[IEEE 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06) - Arlington, VA, USA (2006.11.13-2006.11.13)] 2006 18th IEEE International Conference

A Hybrid Recogniser for Handwritten SymbolsBased on Fuzzy Logic and Self-Organizing Maps

Alex Cronin, John A. Fitzgerald, and Tahar KechadiSchool of Computer Science and Informatics

University College DublinBelfield, Dublin 4, Ireland.

[email protected]

Abstract

In this paper we present a hybrid approach to hand-written symbol recognition based on two different meth-ods and principles. A fuzzy rules based recogniser and aSelf-Organizing Map recogniser are combined to form ourhybrid system. These two systems complement each otherwell, firstly because their feature extraction techniques dif-fer greatly, and secondly because one is a model-based andthe other is a discriminative classifier. Each system gen-erates a ranked list of outputs with associated confidencevalues, and these outputs are combined to produce a sin-gle result. The approach has achieved high recognitionrates in testing on digits and lowercase characters from theUNIPEN database.

keywords: Handwriting Recognition, Self-Organizing Maps, Fuzzy Logic, Multiple ClassifierSystems.

1 Introduction

Online handwriting recognition has been a source ofgreat interest in the academic world for many years. Thereare many situations in which it would be preferable to usean electronic pen and data tablet, rather than a keyboard.For example, mathematical expressions are not easily en-tered using a keyboard. Hand-held devices also require areliable recogniser for handwritten symbols.

Our motivation for developing a symbol recogniser is foruse in a system which recognises handwritten mathematicalexpressions [10]. Such a system would allow authors ofscientific papers to enter mathematics in an intuitive man-ner, rather than having to type a complex set of LATEX com-mands or use a specialised external editor such as MS Equa-tion Editor.

1.1 Related Work

In recent times, the most successful approaches to sym-bol recognition have almost invariably involved the use ofmultiple classifiers. A variety of approaches have been usedto create multiple classifier systems. With the ensemble ap-proach [12], a base classifier is used to generate a set ofclassifiers by changing the training set, the input features,the architecture, or other parameters of the classifier. En-semble methods have been used to tackle word recognition[3] and symbol recognition [13].

Another approach taken is to select the two most likelyresults according to a model-based classifier, and to use adiscriminative classifier to choose between these two results[14, 15] . This approach has been used on the basis that forcertain model-based classifiers, the correct result is almostalways in the top two results, and the majority of errorsare due to confusion between specific pairs of ambiguousclasses (e.g. ‘6’ and ‘b’). However, a discriminative classi-fier must be trained for every ambiguous pair of classes.

Alternatively, the outputs from a diverse set of classifierscan be combined to produce a single result. It is impor-tant for the classifiers to be diverse, because it decreases thelikelihood that all classifiers will fail on the same input [16].Classifiers generated from a single base classifier using en-semble methods are not especially diverse. The method ofcombining the outputs is also important. Simple methodssuch as majority voting can be used, but it is preferable ifthe combination method examines a ranked set of resultswith confidence values from each classifier. The previousperformance of each classifier should also be taken into ac-count [17].

1.2 Our Approach to Symbol Recognition

We propose a hybrid approach which combines the out-puts from two recognisers which operate on very differ-ent principles. One recogniser is based on Self-Organizing

Proceedings of the 18th IEEE InternationalConference on Tools with Artificial Intelligence (ICTAI'06)0-7695-2728-0/06 $20.00 © 2006

Maps (SOMs), while the other is based on fuzzy rules. Thetwo recognisers complement each other in numerous ways.As regards the input features, the SOM System uses a setof equal length vectors, while the Fuzzy System extractsthe set of basic components which form the symbol. TheSOM System is a discriminative classifier while the FuzzySystem is model-based. Also, the SOM System is trainedwhereas the Fuzzy System is prototype-based. Each systemreturns a ranked set of results with confidence values whichare comparable by scale, and a single result is subsequentlydetermined. The remainder of the paper is structured as fol-lows: Sections 2 and 3 discuss the SOM and Fuzzy Sys-tems, Section 4 describes the method of combination, Sec-tion 5 outlines the results achieved and Section 6 concludesthe paper.

