Sequential Cluster Extraction Research Articles

On a Family of New Sequential Hard Clustering

This paper presents a new algorithm of sequential cluster extraction based on hardc-means and hardc-medoids clustering. Sequential cluster extraction means that the algorithm extracts ‘one cluster at a time.’ A characteristic parameter, called a noise parameter, is used in noise clustering based sequential clustering. We propose a novel sequential clustering method called new sequential clustering, extracts an arbitrary number of objects as one cluster by considering the noise parameter as a variable to be optimized. Experimental results with four data sets confirm the effectiveness of our proposal. These results also show that classification results strongly depend on parameter ν and that our proposal is applicable to the first stage in a two-stage clustering algorithm.

On Sequential Cluster Extraction Based onL1-Regularized Possibilisticc-Means

Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hardc-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types ofL1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.

Sequential Cluster Extraction Using Power-Regularized Possibilistic c-Means

The present study proposes an algorithm for sequential cluster extraction using power-regularized possibilistic c-means (pPCM). First, pPCM is derived in a similar manner to two types of entropy-regularized possibilistic c-means (ePCM) derivations, where a power function is utilized instead of the negative entropy in ePCM. The cluster fusion with pPCM is identical to the mean-shift with a generalized Epanichnikov kernel, whereas the proposed method employs sequential cluster extraction with pPCM. Numerical examples show that the cluster number produced by the proposed algorithm did not match with the true class number in real datasets, but the extracted clustering results were partially successful in terms of capturing dense regions of objects.

On Cluster Extraction from Relational Data UsingL1-Regularized Possibilistic Assignment Prototype Algorithm

This paper proposes entropy-basedL1-regularized possibilistic clustering and a method of sequential cluster extraction from relational data.Sequential cluster extractionmeans that the algorithm extracts cluster one by one. The assignment prototype algorithmis a typical clustering method for relational data. The membership degree of each object to each cluster is calculated directly from dissimilarities between objects. An entropy-basedL1-regularized possibilistic assignment prototype algorithm is proposed first to induce belongingness for a membership grade. An algorithm of sequential cluster extraction based on the proposed method is constructed and the effectiveness of the proposed methods is shown through numerical examples.

Algorithms for Sequential Extraction of Clusters

Algorithms for Sequential Extraction of Clusters

Algorithms for Sequential Extraction of Clusters by Possibilistic Method and Comparison with Mountain Clustering

In addition to fuzzy c-means, possibilistic clustering is useful because it is robust against noise in data. The generated clusters are, however, strongly dependent on an initial value. We propose a family of algorithms for sequentially generating clusters “one cluster at a time,” which includes possibilistic medoid clustering. These algorithms automatically determine the number of clusters. Due to possibilistic clustering's similarity to the mountain clustering by Yager and Filev, we compare their formulation and performance in numerical examples.

Modeling Decisions for Artificial Intelligence

In August 2007, the 4th International Conference on Modeling Decisions for Artificial Intelligence (MDAI1) was held in Kitakyushu, Japan. This special issue has its origins in the conference. We present nine papers related to soft computing tool applications. The first paper, by Honda and Okazaki, presents an axiomatization of a generalized Shaply value. The second paper, by García-Lapresta, also related to decision-making, introduces a multistage decision procedure in which decision-makers opinions are weighted by their contribution to an agreement. The third paper, by Torra and Miyamoto, concerns the problem of loading a container, outlining a system for loading nonorthogonal objects. The fourth paper, by Sakai, Koba, and Nakata, is devoted to rule generation based on rough sets. The fifth paper by Hiramatsu, Huynh, and Nakamori, deals with a fuzzy-based model applied to weather information. The sixth paper, by Inokuchi and Miyamoto, discuss fuzzy clustering algorithms for discrete data. The seventh paper, by Miyamoto, Kuroda, and Arai, studies an algorithm for the sequential extraction of clusters compared to mountain clustering. In the eighth paper, Miyamoto formulates fuzzy clustering using the calculus of variations. The ningth and final paper treats fuzzy clustering, in which Endo et al. discuss fuzzy c-means for data with tolerance. In closing, we thank the referees for their work on reviews and Prof. Hirota for editing this special issue. We also thank the Fuji Technology Press Ltd. staff for its advice. 1Work partially funded by Spanish MEC (projects ARES – CONSOLIDER INGENIO 2010 CSD2007-00004 – and eAEGIS – TSI2007-65406-C03-02)

Robust Fuzzy Clustering Based on Similarity between Data

We present a robust fuzzy clustering method that utilizes a sequential cluster extraction scheme. In contrast to heuristic sequential methods, our algorithm is derived from an optimization problem and is an iterative solution to it. Our method is non-parametric and includes no heuristic parameter, and can deal with asymmetric similarity data. The determination of the number of clusters is simple and is based on a monotonic property of extracted cluster volumes. Our method can extract arbitrarily shaped clusters by extending the measure of distance between data to a shortest path length. The performance of the method is demonstrated for clustering of an image database and the segmentation of images.