HAL (Le Centre pour la Communication Scientifique Directe), Jul 16, 2006
Performance of any clustering algorithm depends critically on the number of clusters that are ini... more Performance of any clustering algorithm depends critically on the number of clusters that are initialized. A practitioner might not know, a priori, the number of partitions into which his data should be divided; to address this issue many cluster validity indices have been proposed for finding the optimal number of partitions. In this paper, we propose a new "Graded Distance index" (GD_index) for computing optimal number of fuzzy clusters for a given data set. The efficiency of this index is compared with well-known existing indices and tested on several data sets. It is observed that the "GD_index" is able to correctly compute the optimal number of partitions in most of the data sets that are tested.
This paper aims at presenting a rejection-based and class-selective possibilistic classifier and ... more This paper aims at presenting a rejection-based and class-selective possibilistic classifier and its parameters learning. The classifier is defined as a couple of functions (D,T), D being a labelling one and T being a hardening one in a non exclusive way. The parameters of the classifier (D, T), whose strategy for rejection is not classical, are learned using a suitable clustering algorithm and statistical operators. We illustrate the proposed method on both artificial noisy data and real data. Z(s) using eq. (1) desirable I(%)
Cluster validity indexes aim at evaluating thc degree to which a partition obtain4 from a cluster... more Cluster validity indexes aim at evaluating thc degree to which a partition obtain4 from a clustering algorithm approximates the real structure of w data set. Most of them reduce to the search of the right number of clusters. This paper presents mch a new validity index for fuzzy clustering bascd on the aggregation of the multing membership degrees with no additional informatian, e.g. the geornelrica! stmctum of the data. It exploits the tendency for a data point to helong to a unique cluster, Le, both the tendency to belong to one cluster and the tendency not to belong to the othem dusters. Clustering has been defined as the "art of finding groups (clusters) in data sets" [9]. The underlying idea is that dam pojnts from different clusters are as dissimilar as possible while objects belongjng to any of the dusters are similar. In such a framework, the label of a data point, i,e, the group to which it belongs is unknown. Clustering is then viewed as an instance of unsupervised classification and is one of the most important task in pattern recognition. A major challenge in cluster analysis is the validation of clusters resulting from clustering methods. The performance of a particular method clearly depends on the natural (groups-)structure of the data but also of the algorithm parameters, e.g. the shape of the clusters or their nurnber. Comparative studies of validity indexes, mainly for fuzzy clustering, can be; found in [4], 1141, [I 01. Two kinds of classical indexes are generally admitted: those that only use membership labels and those that exploit some geometrical infomation about the structure of the Carl Wlicat is with the Labomminire Irafonnrrrique-Image-!nrrmair~~t, Universit6 de I-a RochelTe, 17042 Ida Rtxhelle Cedex I , FRANCE (phone: $33 546 458 234; far: c33 546 4% 242; ernail: carl,frclicotQuniv-lr.fr), L a u~n t Mascarillid is with the Lahnrafnire fnjom1aidqu.e-I M~P-!nieracfirjn, UnivcnitE dc La Rochellc, 17042 La Rochclle Cedcx
HAL (Le Centre pour la Communication Scientifique Directe), 2016
Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined ... more Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined with the help of generative functions, and its relationship with additive generating functions of uninorms. In this paper, we also present new aggregation operators, namely the k-uninorms and k-absorbing norms. These operators are a generalization of usual uninorms and absorbing norms for which a set combination of inputs is introduced. Their main ability is to provide reinforcement for contradictory inputs, as nullnorms and as opposed to uninorms. On the other hand it still provides full reinforcement for agreeing inputs, as uninorms and as opposed to nullnorms. Numerous examples are given in order to illustrate the behavior of the proposed operators.
K-step ahead prediction in fuzzy decision space-application to prognosis
ABSTRACT The authors demonstrate the ability and the accuracy of a modified extended Kalman filte... more ABSTRACT The authors demonstrate the ability and the accuracy of a modified extended Kalman filter used as a k -step-ahead predictor to perform a predicted membership function's point in a fuzzy decision space based on fuzzy pattern recognition principles, instead of a predicted state in the feature space. Results obtained with this prediction procedure are presented. A scheme including both fuzzy decision and prediction procedures is proposed for prognosis
Background modeling has emerged as a popular foreground detection technique for various applicati... more Background modeling has emerged as a popular foreground detection technique for various applications in video surveillance. Background modeling methods have become increasing efficient in robustly modeling the background and hence detecting moving objects in any visual scene. Although several background subtraction and foreground detection have been proposed recently, no traditional algorithm today still seem to be able to simultaneously address all the key challenges of illumination variation, dynamic camera motion, cluttered background and occlusion. This limitation can be attributed to the lack of systematic investigation concerning the role and importance of features within background modeling and foreground detection. With the availability of a rather large set of invariant features, the challenge is in determining the best combination of features that would improve accuracy and robustness in
Un systeme adaptatif de diagnostic predictif par reconnaissance des formes floues
La surveillance automatique des systemes technologiques (procede, machine industrielle,. . . ) pe... more La surveillance automatique des systemes technologiques (procede, machine industrielle,. . . ) peut etre assuree par des systemes de diagnostic capables d'identifier en ligne sous quel mode de fonctionnement le systeme evolue et de s'adapter a l'apparition de nouveaux modes. Pour des raisons economiques evidentes, le diagnostic n'est plus suffisant de nos jours et il convient de developper de nouveaux outils capables d'anticiper l'evolution du systeme vers des modes de fonctionnements non desires. Cette these presente les travaux relatifs au developpement d'un systeme adaptatif de diagnostic predictif. Le systeme propose met en oeuvre des principes de reconnaissance des formes floues, tant au niveau de l'apprentissage (adaptatif) que de la decision (diagnostic) et de la prediction. L'approche floue permet de gerer l'incertitude liee aux differentes taches que le systeme doit realiser. Une nouvelle regle de decision floue integrant les notions de rejet d'ambiguite et de rejet d'appartenance a ete proposee. Un algorithme original de prediction multi-pas a horizon fixe (ou variable) a ete developpe dans l'espace de decision floue. Il met en oeuvre un filtre de kalman etendu adaptatif. Cet algorithme est utilise de maniere directe pour realiser la fonction de pronostic (diagnostic predictif), et de maniere indirecte pour resoudre le probleme de la levee d'ambiguite a posteriori
This paper aims at unifying the presentation of twofold rejectionbased pattern classifiers. We pr... more This paper aims at unifying the presentation of twofold rejectionbased pattern classifiers. We propose to define such a classifier as a couple of labelling and hardening functions which are independent in some way. Within this framework, crisp and probabiIistic / fuzzy rejection-based classifiers are shown to be particular cases of possibilistic ones. Classifiers with no reject option remains particular cases of rejection-based ones. Examples of so-defined classifiers are presented and their ability to deal with the reject problem is shown on artificial and real data sets.