2 Self-Organizing Map System

When attempting to classify a set of patterns, it is of-ten useful to employ a technique to reduce the size of thepattern set, such that only a few patterns remain which rep-resent the principle information of the original pattern set.The SOM can be used to implement such an idea. The re-duced pattern set is called the codebook vectors. The SOMcan be defined as a nonlinear, ordered, smooth mapping ofhigh dimensional input data manifolds onto elements of aregular, low-dimensional array [6] .

The SOM attempts to order, while simultaneously gen-erating, the codebook vectors from the training inputs. Theaim of the ordering process is to arrange the codebook vec-tors such that those with common features are positionedgeometrically close to one another. At the conclusion of theordering process codebook vectors which are most similarshould be adjacent to one another and those least similar atmaximal distance, while operating within the constraints ofthe geometry of the map, often a 2D grid.

After training and labelling, a SOM may be used in thefollowing fashions. Traditional SOM: an input is applied toa SOM and the identity of the most similar codebook vectorof the SOM is output. Confidence based SOM: an input isapplied to a SOM and the identity of all codebook vectorsin descending order of similarity may be returned weightedwith some degree of confidence. The confidence based clas-sification result is favoured in this paper as it facilitates thecombination of two classification techniques.

2.1 SOM System - Feature Extraction

When a symbol is drawn by a user it may be logged asa sequence of discrete values. These point values may con-sist of a subset of the following (point index, x position,y position, time, pressure). In this paper we restrict our-selves to (point index, x position, y position). The raw

Figure 1. Original set of data points.

Figure 2. Scaled and continuous data points.

point data may then be subject to a feature extractionprocess which encodes the raw data into a more meaning-ful representation, assisting the identification of aspects ofsymbols that are variant and invariant in each symbol class.The feature extraction process used in the case of the SOMis Equal Length Vectorization.

2.1.1 Equal Length Vectorization

As the user’s speed of writing varies over the length of thestroke and the data points are sampled by the input deviceat constant time intervals, the amount of data recorded isinversely proportional to the speed of the stroke. In orderto ensure that the significance of a stroke segment is de-termined by length rather than speed, each stroke is dividedinto 20 equal length segments which are represented by vec-tors. The stroke is first extracted from the data set [Fig. 1].It is then scaled and made to better approximate a contin-uous set of points using interpolation [Fig. 2]. Next it isdivided in to 20 equal length segments [Fig. 3]. Finallythe equal length strokes are then then represented as equallength vectors.


Figure 3. Twenty equally spaced data points.

2.2 SOM System - Training Phase

All codebook vectors are randomly initialised and nor-malised with respect to the variance of the input. An input isselected at random from the training dataset and applied tothe network. The codebook which presents the highest sim-ilarity to the input is determined and that codebook’s outputnode is declared winner. The codebooks of all nodes inthe lattice are updated with respect to three criteria: i) theirsimilarity to the input, ii) their proximity to the winner andiii) the stage of the learning process. A speedy topologicalordering of the the codebook vectors of the output nodesoccurs as a result of the training. The SOM therefore per-forms two functions: i) the generation of codebook vectorswhich serve as cluster centers of the input data and ii) atopological ordering of these cluster centers along the axisof greatest variance [6].

Upon completion of training the codebook vectors arestatic and labelling may begin. Each training input has anassociated character identity, and attempts to assign thisidentity to the most similar codebook in the SOM in aprocess known as voting. On completion of this processthere are a number of codebook vectors which have not beenassigned an identity. The nodes of these codebooks werenot determined as winners in the latter part of the trainingand may be considered trained to a lower standard then theirlabelled counterparts.

2.3 SOM System - Testing Phase

The codebook vectors of the SOM are now static and anumber of the output nodes have been assigned an identity.Each of the testing inputs are now applied to the networkand the identities of the winning nodes recorded. Typicallywhen using a SOM in a classification task the identity ofthe winner is assigned to the testing input. In our SOM werecorded the identities and respective similarities of the 2nd

place and 3rd place nodes in addition to those of the winner.

2nd place is awarded to the next most similar codebook tothe input with an identity different to that of the winner,3rd place is awarded similarly. It will be shown that theprobability of an identity assigned to an input being correctis, on average, inversely proportionally to the degree of theresponse (winner, 2nd place, 3rd place).

