Mika Sato

Fuzzy clustering model for fuzzy data

In a clustering problem in which the observations of the objects are given by the values involving vagueness, the ordinary fuzzy clustering methods are not available. In this paper, these data are treated as fuzzy data which are defined by convex and normal fuzzy sets (CNF sets), and a new fuzzy clustering model for the fuzzy data is proposed. We define a conical membership function to represent the CNF sets, and propose a fuzzy dissimilarity between a pair of fuzzy observations, which is an extension of the fuzzy distance proposed by L.T. Koczy et al. (1993). This dissimilarity, discussed in this paper, becomes asymmetric. Therefore, we obtain two different clustering results with respect to each asymmetric part. To achieve consistent clustering results, an additive fuzzy clustering model is used to obtain a solution by a multicriteria clustering technique.<<ETX>>

ON A MULTICRITERIA FUZZY CLUSTERING METHOD FOR 3-WAY DATA

In this paper, we discuss the fuzzy clustering for 3-way data which is composed of objects, attributes and situations. In the case of 2-way data, the clustering of objects are usually based on the values of attributes. However, for 3-way data, a clustering of objects is not always coincident for all situations, because the values of attributes vary with each situation. Therefore, the clustering problem for 3-way data can be regarded as a multicriteria optimization problem. It is known that the practical solutions for a multicriteria optimization problem are Pareto efficient solutions. In a multicriteria hard (non-fuzzy) clustering problem, it is difficult to find a Pareto efficient cluster since this is essentially combinatorial problem. But we show that a multicriteria fuzzy clustering, which is an extension of this hard clustering problem, has merit to obtain Pareto efficient clusters. We investigate the features for Pareto efficient clusters using an artificial 3-way data and we show a numerical example applied to the data of the growth of physical constitutions.

On A General Fuzzy Additive Clustering Model

ABSTRACTThe purpose of this article is to define a generalized structural model of similarity between a pair of objects. Applying a classification of a given data set as a structural model, we have developed an additive fuzzy clustering model.7,8 The essential merits of the additive fuzzy clustering models are 1) the amount of computations for the identification of the models are much fewer than a hard clustering model and 2) fewer number of clusters are needed to get a suitable fitness.9 This article proposes a general class of the clustering model, in which fuzzy aggregation operators are used to define a degree of simultaneous belongingness of a pair of objects to a cluster. We discuss some required conditions for the fuzzy aggregation operators. T-norm is a concrete example to satisfy the conditions. Moreover, the validity of this model is shown by investigating the characteristic feature of the model and numerical applications.

Fuzzy clustering model for asymmetry and self-similarity

This paper shows a method of classification for asymmetric similarity data and non-reflexive data. In a clustering problem in which the similarities of the objects are given by the relation like mobility data which shows relation of proximity from one object to another object, the ordinary fuzzy clustering models are not available. In this paper, these data are treated as asymmetric similarity data including non-reflexive elements which are defined by diagonal elements of the similarity matrix. We define asymmetric aggregation operators to classify objects based on asymmetric similarities. Using the asymmetric aggregation operators, clusters which represent the asymmetric structure between objects are obtained. Moreover, the estimated parameter is introduced to show the non-reflexive data. The validity of this model is shown both by investigating the features of the asymmetric aggregation operators and through numerical applications.

Asymmetry for dynamic fuzzy clustering models

This paper presents a clustering model which analyzes asymmetric similarity data through several times. In general, proximity data (for example, mobility data, input-output data, perceptual confusion data, etc.) are observed in an asymmetric form. If such data are obtained over several times, then 3-way data are constructed. In this paper, we focus on the clustering techniques for 3-way data and show that the proposed method can capture the properties of time difference and asymmetry between two objects in spite of the numbering of the clusters.

Asymmetric proximity for clustering model

A clustering model in which the asymmetry of the given data is represented by asymmetric aggregation operators has been discussed. Using the asymmetric aggregation operators, clusters which represent the asymmetric structure between objects are obtained. In this paper, the asymmetric structure in a clustering model is focused on the following two points. 1) By comparison with conventional model for asymmetric proximity, the notion of the asymmetric structure in a clustering model becomes clear. 2) Some investigation of the asymmetric aggregation operator shows the effectiveness of this clustering model, in terms of the features of equi-similarity curves and/or the domain of feasible solutions in the properties for the function family of the clustering model. The ability of the model to capture the latent structure of the given data is shown not only by the fact that the objects in a cluster are similar to each other, but also by the fact that they have the same asymmetric properties.

Time dependency of fuzzy clustering model

We propose the additive fuzzy clustering model which relaxes the condition of an object belonging to the clusters in the additive clustering (ADCLUS) model. We consider an additive clustering model for longitudinal asymmetric three-way data. In this case, weights are introduced each time to show the salience of each cluster and the time dependencies.

A Generalized Fuzzy Clustering Model Based on Aggregation Operators and its Applications

This paper proposes a fuzzy clustering model which defines a generalized structural model of similarity between a pair of objects.

Application of Three-Way Data Clustering to Analysis of Lymphocyte Subset Numbers in Japanese Hemophiliacs Infected with HIV-1

The 3-way data clustering was applied to the analysis of a number of CD4+ and CD8+ cells obtained from Japanese hemophiliacs infected with HIV-1 through non-heat treated clotting factor concentrates. A total of 131 hemophiliacs were classified into four clusters, termed Cluster 1, 2, 3 and 4. The members in Cluster 1 and 2 showed almost continuous decline in the number of CD4+ cells, while members in Cluster 3 and 4 showed unclear declining tendency compared to Cluster 1 and 2. The number of CD8+ cells was declining in Cluster 1, 2 and 3, while it was rising in Cluster 4. Nevertheless, the cumulative onset rates of AIDS in the four clusters cannot be divided into the four groups accordingly. The rate was the highest in Cluster 1 while no eminent differences were found among the other three clusters. Therefore, we could identify that there is a large variety in the time courses of CD4+ and CD8+ cell numbers during AIDS incubation period, even if the onset rates were almost identical. These findings may be helpful to find the clue in preventing the onset of AIDS arid selecting appropriate therapy for HIV-1 infected patients.

Additive Clustering Model and Its Generalization

ADCLUS (ADditive CLUStering) is known as a clustering model which is designated for the purpose of finding the structure of the similarity data. The aim of this paper is to generalize this model from several points of view. The fast point of view is to extend the degree of belongingness of the objects to the continuous value in the interval [0,1], namely to an additive fuzzy clustering model, because the combinatorial optimization is inevitable in the algorithm for ADCLUS. The second point of view is to generalize the model for an asymmetric similarity data. And the third point of view is that we introduce the aggregation operator in the model to represent the degree of simultaneous belongingness of the objects to each cluster.