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Learning decision trees and tree automata for a syntactic pattern recognition task. Pattern

Learning decision trees and tree automata for a syntactic pattern recognition task. Pattern
Learning decision trees and tree automata for a syntactic pattern recognition task. Pattern

Proceedings of the 1st Iberian Conference on Pattern Recognition and Image Analysis, IbPRIA 2003? Lecture Notes in Computer Science Vol. 2652. Springer 2003

Learning decision trees and tree automata for a

syntactic pattern recognition task

Jos′e M.Sempere and Dami′a n L′o pez

Departamento de Sistemas Inform′a ticos y Computaci′o n

Universidad Polit′e cnica de Valencia,Valencia(Spain)

email:{jsempere,dlopez}@dsic.upv.es

Abstract.Decision trees have been widely used for di?erent tasks in

arti?cial intelligence and data mining.Tree automata have been used

in pattern recognition tasks to represent some features of objects to be

classi?ed.Here we propose a method that combines both approaches to

solve a classical problem in pattern recognition such as Optical Charac-

ter Recognition.We propose a method which is organized in two stages:

(1)we use a grammatical inference technique to represent some struc-

tural features of the characters and,(2)we obtain edit distances between

characters in order to design a decision tree.The combination of both

methods bene?ts from their individual characteristics and is formulated

as a coherent unifying strategy.

1Introduction

Syntactic Pattern Recognition is a well known research area from Arti?-

cial Intelligence in which the target task is to recognize objects from the

real world(speech,image,medical signals,...)which are represented as

formal languages[HU79].Mainly,the most common representations in

these tasks have been some families of string languages(regular,context-

free,...),some families of tree languages(regular ones)or some families

of graph languages(graphs based on vertex substitutions or hypergraphs

with edge replacement).So,the goal in any syntactic pattern recogni-

tion learning task is to guess the hidden formal language from examples

(strings,trees or graphs).

By the other hand,decision trees[Qu93]can be considered as tree-like

representations of?nite sets of if-then-else rules.This representation a-

llows to take some decisions for the analysis of a set of attributes of a

given concept.Mainly,the decision can be applied to a classi?cation task,

a predictive task or an advisement task(i.e.expert systems).During the

last years,decision trees have been applied in the very promising area of

data mining[MBK98]to extract knowledge from large databases.

In this work,we combine these two di?erent approaches to the learning

problem in order to construct a system to solve an Optical Character

Recognition(OCR)task.Here,we will work only with handwritten iso-

lated digits from0to9.Our solution is based on a two stages system.

Work supported by the Spanish CICYT under contract TIC2000-1153.

First,the system learns a set of tree automata(one per digit)by using an error-correcting technique based on a grammatical inference method. Basic concepts and methods on grammatical inference can be viewed in [AS83,Sa97].Then,the system obtains a set of edit distances of every digit to every tree automaton.In the last stage,the system learns a decision tree from the last set of distances that will classify any digit according to a set of rules based on distances.

The structure of this work is as follows:First,we will explain the OCR task that the method attempts to solve.We will explain the learning methods on every phase(i.e.learning of tree automata and learning of decision trees).Finally,we will show some preliminary results from an experimentation using our approach and we will give some research guidelines for future works.

2The problem:Optical Character Recognition The target problem of this work is related to the working area of Hand-written Recognition.Here,the general goal is to construct a robust sys-tem which be able to recognize any phrase or text that has been pre-viously handwritten by a human being.This task has not yet completely solved.So,some subproblems are involved to solve this task.For ex-ample,there exists an increasing area that attempts to construct good segmentation rules in order to factorize any phrase in words an any word in letters or digits.Other researchers have focused their interest on cons-tructing good language models for task-oriented systems(for example, some systems are focused on medical writings,or mathematics writings and so on).We will focus on another task which consists on isolated dig-its recognition.The solution to this task is important to construct more sophisticated systems.Here,the task is quite simple given that phrase and word segmentation tasks are avoided.This is the problem that we try to solve with a syntactic pattern recognition approach.

2.1Representation of the digits

First,we will consider how the real world objects will be represented. Let us observe in Figure1a digit2that has been obtained from a handwriting scanning.

Under our approach,the?rst stage to represent any digit is to obtain a quad tree(qtree)[HS79]from its digital image.A qtree can be cons-tructed by drawing a square window around the digit and splitting the window in four windows of the same size recursively up to a prede?ned depth.In Figure2we can observe how the window of digit2is recursively split.

Once the system obtains the windows of the digit,then it assigns a label to every window of the smallest size.The systems assigns one label to e-very window depending on the grey scale(black,white or grey).So,every smallest window is represented by a label of a three symbols alphabet (i.e.{a,b,c}).The relationships between windows can be represented by a tree by using an up-down and left-to-right scanning of the qtree.In

Fig.1.Handwritten digit2.

Fig.2.Constructing a qtree for digit2.

Figure3we can observe the tree obtained for digit2by using a depth that equals to3while constructing the qtree.From now on,we will use this tree representation.

