Te wegts assgned to te connectons between F E and F D layers are bnary values and stored n matrx U, and te values assgned to tese connectons are defned as 1 f e s a yperlne segment u k = of te class dk 0 oterwse for k = 1,,......, p and = 1,,......, m were e s te t F E node and d k s te kt F D node. Te transfer functon of eac F D node performs te unon of te approprate (of same class) yperlne segment fuzzy values, wc s descrbed as d r 1 r n v w v 1, w 1 v n, w n e = f ( R,V,W ) m k = max e u k for k = = 1 1,,......, Eac F C node delvers nonfuzzy output, wc s e p ( 5) ( 6) descrbed as 0 f d ck = 1 f d for k = 1 to p. k k < T were T = max = T ( d ), k for k = 1to p. FHLSNN Learnng Algortm Te supervsed FHLSNN learnng algortm for creatng fuzzy yperlne segments n te yperspace conssts of tree steps as stated below. a. Creaton of yperlne segments b. Intersecton test c. Removng ntersecton Above tree steps are descrbed below n detal. (a) Creaton of yperlne segments: Gven te t tranng par ( R, d ), fnd all te yperlne segments belongng to te class d. After ts followng four steps are carred sequentally for possble ncluson of nput pattern R. Step 1: Determne weter te pattern R falls on any one of te yperlne segments. Ts can be verfed by usng fuzzy yperlne segment membersp functon descrbed n equaton (1). If R falls on any one of te yperlne segment ten t s ncluded, terefore n te tranng process all te remanng steps are skpped and tranng s contnued wt te next tranng par. Step : If te pattern R falls on any one of te yperlne passng troug two end ponts of te yperlne segment, ten extend te yperlne segment to nclude te pattern. Suppose e s tat yperlne segment wt end ponts V and ( 7) W ten l 1, l and l are calculated usng equatons (), (3) and (4). Were l 1 s te dstance of R from end pont W, l s te dstance of R from end pont V and l s te lengt of te yperlne segment. (a): If l 1 > l ten test weter te pont V falls on te yperlne segment formed by te ponts W and R. Ts condton can be verfed usng equaton (1).e. f e V, R, W =, ten yperlne segment s extended by ( ) 1 replacng end pont V by R to nclude R. Hence V = R and W = W. ( 8) (b): If l > l1 ten test weter te pont W falls on te yperlne segment formed by te ponts e ( W, V, R ) = 1 replacng end pont V and R. If, yperlne segment s extended by W wt R to nclude R. Hence W = R and V = V. ( 9)

4 Step 3: If yperlne segment s a pont (.e. l = 0 ) extend t to nclude te pattern R. Terefore, V = R and W = W. ( 10 ) Step 4: If te pattern R s not ncluded by any of above steps ten yperlne segment s created for tat class, wc s descrbed as W = R and V = R ( 11) (b) Intersecton test: Te learnng algortm allows ntersecton of yperlne segments from te same class and elmnates te ntersecton between yperlne segments from separate classes. Terefore, t s necessary to elmnate ntersecton between yperlne segments tat represent dfferent classes. Intersecton test s carred out as soon as te yperlne segment s extended eter by step or step 3. Let W lst = [ x1, x,..., x n ], V lst = [ y1, y,..., y n ] represent two end ponts of extended yperlne segment and ' ' ' ' ' ' W n = [ x1, x,..., xn ], V n = [ y1, y,..., yn ] are end ponts of te yperlne segment of oter class. Frst of all test weter te yperlnes passng troug end ponts of two yperlne segments ntersect. Ts s descrbed by te followng equatons. Te equaton of yperlne passng troug W lst and V lst s a x y x = r1 for = 1,,...., n and te equaton of te yperlne passng troug and V n s b y ' ' x = r ' x for = 1,,..., n ( 1) W n ( 13) were r 1, r are te constants and a, b varables. Te equatons (1) and (13) leads to set of n smultaneous equatons wc are descrbed as ' ' ' ( y x ) + x = r ( y x ) + x ( 14) r1 for = 1,,..., n. Te values of r 1 and r can be calculated by solvng any two smultaneous equatons. If remanng n- equatons are satsfed wt te calculated values of r 1 and r ten two yperlnes are ntersectng and te pont of ntersecton p s t t ( r ( y x ) + x r ( y x ) x ). ( 15) P = ,..., 1 n n n Te pont of ntersecton p t, f falls on bot yperlne segments ten yperlne segments also ntersect. Ts can be verfed by te equaton (1).e. f e lst ( pt, Vlst, Wlst ) = 1 and en ( pt, Vn, Wn ) = 1, means tat te two yperlne segments from separate class are ntersectng. Ts ntersecton s elmnated by contracton of ust extended yperlne segment. (c) Removng ntersecton: If step (a) and step 3 as created ntersecton of yperlne segments from separate classes ten ntersecton s removed by restorng te end pont V as V = V, f step (b) as created ntersecton ten ntersecton s removed by restorng te end pont W as W = W, and yperlne segment s created to nclude te nput pattern R, wc s descrbed by equaton (11). 