2.4 SOM System - Mathematics

The SOM algorithm is relatively simple as introducedabove. Self organization can be achieved in two distinctways, batch training or as in the presented case through se-quential training. Below can be seen the codebook updateequation [Eq.1] and the neighborhood rate equation [Eq.2].

mi(t + 1) = mi(t) + hci(t)[x(t)−mi(t)] (1)

hci(t) = h(‖ rc − ri ‖, t) (2)

where m is the set of all codebook vectors, i is theindex of the current codebook vector, c is the index of thewinner codebook vector, x is the input vector, r is the setof lattice locations of all codebook vectors, and h is theneighborhood function. As rc and ri become more distantin terms of lattice location, hci → 0.

The training algorithm for this SOM is characterised bythree main parameters: learning rate, neighborhood size,and neighborhood rate. They are determined using thefollowing equations:

Learning Rate:

α(t) = 0.8(1− t/tmax) (3)

Neighborhood Size:

γ(t) = latticeWidth ∗ α(t) (4)

Neighborhood Rate:

hci(t) =

{1.0− ‖rc−ri‖

γ(t) if ‖ rc − ri ‖≤ γ(t)0 if ‖ rc − ri ‖> γ(t)

(5)

3 Fuzzy System

Fuzzy rules [9] allow decision making with estimatedvalues under incomplete or uncertain information. Theyprovide a way of enabling approximate human reason-ing capabilities to be applied to knowledge-based systems.Their use in handwriting recognition problems is thereforehighly appropriate, due to the amount of ambiguity andimprecision in handwritten input. Here we present an ap-proach to symbol recognition in which fuzzy rules are usedextensively [8]. The approach consists of three phases:chording, feature extraction and classification.


3.1 Chording

The purpose of chording is to eliminate noise in the orig-inal written strokes and to retain only the information whichis essential for the feature extraction task. Each stroke s istransformed into a chord vector

−→C = 〈c0, . . . , cn−1〉, where

each chord ci is a section of s which approximates a sectorof a circle. This phase simplifies the input data so that fea-ture extraction rules can be written in terms of chords ratherthan sequences of points. Furthermore, chording identifiesthe locations in the stroke where new features may begin,such as sharp turning points or intersection points, so thenumber of sections of the stroke which need to be assessedas potential features is drastically reduced.

Figure 4. Feature Extraction process for a handwritten digit.

3.2 Feature Extraction

A feature extraction algorithm should determine a set offeatures which characterises the input, and which can there-fore be used to classify the input. It should be robust enoughthat for a variety of instances of the same symbol, similarfeature sets are generated. Therefore, we aim to representeach handwritten symbol as a combination of three basicfeature types: Line, C-shape and O-shape [7]. We believethat by representing each symbol in this manner, we are cap-turing the essence of the symbol and what distinguishes itfrom other symbols.

The feature extraction result will be the set of sub-strokes F = {f0, . . . , fm−1} encompassing the entire sym-bol which is of a higher quality than any other possible setof substrokes. Each substroke fj is a sequence of consecu-tive chords. The quality of a set of substrokes, representedby q(F ), is dictated by the membership values of the sub-strokes in F in the fuzzy sets Line, C-shape and O-shape,and also by the number of substrokes in F .

Example: For the symbol shown in Figure 4, theeffect of feature extraction is a partition of the in-put

−→C = {c0, . . . , c4} into a set of features F =

{(c0, c1), (c2), (c3, c4)}, where µLine(c0, c1) = 0.66,µLine(c2) = 0.98, and µCshape(c3, c4) = 0.93.

Fuzzy Rules: Membership values in fuzzy sets are deter-mined by fuzzy rules. The fuzzy rules in the rule base can bedivided into high-level and low-level rules. Each high levelfuzzy rule defines the properties required for a particularfeature type, and is of the form:

T (Z) ← P1(Z) ∩ . . . ∩ Pk(Z) (6)

Membership values in fuzzy sets corresponding to prop-erties are determined by low-level fuzzy rules. In each low-level rule the fuzzy value Pi(Z) is defined in terms of valuesrepresenting various aspects of Z. To express varying de-grees of these aspects we use fuzzy membership functions[9].

Other feature extraction methods have used fuzzy rules[11], but our rules are more elaborate, assessing the extentto which a wide range of properties are present in eachsubstroke [8]. The properties assessed include straight-ness, sharp changes in direction, number of degrees turned,and roundness. The requisite properties for each featuretype, and the rules which assess these properties, were up-dated over time until the memberships being produced weredeemed satisfactory.

