Self-Fuzzification Method according to Typicality Correlation for Classification on tiny Data Sets

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1 Self-Fzzification Method according to Typicality Correlation for Classification on tiny Data Sets Emmanel Schmitt, Vincent Bombardier, Patrick Charpentier To cite this version: Emmanel Schmitt, Vincent Bombardier, Patrick Charpentier. Self-Fzzification Method according to Typicality Correlation for Classification on tiny Data Sets. 6th International Conference on Fzzy Systems, FUZZIEEE 07, Jl 2007, Londres, United Kingdom. IEEE, pp , <hal > HAL Id: hal Sbmitted on 7 Jan 2008 HAL is a mlti-disciplinary open access archive for the deposit and dissemination of scientific research docments, whether they are pblished or not. The docments may come from teaching and research instittions in France or abroad, or from pblic or private research centers. L archive overte plridisciplinaire HAL, est destinée a dépôt et à la diffsion de docments scientifiqes de nivea recherche, pbliés o non, émanant des établissements d enseignement et de recherche français o étrangers, des laboratoires pblics o privés.

2 Self-Fzzification Method according to Typicality Correlation for Classification on tiny Data Sets Emmanel Schmitt, Vincent Bombardier and Patrick Charpentier Abstract This article presents a self-fzzification method to enhance the settings of a Fzzy Reasoning Classification adapted to the atomated inspection of wooden boards. The spervised classification is made thanks to fzzy lingistic rles generated from small training data sets. This stdy especially answers to a doble indstrial need abot the pattern recognition in wooden boards. Firstly, few samples are available to generate the recognition model. This aspect makes lesser efficient compilation methods like neral networks in terms of recognition rates. Secondly, the settings of the classification method mst be simplified, becase the sers are not experts in fzzy logic. In this article, two points are presented. The first part demonstrates the generalization capability of the presented classification method in comparison to more classical algorithms. In the second part, we propose a new atomatic method of parameter fzzification, by sing the typicality correlation coefficients of each class. I. INTRODUCTION The wooden manfactring indstries are placed in a highly competitive market. They express the need of atomated vision systems more and more adapted to the wood qality control (defect detection, color matching). In this field, the processes are generally made by hman operators. These people own all the knowledge and the competencies reqired to make this qality control. That s why, it is important to integrate this knowledge in the vision system in the aim to specify the processes []. Bt, it is not always easy to configre and se the developed systems. To improve the yield, the installation time mst be the smallest to allow a fast profitability. So, the systems mst not be only accessible to experts becase of the setting complexity. The second encontered problem concerns the training samples set. Indeed, the cstomers do not provide lots of samples which are indispensable to train a spervised model. Ths, the otpt classes which define the training sample set are sbjective, small and heterogeneos in terms of points per class. In the case of color matching, the sbjectivity has an effect in the class definition, becase the color perception is not the same for all people. The aim of this paper herein is to present an original method to recognize the different otpt classes: colors (red, Emmanel Schmitt is with the Research Centre for Atomatic Control, CRAN, France ( emmanel.schmitt@cran.hp-nancy.fr). Vincent Bombardier is with the Research Centre for Atomatic Control, CRAN, CNRS, UMR 7039, Faclté des Sciences, Bd des Aigillettes, BP 239, Vandoevre-lès-Nancy Cedex, France (phone: ; fax: ; vincent.bombardier@cran.hpnancy.fr). Patrick Charpentier is with the Research Centre for Atomatic Control, CRAN, France ( patrick.charpentier@cran.hp-nancy.fr). brown, white) or defects (knots, cracks, wanes). In the pattern recognition field, there exist lots of techniqes to identify the objects characterized on the acqired images: Bayesian classifiers, non-bayesian classifiers, neral networks, fzzy logic classifiers In this stdy, the fzzy logic seems to be appropriated to this kind of sbjective problems. After giving the framework of these works, we jstify and expose the chosen method based on fzzy lingistic rles. Then, we show the generalization capabilities of or algorithm according to the nmber of training samples. Finally we essentially stress the simplification