Abstract—Recently, the community has shown a growing interest in building online learning models.... more Abstract—Recently, the community has shown a growing interest in building online learning models. In this paper, we are interested in the framework of fuzzy equivalences obtained by residual implications. Models are generally based on the relevance degree between pairs of objects of the learning set, and the update is obtained by using a standard stochastic (online) gradient descent. This paper proposes another method for learning fuzzy equivalences using a Quasi-Newton optimization. The two methods are extensively compared on real data sets for the task of nearest sample(s) classification. Index Terms—Fuzzy similarity, nearest-neighbor classification, online learning. A. Preliminaries I.
Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined ... more Aggregation operators Reinforcement ... We propose a n-ary extension of absorbing norms, defined with the help of generative functions, and its relationship with additive generating functions of uninorms. In this paper, we also present new aggregation operators, namely the k-uninorms and k-absorbing norms. These operators are a generalization of usual uninorms and absorbing norms for which a set combination of inputs is introduced. Their main ability is to provide reinforcement for contradictory inputs, as nullnorms and as opposed to uninorms. On the other hand it still provides full reinforcement for agreeing inputs, as uninorms and as opposed to nullnorms. Numerous examples are given in order to illustrate the behavior of the proposed operators.
Background modeling has emerged as a popular foreground detection technique for various applicati... more Background modeling has emerged as a popular foreground detection technique for various applications in video surveillance. Background modeling methods have become increasing efficient in robustly modeling the background and hence detecting moving objects in any visual scene. Although several background subtraction and foreground detection have been proposed recently, no traditional algorithm today still seem to be able to simultaneously address all the key challenges of illumination variation, dynamic camera motion, cluttered background and occlusion. This limitation can be attributed to the lack of systematic investigation concerning the role and importance of features within background modeling and foreground detection. With the availability of a rather large set of invariant features, the challenge is in determining the best combination of features that would improve accuracy and robustness in
Superpixel-based online wagging one-class ensemble for feature selection in foreground/background... more Superpixel-based online wagging one-class ensemble for feature selection in foreground/background separation, Pattern
K-step ahead prediction in fuzzy decision space-application to prognosis
[1992 Proceedings] IEEE International Conference on Fuzzy Systems
ABSTRACT The authors demonstrate the ability and the accuracy of a modified extended Kalman filte... more ABSTRACT The authors demonstrate the ability and the accuracy of a modified extended Kalman filter used as a k -step-ahead predictor to perform a predicted membership function's point in a fuzzy decision space based on fuzzy pattern recognition principles, instead of a predicted state in the feature space. Results obtained with this prediction procedure are presented. A scheme including both fuzzy decision and prediction procedures is proposed for prognosis
1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228)
This paper aims at presenting a rejection-based and class-selective possibilistic classifier and ... more This paper aims at presenting a rejection-based and class-selective possibilistic classifier and its parameters learning. The classifier is defined as a couple of functions (D,T), D being a labelling one and T being a hardening one in a non exclusive way. The parameters of the classifier (D, T), whose strategy for rejection is not classical, are learned using a suitable clustering algorithm and statistical operators. We illustrate the proposed method on both artificial noisy data and real data. Z(s) using eq. (1) desirable I(%)
This paper aims at unifying the presentation of twofold rejectionbased pattern classifiers. We pr... more This paper aims at unifying the presentation of twofold rejectionbased pattern classifiers. We propose to define such a classifier as a couple of labelling and hardening functions which are independent in some way. Within this framework, crisp and probabiIistic / fuzzy rejection-based classifiers are shown to be particular cases of possibilistic ones. Classifiers with no reject option remains particular cases of rejection-based ones. Examples of so-defined classifiers are presented and their ability to deal with the reject problem is shown on artificial and real data sets.
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Papers by Carl Frélicot