Chi-Hyon Oh

Fuzzy clustering for categorical multivariate data

This paper proposes a new fuzzy clustering algorithm for categorical multivariate data. The conventional fuzzy clustering algorithms form fuzzy clusters so as to minimize the total distance from cluster centers to data points. However, they cannot be applied to the case where only cooccurrence relations among individuals and categories are given and the criterion to obtain clusters is not available. The proposed method enables us to handle that kind of data set by maximizing the degree of aggregation among clusters. The clustering results by the proposed method show similarity to those of correspondence analysis or Hayashis (1952) quantification method Type III. Numerical examples show the usefulness of our method.

Initialization of Q-values by fuzzy rules for accelerating Q-learning

We demonstrate that Q-learning can be accelerated by appropriately specifying initial Q-values using fuzzy rules. Fuzzy rule-based Q-learning is fast but unstable. On the other hand, the conventional Q-learning is not fast while it has the theoretical convergence property. In our approach, advantages of both algorithms are combined into a single hybrid algorithm where the fuzzy rule-based Q-learning is first employed for specifying initial Q-values for the conventional Q-learning. The conventional Q-learning with appropriately specified initial Q-values requires much less iterations for obtaining good results than that with uniformly or randomly specified initial values. We examine the performance of the fuzzy rule-based Q-learning, the conventional Q-learning and the hybrid algorithm by computer simulations on gridworld problems.

Exclusive condition on item partition in fuzzy co-clustering based on K-L information regularization

FCCM based on K-L information regularization is an FCM-type co-clustering model, which is a fuzzy counterpart of the probabilistic Multinomial Mixture Models (MMMs). In MMMs and other FCM-type co-clustering models, whose goal is to simultaneously partition objects and items considering their mutual cooccurrence information, memberships of objects are forced to be exclusive in a similar way to FCM while item-memberships only represent the relative typicality in each cluster and are not forced to be exclusive. In this paper, a new co-clustering model is proposed by introducing the penalty for avoiding cluster overlapping in sequential fuzzy cluster extraction, which brings exclusive partition of items.

Cluster validation in k-Means clustering based on PCA-guided k-Means and procrustean transformation of PC scores

PCA-guided k-Means is a technique for analytically estimating a relaxed solution for k-Means clustering, while the derived cluster indicator is a rotated solution and the rotation matrix cannot be explicitly estimated. Then, an approach such as visualization by ordering of samples in connectivity matrices is applied for visually accessing cluster structures. This paper introduces a technique for estimating a rotation matrix by Procrustean transformation of principal component scores in order to select the optimal solution from multiple solutions derived by k-Means, and proposes a cluster validation measure calculating the deviation between k-Means solutions and a re-constructed membership indicator matrix.

A fuzzy model-based community simulator for behavior analysis in virtual theme park

In order to achieve universal contents creation/distribution in a network community, it is necessary to create an environment in which anyone can produce any content they wish and in which content can be accessed while ensuring reliability. This paper considers a fuzzy model of a community simulator for behavior analysis in a virtual theme park that can be identified with a constrained network community. A number of agents with various tastes, whose action patterns are modeled based on answers from respondents to a questionnaire, act autonomously according to their action rules in the multi-agent system. Experimental results demonstrate that such fuzzy model-based agents are useful for analyzing the behaviors of guests in a large scale theme park.

Fuzzy clustering algorithm extracting principal components independent of subsidiary variables

Fuzzy c-varieties (FCV) is one of the clustering algorithms in which the prototypes are multidimensional linear varieties. The linear varieties are represented by some local principal component vectors and the FCV clustering algorithm can be regarded as a simultaneous algorithm of fuzzy clustering and principal component analysis. However, obtained principal components are sometimes strongly influenced by the dominant factors which are already known as common knowledge. To diminish the influences, we propose a new method of fuzzy clustering algorithm which extracts principal components independent of subsidiary variables. In the algorithm, the dominant factors are used as subsidiary variables. We apply the proposed method to a POS (point-of-sales) transaction data set in order to discover associations among items without being influenced by the explicit dominant factors.

Approximate realization of fuzzy mappings by regression models, neural networks and rule-based systems

We discuss the approximate realization of fuzzy mappings by fuzzy regression models, fuzzy neural networks, and fuzzy rule-based systems. These mathematical models are used as approximators of fuzzy mappings from fuzzy input vectors to fuzzy outputs (i.e., fuzzy numbers). First, we explain fuzzy regression models, which are extensions of linear regression models to the case of fuzzy inputs, fuzzy coefficients and fuzzy outputs. Next, we explain fuzzified neural networks where inputs, connection weights, biases and targets are fuzzy numbers. Then we explain the approximate realization of fuzzy mappings by fuzzy rule-based systems. We modify the simplified fuzzy reasoning method used in many fuzzy controllers in order to infer a fuzzy output (i.e., fuzzy number) from fuzzy if-then rules.

Handling Very Large Cooccurrence Matrices in Fuzzy Co-clustering by Sampling Approaches

Handling very large data sets is a significant issue in many applications of data analysis. In Fuzzy c-Means (FCM), several sampling approaches for handling very large data have been proved to be useful. In this paper, the sampling approaches are applied to fuzzy co-clustering tasks for handling cooccurrence matrices composed of many objects. The goal of co-clustering is simultaneously partition both objects and items into co-clusters and item memberships are used for characterizing each co-cluster instead of cluster centers in the conventional FCM. In some modified approaches, item memberships are utilized in conjunction with other objects for inheriting the property of other sample sets.

Dual Exclusive Partition in Fuzzy CoDoK and SCAD-based Fuzzy Co-clustering

Abstract Fuzzy co-clustering is a basic technique for revealing intrinsic co-cluster structures from cooccurrence information among objects and items. In most of fuzzy co-clustering algorithms, objects and items are partitioned based on different constraints. Objects are forced to be exclusively partitioned like as Fuzzy c -Means (FCM), while item memberships often represent just the relative significance of items in each cluster, i.e., items can be shared by multiple clusters. In a previous work, exclusive partition of items were achieved by introducing a penalty term in Fuzzy Clustering for Categorical Multivariate data (FCCM), which is an FCM-type co-clustering with entropy regularization mechanism. In this paper, the applicability of dual exclusive partition of objects and items are discussed in the frameworks of Fuzzy CoDoK and SCAD-based fuzzy co-clustering.

Quantification of multivariate categorical data considering clusters of items and individuals

This paper proposes a simultaneous application of homogeneity analysis and fuzzy clustering which simultaneously partitions individuals and items in categorical multivariate data sets. Taking the similarity between the loss of homogeneity in homogeneity analysis and the least squares criterion in principal component analysis into account, the new objective function is defined in a similar formulation to the linear fuzzy clustering.