of the setting part in or method by explaining a self-fzzification method based on the stdy of the otpt class typicality coefficients. II. FRAMEWORK This stdy takes place in a franco-lxemborger collaboration between the Research Centre for Atomatic Control of Nancy and the Lxscan Technologies company. The main topic of these works is the development of a color matching vision system on wooden boards in order to improve the qality of manfactred prodcts. A. Presentation of the prodction system The wooden board color recognition is made in real-time on an indstrial environment. The sed prodction lines can reach speeds of 220 meters of board length per minte. After the color identification, each piece of wood is sorted or ct according to the qality optimization criteria of the cstomers. Figre illstrates an indstrial process strctre with its information flows. Knowledge Vision System Vision data Decision System Information System of the Company Cost Price Optimization Need Prodct Qality Prodction System Sorting or Ctting Control Fig.. Schematic representation of a prodction line. The arrows correspond to the information flows /07/$ IEEE. 072

3 B. Presentation of the vision system The vision system is composed of color linear cameras which acqire the RGB components. These signals are sampled at 2 khz. The measrements realized on the wooden boards are color images. These images are 24 bit RGB (Red, Green, Ble) images where each component takes a vale between 0 and 255. In order to obtain a vision system nearest to hman perception, the choice of another colorimetric reference space is necessary. The CIE (Commission Internationale de l Eclairage) does not recommend the se of this RGB space. This space is non linear and its components are correlated. The information of lminance and chrominance are not separated. Ths, the CIE recommends the se of other spaces like HSI (He- Satration-Intensity), Yv, Lv, Lab. Several stdies have been made on the colorimetric spaces [2][3]. Or choice concerns the Lab space, becase it accrately retranscribes the colors seen by a hman. After several tests on intra and interclass inertial vales (Figre 2), we choose this colorimetric space which provides the better discrimination of the different color classes. The criteria of selection are the maximization of the eqation () and the minimization of the eqation (2). Interclass inertia: K I n d CG C interclass Intraclass inertia: intraclass =.( (, ) 2 k ecl N G k ) () N k = K n k I d X = ( ecl ( ki, k )) N k = i = with N the global point nmber, n k the point nmber for the class k, K the class nmber, CG N the gravity centre of the sample set, CG k the gravity centre for the class k, d ecl (, 2 CG (2) x y) the Eclidian distance between the vectors x and y, X ki the i th point of the class k. LAB TLS RVB 0 0,05 inertia 0, 0,5 inertia interclass inertia intraclass Fig. 2. Variation of the intra and interclass inertia coefficient for 3 colorimetric spaces. To represent a color throgh the images, we have defined a simple characteristic vector from the indstrial constraints (real-time aspect of the data processes). The data classically sed are obtained from the color histograms [4][5]. The reslts of these stdies are not reprodcible in an indstrial environment, becase the colorimetric space is not chosen from its capability of discrimination. Bt, we retain the se of the proposed characteristic vector: the average of the different color components on a ROI (Region Of Interest). This choice is also jstified by the simplicity of the calclations. Ths, it replies to the real-time constraints of the system. Several tests have allowed checking the good reslts obtained with this vector. III. PROPOSED METHOD OF CLASSIFICATION In the field of wooden board classification, several techniqes are generally sed. Some examples state the se of neral networks [6][7]. However, these methods have an important drawback dring the step of model generation. The training sample nmber mst be consistent in order that the nerons cold focs on the wished otpt classes. In spite of the good reslts exposed in these articles, we focs on an original approach based on the fzzy set theory [8][9]. Or choice is jstified in two ways. - The colors which mst be classified are intrinsically fzzy: impact of the wood grain in the wood color characterization, progressive transition between dark red and medim red in a same board for example. Ths, the extracted color descriptors are ncertain. So, the fzzy logic allows working with this ncertainty. - The cstomers express their needs nder a nominal form with lingistic words. Ths, the otpt classes of the system are sbjective and often not disjointed. There do not exist