3.3 Classification

In the classification phase fuzzy rules are used to deter-mine the most likely identity of the symbol according to thefeature extraction result F = {f0, . . . , fm−1}. The likeli-hood that the features in F form a b, for example, is repre-sented by the membership value µb(F ).

Each fuzzy classification rule states the attributes (suchas orientation) and relationships (such as connectivity or rel-ative lengths) that the features in F should have, if they areto collectively form a particular symbol. The rules are de-signed to be writer independent, but the more the attributesand relationships in F deviate from those stated in the rule,the lower the membership value for that symbol will be.

µ3(F ) ← µOri3(F ) ∩ µLen3(F )∩µQua3(F ) ∩ µCon3(F ) ∩ µV er3(F )

As was the case with the feature extraction rules, theclassification rules are divided into high-level and low-levelrules. Rules which determine the likelihood that a featureset forms a symbol, such as the rule for 3 above, are high-level rules. Each low level rule determines the extent towhich some attribute or relationship is appropriate for a par-ticular symbol. The low-level rule for orientation in a 3 isshown below, where Λ is a fuzzy membership function [11].

µOri3(c1, c2) ← µWest(c1) ∩ µWest(c2)µWest(c1) ← Λ(orientation(c1), 120, 180)


Output: The Fuzzy System outputs a ranked list of iden-tities for the symbol, in an identical format to that of theSOM System, where each identity has an associated confi-dence value. There will not be an entry in the list for everycandidate, because only certain classification rules are ap-plied, ie. those which could match the feature extractionresult.

4 Hybrid System

Here we shall present the combination of two diverserecognition systems, using a variation of weighted voting[3]. If we take a high level look at the Hybrid System wecan see that it attempts to capture and integrate some of thelearning techniques employed by humans as they learn toform symbols. As children we are taught to produce sym-bols in two distinct but complementary ways:

• We are shown the path the pen follows when forminga symbol and asked to imitate it.

• We are shown the arrangement of basic shapes whichform the symbol.

When attempting to devise methods for automatic sym-bol recognition, we can use these two strategies to assistus in our task. The ELV feature extraction process out-lined in section 2.1.1 models the first strategy and the fuzzyrules based feature extraction process outlined in section 3.2models the second strategy. Therefore the SOM System andthe Fuzzy System approach the recognition task in funda-mentally different ways, so it is sensible to combine theiroutputs to form a hybrid system.

4.1 Labelling Terms

To facilitate the discussion of the Hybrid System the fol-lowing terms have been defined:

• target label: a label manually assigned to an inputby a human user, representing its true identity.

• candidate label: a label applied to an input by arecognition system, with varying confidence ≤ 1.

• candidate label set: this contains the 3 most likelydistinct candidate labels assigned to an input by arecognition system.

• combined candidate label set: the concatenated setof candidate label sets of multiple recognition sys-tems.

• label set: this consists of the target label and thecombined candidate label set.

Figure 5. Labels assigned to each input.

• recognition label: the label assigned to an input oncompletion of the recognition phase of the Hybrid Sys-tem.

The labelling convention can be seen clearly in Fig. 5.

4.2 Hybrid System - Overview

The two systems operate independently in the main. It isonly the outputs of the two systems that are combined; theoutput of the SOM System does not influence the operationof the Fuzzy System and vice versa. The operation of theHybrid System may be seen to have two distinct phases, atraining and testing phase.

4.2.1 Hybrid System - Training Phase

The dataset on which the recognition will be attempted isdivided into a training and testing set. The training set isapplied to the SOM System and upon stabilisation the SOMis labelled by voting. The training set is again applied to theSOM System and each input is assigned a target label anda candidate label set by the SOM System. The training setis then applied to the Fuzzy System and each input assignedan additional candidate label set. Each input now has a la-bel set. It is now necessary to decide on a selection policysuch that the correct recognition label is selected from thecombined candidate label set of each input.

