Noise Rejection in MMMs-Induced Fuzzy Co-Clustering

Noise rejection is an important issue in practical application of FCM-type fuzzy clustering, and noise clustering achieves robust estimation of cluster prototypes with an additional noise cluster for dumping noise objects into it. Noise objects having larger distances from all clusters are designed to be assigned to the noise cluster, which is located in an equal (fixed) distance from all objects. Fuzzy co-clustering is an extended version of FCM-type clustering for handling cooccurrence information among objects and items, where the goal of analysis is to extract pair-wise clusters of familiar objects and items. This paper proposes a novel noise rejection model for fuzzy co-clustering induced by multinomial mixture models (MMMs), where a noise cluster is defined with homogeneous item memberships for drawing noise objects having dissimilar cooccurrence features from all general clusters. The noise rejection scheme can be also utilized in selecting the optimal cluster number through a sequential implementation with different cluster numbers.

ESTIMATION OF WEIBULL PARAMETERS USING A FUZZY LEAST-SQUARES METHOD

The purpose of this paper is to find a robust estimation method for a two-parameter Weibull distribution when outliers are present. This is a relevant problem because of the usefulness of the Weibull distribution in life testing and reliability theory. For that purpose, a cluster-wise fuzzy least-squares algorithm with a noise cluster is used. This is because a noise cluster can be used for compensating the effects of outliers. Numerical comparisons between this fuzzy least-squares algorithm and the existing methods are implemented. According to these comparisons, it is suggested that the proposed fuzzy least-squares algorithm is preferable when the sample size is large.

FUZZY C-MEANS AND MIXTURE DISTRIBUTION MODELS IN THE PRESENCE OF NOISE CLUSTERS

This paper discusses the relationship between the K-L information based FCM method and a mixture distribution model with the EM algorithm when a noise cluster is assumed. Equivalence between the two methods in the sense that the derived solutions are the same is proved. From the equivalence a parameter in the fuzzy model can be estimated by using the mixture distribution model. A regularized FCM algorithm with the noise cluster is moreover derived for which the equivalent statistical model with the EM algorithm does not exist.

Fuzzy Clustering for Detecting Linear Structures with Different Dimensions

One recent interest in fuzzy clustering is the simultaneous determination of a fuzzy partition of a given dataset and parameters of assumed models having different shapes that explain partitioned datasets. We propose an objective function to detect linear varieties with different dimensionalities. The noise cluster suggested by Dave is introduced. Since this is not all-purpose method, some techniques are suggested using artificial examples to show how to implement clustering successfully.