a strict bondary between medim brown and light brown in the color distribtion. In this sense, we can say that the color perception is gradal. In fact, the fzzy logic concept is more adapted to the system which mst reprodce the hman reasoning [0]. To simplify the integration of the otpt lexical niverse (otpt color classes defined by lingistic terms), we have chosen to se fzzy lingistic rles []. The inference system sed to identify the color is based on a fzzy reasoning. The concepts introdced in this methodology are the elementary fzzy proposition, the general fzzy proposition, the fzzy rles, the fzzy inferences and the fzzy relations [9]. There exist different kinds of rles which can define a fzzy inference engine: the conjnctive rles and the implicative rles. These rles respectively gather, on the one hand, the possibility rles and the anti-gradal rles, on the other hand, the certainty rles and the gradal rles []. Two ways allow to obtain these rles; either from the expert knowledge (implicative rles), or from a training sample set 073

4 (conjnctive rles). In or stdy, we generate the rles from nmerical data, that s why we se conjnctive rles. This inference mechanism depends on a parallel activation of rles. Each rle provides a partial conclsion which is so aggregated to the others in the aim to give the final conclsion. Or Fzzy Reasoning Classifier (FRC) is based on an atomatic generation of fzzy rles according to a training sample set. The fzzy inference engine follows a Larsen model becase the Prodct operator is more adapted than the Minimm in the se of several premises [2]. Or rle generation part is based on the iterative form of the Ishibchi-Nozaki-Tanaka s algorithm. It allows generating IF THEN fzzy rles to define the different otpt classes. We distingish three parts: the parameter fzzification, the rles generation and the model adjstment [3]. Then the obtained rles are sed to identify the different non-labelled samples. Figre 3 illstrates the principle of or FRC method. The methods compared to the FRC algorithm are techniqes freqently sed in classification: Bayesian classifier, neral networks (NN), k nearest neighbor (knn). Figre 5 illstrates the evoltion of the recognition rates in generalization according to the size of the training sample nmber per class. The presented reslts are a mean vale on several tests (30 attempts by training sample nmber). Training samples Membership fnctio ns Training step Fzzificatio n Generalization step Characteristic Vector Membership fnction s Fzzificatio n Rles Generatio n Adjstment Fzzy inferenc e Matrix translation of fzzy rles Decision Fig. 4. Representation of the 6 artificial color classes in the La colorimetric space. Recognition rates Recognition rates FRC knn Bayes NN Fig. 3. Recognition modle IV. GENERALIZATION CAPABILITIES OF THE FRC The training step is one of the stronger points of or method. Indeed, or project concerns a field in which the nmber of training data is small. It is possible that the otpt classes are represented with only ten or twenty samples. That s why, methods needing lots of points, like the neral networks, seem lesser adapted to or problem. We have realized a stdy concerning the impact of training sample nmber on the recognition rates. To make these tests, we se an indstrial color data base which is composed of 900 points distribted in 6 color classes. Each class is represented by 50 samples. However, to evalate and compare the different classifiers, points have been randomly generated by noising the real data with a white Gassian noise. So, the final test base is composed of 5000 samples per class. Figre 4 represents the sample distribtion in the La plan of the Lab colorimetric space. We notice that there exist some confsion zones between the different color classes, and particlarly between the lightest colors. After the comparison of classifiers, we will analyse the recognition rates per class Sample nmber per class Sample nmber per class Fig. 5. Evoltion of the recognition rates according to the training sample nmber per class. We note that, the more there are points in the training sample set, the more the recognition rate increases. That is checked for all presented classification methods. An horizontal asymptote even appears: 80% for the Bayesian classifier, 83% for the knn (k=5), 86% for the NN, 86% for the FRC. The different methods converge more or less qickly on these asymptotes. Typically, the neral networks need lots of samples dring the training phase in order to be efficient in generalization. For eqivalent performances, the neral networks need 40 times more points in the training step for the recognition rate to reach the one obtained with or method. This aspect is very important in or stdy, becase it is very difficlt to have big data sets in an indstrial context. 074