The statistical accuracy of each system is then deter-mined with respect to the training set. The relative accu-racy of the SOM System to the Fuzzy System is expressedin the form of a hybrid weight set. The hybrid weight setis used to determine the influence of each subsystem’s can-didate label set on the final recognition label assigned toa member of the testing set during the testing phase. Thehybrid weight set consists of 6 weights: 3 identical weightscorresponding to the percentage recognition achieved by thewinner of the SOM System on the training set, and 3 iden-tical weights corresponding to the percentage recognition


achieved by the winner of the Fuzzy System on the trainingset. The hybrid weight set is then normalised for use in thetesting phase. This technique is similar to that of weightedvoting [3].

4.2.2 Hybrid System - Testing Phase

The testing set is then applied to the trained SOM Systemand the Fuzzy System. Each input is assigned a target labeland a candidate label set by each of the systems whichequivocates to a label set. Each label set is then in turnsubjected to weighted voting using the hybrid weight setidentified in the training phase, and a recognition label isdetermined.

5 Experiments

Both systems are capable of recognising the followingcharacters: 0-9 and a-z. As the task being performed is indi-vidual symbol recognition there is no context to resolve theidentities of structurally identical symbols. Therefore thefollowing sets of symbols are considered equivalent {0,o},{l,1},{9,q},{9,g} [4].The set of possible symbol identitieswill hence forth be referred to as the alphabet. We cantherefore say that our alphabet size is 36.

5.1 Dataset

The dataset used for these experiments is the UNIPENtrain-r01-v07 benchmarks 1a and 1c [5]. A subset of thisdataset was generated for training and testing of the hy-brid and sub systems in the following way: 300 examplesymbols were automatically selected at random for each ofour 36 character alphabet, 10,800 symbols in total. Fromthis set, any symbol which did not resemble its target labelwas removed. Also, any symbol which more closely resem-bled another character in the alphabet than the specified tar-get label was removed. From the remaining clean symbols200 instances of each character were automatically selectedat random for each character of the alphabet, 7200 symbolsin total. The cleaned dataset was then divided into a trainingset and a testing set each consisting of 100 example symbolsof each character in the alphabet, 3600 symbols in each set.

5.2 Experimental Setup

In the case of the SOM System the input layer contains40 nodes and is configured in 20 rows each of 2 nodes. Theinput is applied to all nodes of the input layer simultane-ously at fixed time steps. The output layer has 600 nodesin total configured in a regular rectangular sheet lattice of30 rows each of 20 nodes. The input layer node is fullyconnected to all output layer nodes. A linear decay learning

Figure 6. Digits 0 to 9.

Figure 7. Lowercase a to z.

rate function is used [Eq.3]. A two phase neighborhood hasbeen adopted, with linear decay employed from the winningnode to neighboring nodes within a fixed distance d, and aneighborhood rate of zero to all other nodes of the lattice[Eq.5]. A sequential application of training inputs is im-plemented with updates taking place after each application.300,000 training iterations were performed.

The Fuzzy System and Hybrid System experiments wereexecuted on the aforementioned datasets in the manner out-lined in sections 3 and 4.2 respectively.

5.3 Results

5.3.1 Digits Alphabet

When processing the testing set the Fuzzy System outper-forms the SOM System when only the winner is taken intoaccount (93.5% versus 89.5%), Fig. 6. The Fuzzy Systemhas a highly developed rules system for this alphabet withwhich the unsupervised training of the SOM System couldnot compete. Many of the Fuzzy System’s errors were dueto highly ambiguous symbols, for example certain instancesof 1 and 7 were mistaken for one another. These rules are


Figure 8. Digits 0 to 9 and lowercase a to z.

continually improved over time according to testing. TheSOM System out performs the Fuzzy System when the 2nd

and 3rd answers are also taken into consideration (97.6%versus 96.7%). The candidate label set of the SOM Sys-tem is more likely to contain the target label then that ofthe Fuzzy System, but its resolution power to determine thefinal identity is not as good as that of the Fuzzy System.

The SOM and Fuzzy Systems achieved 98.9% and90.2% respectively in the hybrid training phase resultingin a hybrid weigh set for the digits alphabet of (0.174,0.174, 0.174, 0.158, 0.158, 0.158). This favours the candi-date label set of the SOM System which was identified intraining to be statistically more accurate, although we seea role reversal here. In the situation where the confidencevalues of the Fuzzy System are low the SOM System’s can-didate label set will dominate the weighted voting. Hybridresults were 96.4% when only the winner was taken intoaccount and 98.6% when 2nd and 3rd responses were in-cluded.