3Learning methods

We will use two di?erent learning paradigms to solve the learning stage of the previously de?ned problem.First,we will use grammatical inference methods to construct a tree automaton from every set of trees represen-ting the same digit.Then,we will go to a second learning stage to obtain a di?erent representation of the digit based on distances of every digit (every tree)to every concept(every automaton).From this second repre-sentation we will infer a decision tree by using standard methods based on the entropy of the examples and distances.The learning scheme is showed in Figure4.

Now we will explain the di?erent methods that we have used at every learning stage.

3.1Grammatical Inference of error-correcting tree automata

The?rst stage of our learning approach is based on a grammatical infer-ence method for tree languages.Grammatical inference[AS83,Sa97]is an

σ

b b b b b b b b b b b b b b b b b b b b b b

Fig.3.Handwritten digit qtree with a depth that equals https://www.doczj.com/doc/7e11236143.html,bel a corresponds to a at least75%white square,label b corresponds to a at least75%black square,and label c corresponds to a grey square.

inductive approach to the learning problem based on the representation

of concepts as formal languages.Here,as previously explained,we use

trees to represent the digits for the OCR task.

Several methods have been proposed to infer tree languages from exam-

ples[Ga93,GO93,Sa92].We will apply a method based on error-correcting

distances from trees to tree automata.The de?nition of such distance is

based on classical editing distances for strings to?nite string automata

[LSG00].Once,the distance has been de?ned then,the learning method

is an error-correcting grammatical inference technique[LE02].

3.2C

4.5learning algorithm

Learning decision trees is a classical topic on machine learning.A decision

tree is a representation of a?nite set of if-then-else rules.The main

characteristics of decision trees are the following:

1.The examples can be de?ned as a set of numerical and symbolic

attributes.

2.The examples can be incomplete or contain noisy data.

3.The main learning algorithms work under Occam’s razor principle

and Minimum Description Length approaches.

The main learning algorithms for decision trees have been proposed by

Quinlan[Qu93].First,Quinlan de?ned ID3algorithm based on the in-

formation gain principle.This criterion is performed by calculating the

entropy that produces every attribute of the examples and by selec-

ting the attributes that save more decisions in information https://www.doczj.com/doc/7e11236143.html,ter,

Quinlan de?ned C4.5algorithm[Qu93]which is an evolution of ID3al-

gorithm.We will use C4.5algorithm for the second learning phase.The

main characteristics of C4.5are the following:

1.The algorithm can works with continuous attributes(i.e.real data).

https://www.doczj.com/doc/7e11236143.html,rmation gain is not the only learning criterion.

3.The trees can be post-pruned in order to re?ne the desired output.

4Experiments and results

We have performed two experiments in order to carry out a?rst eva-

luation of our learning strategy.The digits that we have used for training

Fig.4.Our learning strategy to solve the OCR problem.

and test is a subset from the data set”NIST SPECIAL DATABASE3, NIST Binary Images of Handwritten Segmented Characters”[Ga94].

The protocol that we have performed in both experiments is the following one:First,we obtain the qtree representations of every digit in the data set.Then,we divide this set in two disjoint subsets(Set1and Set2) and we apply to Set1the Error-Correcting inference technique in order to obtain a tree automaton for every digit.We calculate the distance of every digit to every automaton(so,every digit has ten attributes that represent the distances to every model).Then,we calculate the distances of every digit in Set2to every tree automaton.

From Set1and Set2we perform a learning plus testing phase for decision trees.We have used an implementation of C4.5algorithm in C which is available from internet at J.R.Quinlan’s Home Page[QuHTTP].Observe that for every digit at Set1there is at least one distance with value0, while this is not true in general for digits of Set2.

Experiment1

We have selected3000digits for Set1(300samples for every digit)and 1000digits for Set2(100samples for every digit).We have performed three rounds on C4.5algorithm in order to use di?erent samples with or without distance0.The results of this experiment are showed in Figure 5.

Round1Round2 Evaluation on training data(2666items)

Before Pruning After Pruning

Size Errors 18944(1.7%)Size Errors Estimate 17348(1.8%) 5.8%

Evaluation on test data(1334items) Before Pruning After Pruning

Size Errors 189122(9.1%)Size Errors Estimate

173120(9.0%) 5.8%

Evaluation on training data(2667items)

Before Pruning After Pruning

Size Errors

16754(2.0%)

Size Errors Estimate

15955(2.1%)(5.7%)

Evaluation on test data(1333items)

Before Pruning After Pruning

Size Errors

167116(8.7%)

Size Errors Estimate

159114(8.6%)(5.7%)

Round3

Evaluation on training data(2667items)

Before Pruning After Pruning

Size Errors

20556(2.1%)

Size Errors Estimate

18760(2.2%) 6.5%

Evaluation on test data(1333items)

Before Pruning After Pruning

Size Errors

20587(6.5%)

Size Errors Estimate

18786(6.5%) 6.5%

Fig.5.Results for the?rst experiment.