5 Hman Classification TABLE I CONFUSION MATRIX FOR THE COLOR DATABASE IN GENERALIZATION FRC F.R.C. Classification Nmber of Recognition DB B LB DR R LR UK samples rates DB % B % LB % DR % R % LR % UK % Nmber of samples % (DB: Dark Brown, MB: Medim Brown, LB: Light Brown, DR: Dark Red, MR: Medim Red, LR: Light Red, UK: Unknown) In fact, the labelling is too drdgery and implies the intervention of qalified employees. As said before, it is important to analyse the behavior of or method for the classification of the different color classes. Indeed, these classes are heterogeneos in terms of sample qantity. Moreover, there exist some overlapping zones between the defined cstomer colors. Table I represents the confsion matrix corresponding to the recognition rate in generalization for a real color data set which contains 943 samples (33 for the training step and 630 for the generalization step). In this matrix, the nmber at the row i and the colmn j indicates the nmber of samples which are labelled in the class i by a hman operator and recognized in the class j by the classification method. For instance, if we consider the DB class (Dark Brown), the classification modle has recognized 47 samples in DB and 5 in the MB class (Medim Brown) whereas all these samples were labelled in the DB class by the hman operator. From this matrix, it is possible to evalate the acceptable confsions. The cstomer can accept confsions according to the intensity (Dark, Medim, Light), bt he cannot accept he variations (Red and Brown) which wold downgrade the final prodct. For instance, if we consider the LR class (Light Red), we notice that 7 samples are recognized in the MR class (Medim Red). In this case, we can consider the classification as right. However, there still remain 8 false classifications (5 in the class Light Brown and 3 in the class Medim Brown). In this case, if we accept the confsions, e.g. LR class recognized as MR class, the recognition rate is approximately increased by 0% to reach 94.6%. The confsion matrix also allows the evalation of the recognition model qality thanks to the calclation of the ˆκ Kappa coefficient (6) [4]: where r ( + * + ) N X X X ˆ κ = N X X ii i i i= i= r 2 ( i+ * + i) i = r N is the total nmber of samples X ii is the vale in the row i and the colmn i r is the nmber of otpt classes X i+ is the sample nmber of the row i (6) X +i is the sample nmber of the colmn i. In the presented case (Table. ), this coefficient is eqal to According to the scale defined by Landis and Koch [4] or model is considered as excellent. Nevertheless, these reslts strongly depend on the fzzification step [3]. V. SELF-FUZZIFICATION OF THE INPUT PARAMETERS In an indstrial environment, it is very difficlt to employ experts in classification methods. So, it is important to simplify the setting step of or classification method and more precisely the fzzification step. The main self-tning methods are based on genetic algorithms [5] or clstering methods [6]. They are sed to atomatically tne the membership fnctions. However, the main drawback of techniqe based on genetic algorithms is the nmber of training samples per otpt class. Moreover, these methods directly work on the inpt data withot taking into accont the otpt classes and the expert needs. A. Presentation of the fzzification The fzzification consists in splitting in several terms the parameters which compose the characteristic vector. Each decomposition or term gets closer to a word of the natral langage. For instance, the lminance can be light, medim or dark. There exit two ways to set the fzzification: a fzzification with an eqal distribtion of the terms, and a fzzification with a repartition adapted to the training data set. There are two parts of the fzzification step which can have an impact on the recognition rates: the nmber of terms and the fzzification crve form. Usally, the nmber of terms is empirically chosen. Figre 6 illstrates an example of 3-term decompositions. We will present in the section IV.C a set of reslts concerning the impact of the fzzification on the recognition rates. B. Analysis of the parameter typicalities The sers of or method prefer to qickly configre the parameter space decomposition, becase they do not have the sfficient knowledge of the classification method. Ths, they define an eqal distribted fzzification. However, if the splitting does not correspond to the variation space of the 075