3 Problem Soluton 3.1 Expermental Results We ave mplemented te proposed approac usng MATLAB 5.1 and ran on Pentum MMX, 00MHz PC. Several experments are carred out to compare te proposed approac wt FNN and FMN algortms. Detals of four data sets prepared from te database and used n te experments are gven below. Set 1 s unrotated tranng set,.e. orgnal tranng set consstng of one tousand tranng patterns, wc s reused to verfy te recognton. Set s rotated tranng set extracted from set 1,.e. eac sample of set s a rotated verson of sample n set 1 wt an angle of Set 3 s unrotated testng set consstng of remanng one tousand patterns n te database tat s used to evaluate generalty. Set 4 s rotated testng set extracted from set 3,.e. eac sample of set 4 s a rotated verson of sample n set 3, wt an angle of All te results stated n ts paper are for γ equal to one. Te FNN algortm proposed by Kwan and Ka constructs neurons n te output layer n unsupervsed envronment usng smlarty measure [8]. We ave modfed ts algortm to work under supervsed envronment. Te modfed FNN also uses smlarty measure and f te nput pattern s smlar to already learned pattern of tat class ten only t s accommodated by tat neuron oterwse neuron of tat pattern class s constructed. Terefore, eac neuron n te output layer learns to recognze te patterns of same class. Te recognton rate of FHLSNN algortm s compared wt FNN and FMN algortms and lsted n Table 1. Te recognton rate s defned as te rato of te number of correctly classfed test patterns to te total number of tested patterns. Table 1 reveals tat te FHLSNN algortm gves better recognton rate for all te tranng sets compared to FMN and FNN algortms. For set 3 and set 4 FHLSNN algortm gves above 99%

5 recognton rate ndcatng ts extremely good generalzaton ablty. Tus nonlnear normalzaton, wc s sutable for generalzaton s redundant for FHLSNN algortm. Classfer Set 1 Set Set 3 Set 4 Average FNN 100% 76.1% 31.4% 7.5% 58.75% FMN 100% 97.4% 4.7% 41.0% 7.75% FHLSNN 100% 99.7% 99.5% 99.3% 99.65% Table 1: Recognton rates of caracter sets usng FNN, FMN and FHLSNN algortms for one tousand patterns. Te performance of te FHLSNN algortm s also compared wt tese two classfers for te tranng tme, and recall tme per pattern and tese results are tabulated n Table. Te last row n te Table sows tat te number of yperlne segments created by FHLSNN s very less compared to yperboxes n FMN and neurons n output layer of FNN. Due to ts tranng tme and recall tme per pattern s sgnfcantly reduced. Classfer Neurons n output layer/ yperboxes/ Hyperlne segments Tranng tme n seconds Recall tme per pattern n seconds FNN FMN FHLSNN Table : Performance comparson wt neurons n output layer/yperboxes/yperlne segments between FNN, FMN and FHLSNN algortms wt tousand patterns of set1 for 100% recognton rate. Te FHLSNN wen traned wt set 1, wtout ntersecton test and ts removal, no cange s observed as far as number of yperlne segments s concerned, because te probablty of ntersecton of two yperlne segments n n-dmensonal space s less wen n s moderately large. Te results of ts experment are tabulated n Table 3. Classfer No. of Hyperlne segments Recognton rate FHLSNN % FHLSNN * % * FHLSNN wtout ntersecton test Table 3: Performance of FHLSNN algortm wt and wtout ntersecton test and ts removal. To verfy te effect of sze of database on te generalzaton, we selected frst two undred patterns from eac data set (.e. set 1 to set 4). Tese extracted data sets are desgnated as set 5, set 6, set 7 and set 8 accordngly. Ten te performance of FHLSNN s compared wt FMN and FNN algortms for recognton rate. Tese results are lsted n table 4. Classfer Set 5 Set 6 Set 7 Set 8 Average FNN 100% 96.5% 6.5% 6% 6.5% FMN 100% 97.5% 33.5% 33.5% 66.15% FHLSNN 100% 100% 91.5% 91.5% 95.75% Table 4: Recognton rates of caracter sets usng FNN, FMN and FHLSNN algortms for two undred patterns. Te comparson of Table 1 and Table 4 sows tat generalzaton of FNN and FMN algortms s mproved to certan extent, wereas te generalzaton of FHLSNN s approacng to deal fgure of 100%. Hence to reac close to ts deal fgure large database s needed for FNN and FMN algortms as compared to FHLSNN algortm. Ts means tat te FHLSNN algortm gves better generalzaton even wt small database. 