Experiment2

We have selected3000digits for Set1(300samples for every digit)and 2000digits for Set2(200samples for every digit).We have performed three rounds on C4.5algorithm in order to use di?erent samples with or without distance0.The results of this experiment are showed in Figure 6.

Round1Round2 Evaluation on training data(3333items)

Before Pruning After Pruning

Size Errors 31588(2.6%)Size Errors Estimate 29393(2.8%)8.1%

Evaluation on test data(1667items) Before Pruning After Pruning

Size Errors 315189(11.3%)Size Errors Estimate

293185(11.1%)8.1%

Evaluation on training data(3333items)

Before Pruning After Pruning

Size Errors

30586(2.6%)

Size Errors Estimate

28193(2.8%)7.9%

Evaluation on test data(1667items)

Before Pruning After Pruning

Size Errors

305186(11.2%)

Size Errors Estimate

281185(11.1%)7.9%

Round3

Evaluation on training data(3334items)

Before Pruning After Pruning

Size Errors

32388(2.6%)

Size Errors Estimate

28997(2.9%)8.1%

Evaluation on test data(1666items)

Before Pruning After Pruning

Size Errors

323207(12.4%)

Size Errors Estimate

289208(12.5%)8.1%

Fig.6.Results for the second experiment.

Conclusions

It can be observed that,for every round that we have carried out on the experiments,the error median in training data is less than the one in test data.This is a trivial result that all learning methods would hold. After,the pruning of the decision trees the median error decreases.It implies that some rules that C4.5obtains are not useful for the classi?-cation task.

The results on the?rst experiment are better than in the second.Here, the input sample de?nes how the rules are extracted.In the?rst expe-riment,there is a number of examples with distance0to any tree au-tomata which is three times those examples whose distances to every tree automata is not equal to0.So,the input sample for constructing the tree automata is very important to obtain not only the distances but the decision tree.

Finally,an important remark is that the method has a better perfor-mance than some other methods that uses only a grammatical inference approach[LE02].Furthermore,if we compare this method with some other methods based on geometrical approaches then,the di?erences between median errors can be balanced with the complexity behaviors (i.e.geometrical methods have a worst behavior than our approach under time and space complexities).

5Future works

From the initial results that we have obtained,our approach to the OCR problem has showed itself as a promising one.Anyway,we can point out to the following research guidelines in order to improve this work.

–We should enrich the attributes of every digit by including not only the distances but some other structural features.

–The criteria for decision tree learning could be change in order to take into account the distribution of the distances obtained from tree automata.

–Finally,we should apply this method to other pattern recognition tasks.

References

[AS83] D.Angluin,C.Smith.Inductive Inference:Theory and Methods.

Computing Surveys,vol.15.No.3,pp237-269.1983.

[Ga93]P.Garc′?a.Learning k-testable tree sets from positive data.Tech-nical Report DSIC II/46/1993.Departamento de Sistemas In-form′a ticos y Computaci′o n.Universidad Polit′e cnica de Valencia.

1993.

[GO93]P.Garc′?a and J.Oncina.Inference of recognizable tree sets.

Technical Report DSIC II/47/1993.Departamento de Sistemas In-form′a ticos y Computaci′o n.Universidad Polit′e cnica de Valencia.

1993.

[Ga94]M.D.Garris.Design and Collection of a handwriting sample im-age database.Encycl.of Comp.Sci.&Tech.Marcel Dekker,N.Y.

Vol31,Supp.16,pp189-214.1994.

[HU79]J.Hopcroft,J.Ullman.Introduction to Automata Theory,Lan-guages and Computation.Addison-Wesley Publishing Co.1979. [HS79]G.M.Hunter and K.Steiglitz.Operations on images using quad trees.IEEE Transactions on Pattern Analysis and Machine Intelli-gence Vol.1,No.2,pp145-153.1979.

[LSG00] D.L′o pez,J.M.Sempere,P.Garc′?a.Error Correcting Analysis for Tree Languages.International Journal on Pattern Recognition and Arti?cial Intelligence,Vol.14,No.3,pp357-368.2000.

[LE02] D.L′o pez,S.Espa?n a.Error-correcting tree language inference.

Pattern Recognition Letters23,pp1-12.2002.

[MBK98]R.Michalski,I.Bratko and M.Kubat.Machine Learning and Data Mining.Methods and Applications.John Wiley and Sons LTD.

1998.

[Qu93]J.R.Quinlan.C4.5:programs for machine learning.Morgan Kaufmann.1993.

[QuHTTP]R.Quinlan’s Home Page

https://www.doczj.com/doc/7e11236143.html,.au/~quinlan/

[Sa92]Y.Sakakibara.E?cient learning of context-free grammars from positive structural https://www.doczj.com/doc/7e11236143.html,rmation and Computation97,pp 23-60.1992.

[Sa97]Y.Sakakibara.Recent advances of grammatical inference.Theo-retical Computer Science185,pp15-45.1997.

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