6 real data set, the defined terms can be inappropriate. We can say that the data are not typical of the obtained sbspaces. We propose to base or self-fzzification method on the typicality of the characteristic vector [7]. This notion is evalated with the calclation of the typicality coefficient for the different parameters. The typicality calclation (5) is based on the intern dissimilarity (3) and extern likeness (4) evalations for all samples. ( a ) R V ( a ) D V T where ( Va ) = = n f i (, ) d V V i = ecl a a m n e ( ) i = d ecl Va Va, i m RD. = R. D +. D ( R) ( ) Va is the vale of the parameter a for the point ; 3) For i = C to C K, if ρcorr/xcorr ( Ci, Ci+ ) = max ρcorr/xcorr ( Ci, Cj) j [, K], j i then C i and C i+ are represented with the same term (3) (4) (5) f V i a is the vale of the parameter a for the friend point f of the class i; V is the vale of the parameter a for the enemy e i a point e of the class i; d x y)is the Eclidian distance between x and ecl (, y; n is the nmber of friend points; m is the nmber of enemy points; R and D correspond to ( R V a ) and ( a ) DV. Figre 6 represents the variation of the typicality coefficients for or indstrial color data base. There are 6 wooden color classes: Dark Brown (DB), Medim Brown (B), Light Brown (LB), Dark Red (DR), Medim Red (R) and Light Red (LR). From the typicality coefficients, we have evalated the ratio ρ corr/xcorr between the correlation coefficient and the cross-correlation for the different otpt classes. Then, these coefficients allow defining the fzzification terms from the maximm vale of the ratio. If two classes are sccessive and if the ratio between these two classes is the maximm vale, we consider that these classes cold be represented by the same term. Algorithm: ) Calclation of ρ corr/xcorr ratio for all classes 2) Ascending class sorting from the parameter vales Ex : DR DB R B LR LB class C C 2 C 3 C 4 C 5 C 6 else the term only represents the class C i, and another term is created for the class C i+. By applying this methodology on the previos example (Figre 6), the parameter L has been fzzified in 3 terms. typicality coefficient DB DR R LR Dark Medim Light LB parameter L Fig. 6. Typicality coefficient and fzzification crves (bold line) for the lminance. C. Fzzification impact on the recognition rates As said in the section IV.A, the fzzification has a direct impact on the recognition rates. To stdy this effect, we se the indstrial color data base labeled by a cstomer presented in the IV section. The 943 samples are distribted in the previosly 6 classes. For each class, one training set and one checking set have been bilt. Table II present the generalization recognition rates according to the fzzification crve form and the nmber of terms, in the case of an eqal distribtion. Nmbers of fzzification terms TABLE II B RECOGNITION RATES IN GENERALIZATION EQUAL DISTRIBUTED FUZZIFICATION Gassian crves Trianglar crves Trapezoidal crves Trapezoidal Trianglar crves % 48.2% 49.8% 49.8% 3 55.% 69.8% 74.3% 77.0% % 75.5% 78.6% 83.7% % 80.0% 8.8% 85.9% 9 7.6% 74.3% 79.6% 82.% 7.0% 72.9% 76.% 79.6% The best reslts are obtained for a 7-term eqal distribted fzzification with Trapezoidal-Trianglar crves. If the parameter representation space is too mch split, the recognition rates decrease becase the color classes are not represented by the sbspace of each term. In fact, there are more confsion zones in the representation space. Then, we apply or self-fzzification method on the same data base. Table III illstrates a comparison between the better eqal distribted fzzification, a manally adapted fzzification and the self-fzzifications. For these tests, the fzzification crves are trapezoidal-trianglar. Moreover, we compare the FRC reslts with the crrent indstrial classifier. 076

7 TABLE III EQUAL DISTRIBUTED FUZZIFICATION VERSUS ADAPTED FUZZIFICATION COMPARISON WITH THE CURRENT INDUSTRIAL CLASSIFIER ( NEAREST NEIGHBOUR) * ** Indstrial classifier Bayesian Classifier Neral Networks Rates Rates Rates Rates 7-eqal distribted fzzification - FRC Nmber of rles Manally adapted Fzzification - FRC Rates Nmber of rles Self-fzzification - FRC Data Set * 8.37% 79.2% 73.92% 85.87% % % 24 Data Set 2 ** 80.29% 78.85% 7.25% 84.92% % % 45 Data Set is composed of 943 samples distribted in 6 classes (33 for the training step and 630 for the generalization step) Data Set 2 is composed of 34 samples distribted in 6 classes (209 for the training step and 05 for the generalization step) Rates Nmber of rles Two aspects are interesting: the recognition rates and the nmber of generated fzzy rles. When the fzzification is adapted to the training data, the nmber of rles is smaller than the one obtained with an eqal distribtion. Moreover, in or case, the fzzification based on expert knowledge [8] doesn t really provide better classification