3. Two class example n -D space It s sad tat patterns of same class fall close to eac oter n te pattern space. But n te andwrtten caracter recognton applcaton caracters of dfferent wrters vary n style and sape. Terefore, te dstrbuton of patterns s random and t s not necessary tat te patterns of same class sould fall close to eac oter n te pattern space. In te example descrbed below, we cose twelve patterns suc tat patterns of same class are not close to eac oter and are dstrbuted randomly n te pattern space as sown n Fg. 3. pattern class Fg. 3: Dstrbuton of twelve patterns of class 1 and n -D space, represents class 1 and represents class patterns. Wt tese patterns we ave compared performance of FHLSNN wt FMN algortm. It s observed tat FHLSNN algortm created seven yperlne segments, compared to twelve yperboxes of FMN algortm to obtan 100% recognton rate as sown n Fg. 4. Wen we ran FMN algortm by varyng sze of yperboxes to get 100% recognton effcency for te selected twelve patterns, t s observed

6 tat te yperboxes created are te ponts same as te patterns n te pattern space. (a) Fg. 4: (a) Hyperboxes created by FMN algortm n pattern space, (b) Hyperlne segments created n pattern space by FHLSNN algortm. 4 Concluson A neural network classfer tat utlzes yperlne segments as fuzzy sets tat are aggregated nto fuzzy set classes s ntroduced. Ts learnng algortm as te ablty to learn n a sngle pass troug te data and can be adapted for real tme applcatons. Te performance of te proposed approac usng lnear normalzaton s good enoug terefore non-lnear normalzaton s redundant to te proposed approac. Te FHLSNN learnng algortm s found to be superor compared to FNN and FMN algortms. Te learnng and recall tme s drastcally reduced due to less number of yperlne segments created durng tranng of FHLSNN compared to neurons n output layer of FNN and yperboxes of FMN. It s observed tat te probablty of ntersecton of two yperlne segments n n-dmensonal space s less wen n s moderately large. It s also observed tat to get same generalzaton performance te sze of database needed for FHLSNN algortm s muc small as compared to FNN and FMN algortms Fnally, t s mportant to note tat te generalzaton capablty of te FHLSNN s extremely good compared to te FNN and FMN algortms. (b) Pattern recognton, Vol.6, No.5, 1993, pp [5] Fukusma K., Caracter recognton wt neural networks, Neurocomputng, Vol.4, 199, pp [6] Hussan B. and M.R. Kabuka, A novel feature recognton neural network and ts applcaton to caracter recognton, IEEE Trans. Pattern Anal. Macne Intell., Vol.16, No.1, 1994, pp [7] Kotanzad A. and J.H. Lu, Classfcaton of nvarant mage representatons usng a neural network, IEEE Trans. ASSP, Vol.38, No.6, pp [8] Kwan H.K. and Yalng Ca, A fuzzy neural network and ts applcatons to pattern recognton, IEEE Trans. on fuzzy systems, Vol., No.3, 1994, pp [9] Smpson P.K., Fuzzy mn-max neural networkspart1: classfcaton, IEEE Trans. neural networks, Vol.3, No.5, 199, pp [10]Smpson P.K., Fuzzy mn-max neural networks- Part: clusterng, IEEE Trans. fuzzy systems, Vol.1, No.1, 1993, pp [11]Hung-Pn Cu and Dn-Cang Tseng, Invarant andwrtten Cnese caracter recognton usng fuzzy mn-max neural networks, Pattern recognton letters, Vol.18, 1997, pp [1]Yamade H., K. Yamamoto, and T. Sato, A nonlnear normalzaton metod for andprnted Kan caracter recognton - Lnear densty equalzaton, Pattern recognton, Vol.3, No.9, 1990, pp [13]Perantons S.J. and P.J.G. Lsboa, Translaton, rotaton and scale nvarant pattern recognton by g-order neural networks and moment classfers, IEEE Trans. neural networks, Vol.3, No., 199, pp [14]Udea K. and Y.Nakamura, Automatc verfcaton of seal-mpresson pattern, In: Proc. 9t nternat. conf. on pattern recognton,vol., 1984, pp References: - [1] Lppmann R.P., An Introducton to computng wt neural nets, IEEE ASSP magazne, Vol.4, No., 1987, pp.4-. [] Pal S.K., Soft computng tools and pattern recognton, IETE ournal of researc, Vol.44, No.1, 1998, pp [3] Pal S.K. and Muumdar D.K.D., Fuzzy matematcal approac to pattern recognton, New Del, Inda: Wley Eastern Ltd., [4] Yuceer C. and K. Oflazer, A rotaton scalng and translaton nvarant pattern classfcaton system,