5.3.2 Lowercase Alphabet

When processing the testing set the SOM System out per-forms the Fuzzy System when only the winner is taken intoaccount (78.1% versus 68.3%), Fig. 7, and also when 2nd

and 3rd answers are included (90% versus 76.6%). Somesymbols were not recognised by the Fuzzy System becausethey were written with an unorthodox set of features, andtherefore none of the classification rules for the intendedsymbol matched the written version of the symbol. Onthese occasions the Fuzzy System yielded lower confidencevalues. To combat this problem, we are developing an ap-proach whereby the feature extraction result is used as inputto a trained recurrent neural network classifier [18]. Alter-natively, fuzzy rules can be generated automatically [19].However, more control over how the classifier operates isachieved when rules are designed by hand. The SOM Sys-tem exhibits the quality of scalability allowing these un-

orthodox symbols to be recognised provided similar sym-bols have presented in the training set.

The SOM and Fuzzy Systems achieved 90% and 69.8%respectively in the hybrid training phase resulting in a hy-brid weigh set for the lowercase alphabet of (0.187, 0.1870.187, 0.145, 0.145, 0.145). Hybrid results were 83.8%when only the winner was taken into account and 93.6%when 2nd and 3rd responses were included.

5.3.3 Digits and Lowercase Alphabet

When processing the testing set the SOM System out per-forms the Fuzzy System when only the winner is taken intoaccount (76.2% versus 71.3%), Fig. 8. It is again the abilityof the SOM System to generalise which allows it to get bet-ter results than the Fuzzy System when 2nd and 3rd answersare included (89.4% versus 79.8%).

The SOM and Fuzzy Systems achieved 86.7% and71.4% respectively in the hybrid training phase resultingin a hybrid weigh set for the lowercase alphabet of (0.182,0.182, 0.182, 0.151, 0.151, 0.151). Hybrid results were82.8% when only the winner was taken into account and93.3% when 2nd and 3rd responses were included.

6 Conclusions and Future Work

We have shown that through the intelligent combinationof two fundamentally different recognition systems, eachwith their own areas of expertise, we can solve symbolrecognition problems to a high degree of accuracy utilis-ing higher order responses of the recognition subsystems toresolve confusion.

Each of our subsystems when presented with an inputsymbol outputs a set of labels with respective confidencevalues. By virtue of the alphabet and training set specificweighted combination of these values we have achieved in-creased recognition rates from 76.2% to 82.8% with respectto the digits and lowercase alphabet, and from 93.5% to96.4% with respect to the digit alphabet.

Broadly speaking it is the Fuzzy System, by virtue of itshighly developed rules, which performs the primary recog-nition task, and if it is able to determine the identity of theinput symbol with sufficiently high confidence then its pri-mary response will be the principle factor in determiningthe final identity of the symbol. If the response is not ofa sufficiently high confidence then the SOM System’s re-sponses will play a more central role. The Hybrid System isresponsible for the calculation of the weights by which thetwo subsystems responses are combined, and it is here thatthe “sufficiently high” confidence is implicitly determined.

We are currently working on combining the Hybrid Sys-tem outlined in this paper with an Exponential CorrelationAssociative Memory (ECAM) recognition system [1]. The


ECAM stores a large number of prototype symbols in itsmemory in bitmap format. Symbols which are to be iden-tified are then encoded in bitmap format and applied to theECAM. The ECAM identifies the most similar prototype tothe input in memory and outputs it as the recognition result.This bitmap format does not encode the temporal orderingof the data points. Therefore the ECAM can identify sym-bols whose data points were not drawn in a standard tem-poral ordering, becoming a valuable tool in our recognitionsuite by further diversifying our technique base.

References

[1] A. Cronin, O. McEnery, T. Kechadi, F. Geisel-brechtinger, “Comparative Analysis of Two Associa-tive Memory Neural Networks”, 16th IEEE Interna-tional Conference on Tools with Artificial Intelligence(ICTAI’04), Boca Raton, Florida, USA, pp. 120-127,2004.

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[IEEE 2006 18th IEEE International Conference on Tools with Artificial Intelligence (ICTAI'06) - Arlington, VA, USA (2006.11.13-2006.11.13)] 2006 18th IEEE International Conference