rates, even if it decreases the nmber of rles. Or fzzification method combines both advantages. Indeed, by decreasing the rle nmber and in the same way the consmed time for classification, the recognition rate increases by.2%. Or self-fzzification method have been compared to others methods like clstering [6] and genetic algorithms [5], bt the reslts are worse than those obtained with or proposition. (approximately 2%). VI. CONCLUSIONS In this article, we have presented a method allowing a fzzy lingistic rle classification from a redced training data set. Moreover, a techniqe of self-fzzification has been proposed to redce the difficlties of the system settings. The aim of this method is doble. Firstly, having few samples at or disposal to generate the nmerical model, we mst find a method with a strong capability of generalization. This stdy realized on color data clearly shows this capability of or method. Indeed, with only 25 training samples per class, we obtain the better recognition rates. Moreover, even if the otpt classes present overlapping zones, or methodology does not perform many misclassifications. Secondly, by sing a self-fzzification based on the typicality coefficient analysis, or methodology provides better reslts than an eqal-distribted fzzification. The typicality has the advantage to represent the common points between the different otpt classes. Or fzzification method allows obtaining a fzzification based on the cstomer s specified otpt classes. In addition to the recognition rate improvement, the effective classification time is redced thanks to few generated fzzy rles. To improve or classification method, it is possible to extend or self-fzzification to a techniqe of knowledge integration in the model generation [8]. ACKNOWLEDGMENT The athors wish to thank their indstrial partner the LxScan Technologies Company who follows and spports the present works. REFERENCES [] A. H. Hber, S. Rddell and C. W. McMillin, Indstry standards for recognition of marginal wood defects, Forest Prodcts Jornal, vol. 40(3), pp , 990. [2] I. Philipp and T. Rath, Improving plant discrimination in image processing by se of different color space transformations, Compters and electronics in agricltre, vol. 35, pp. -5, [3] K. Leon, D. Mery, F. Pedreschi and J. Leon, Color measrement in L*a*b* nits from RGB digital images, Food research international, vol. 39, pp , [4] Q. L, A Real-Time System for Color Sorting Edge-Gled Panel Parts, Ph.D. Dissertation, Faclty of the Virginia Polytechnic Institte and State University, Blacksbrg, Virginia, 997. [5] A. Hanbry, Mathematical morphology on the Unit Circle with applications to the hes and the oriented textres (in French), Ph.D. Dissertation, Ecole Nationale Spériere des Mines, Paris, [6] D. T. Pham and S. Sagirogl, Training mltilayered perceptrons for pattern recognition: a comparative stdy of for training algorithms, International Jornal of Machine Tools and Manfactre, vol. 4, pp , 200. [7] P. A. Estevez, C. A. Perez and E. Goles, Genetic inpt selection to a neral classifier for defect classification of radiata pine boards, Forest Prodcts Jornal, vol. 53, pp , [8] L. A. Zadeh, Fzzy sets, Information and control, vol. 8, pp , 965. [9] B. Bochon-Menier, The fzzy logic and its applications (in French), Edited by Addison-Wesley, 995. [0] L. A. Zadeh, Otline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-3, pp , 973. [] D. Dbois and H. Prade, What are Fzzy rles and how to se them?, Fzzy Sets and Systems, vol. 84, pp , 996. [2] H. Ishibchi, K. Nozaki and H. Tanaka, Distribted representation of fzzy rles and its application to pattern classification, Fzzy Sets and Systems, vol. 52, pp. 2-32, 992. [3] E. Schmitt, C. Mazad, V. Bombardier and P. Lhoste, A Fzzy Reasoning Classification Method for Pattern Recognition, Fzzy IEEE, Vancover, Canada, [4] J. R. Landis and G. G. Koch, The measrement of observer agreement for categorical data, Biometrics, vol. 33, pp , 977. [5] O. Cordon, F. Gomide, F. Herrera, F. Hoffmann and L. Magdalena, Ten years of genetic fzzy systems: crrent framework and new trends, Fzzy Sets and Systems, vol. 4, pp. 5-3, [6] F. A. T. De Carvalho, Fzzy c-means clstering methods for symbolic interval data, Pattern Recognition Letters, vol. 28, pp , [7] J. Forest, M. Rifqi and B. Bochon-Menier, Class Segmentation to Improve Fzzy Prototype Constrction: Visalization and Characterization of Non Homogeneos Classes (in French), Rencontres Francophones sr la Logiqe Floe et ses Applications LFA, Tolose, France, pp , [8] V. Bombardier, C. Mazad, P. Lhoste and R. Vogrig, Contribtion of fzzy reasoning method to knowledge integration in a defect recognition system, Compter in Indstry, In Press,