Granular prototyping in fuzzy clustering

2007 IEEE International Fuzzy Systems Conference, 2007

In contrast to standard fuzzy clustering, which optimizes a set of prototypes, one for each cluster, this paper studies fuzzy clustering without prototypes. Starting from an objective function that only involves the distances between data points and the membership degrees of the data points to the different clusters, an iterative update rule is derived. The properties of the resulting algorithm are then examined, especially w.r.t. to schemes that focus on a constrained neighborhood for each data point. Corresponding experimental results are reported that demonstrate the merits of this approach.

Prototype Reasoning using granular objects is an important technology for knowledge discovery. Fuzzy clustering can be used to generate prototypes with different granularities. In order to find optimal granular prototypes through fuzzy clustering, for given data, two conditions are necessary: a good cluster validity function, which can be applied to evaluate the goodness of cluster schemes for varying number of clusters (different granularity); a good cluster algorithm that can produce an optimal solution for a fixed number of clusters. To satisfy the first condition, a new validity measure called granularity-dissimilarity (GD) measure is proposed, which is stable in evaluating granularities and works well even when the number of clusters is very large. For the second condition, we propose a new algorithm called multi-step maxmin and merging algorithm (3M algorithm). Experiments show that, when used in conjunction with the new cluster validity measure, 3M algorithm produces better results on the experimental data sets than several alternatives.

While in standard fuzzy clustering one optimizes a set of prototypes, one for each cluster, we study fuzzy clustering without prototypes. We define an objective function, which only depends on the distances between data points and the membership degrees of the data points to the clusters, and derive an iterative membership update rule. The properties of the resulting algorithm are then examined, especially w.r.t. to an additional parameter of the objective function (compared to the one proposed in [7]) that can be seen as a more flexible alternative to the fuzzifier. Corresponding experimental results are reported that demonstrate the merits of our approach.

IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 1999

IEEE Transactions on Systems, Man, and Cybernetics, 1999

Clustering algorithms aim at modeling fuzzy (i.e., ambiguous) unlabeled patterns efficiently. Our goal is to propose a theoretical framework where the expressive power of clustering systems can be compared on the basis of a meaningful set of common functional features. Part I of this paper reviews the following issues related to clustering approaches found in the literature: relative (probabilistic) and absolute (possibilistic) fuzzy membership functions and their relationships to the Bayes rule, batch and on-line learning, prototype editing schemes, growing and pruning networks, modular network architectures, topologically perfect mapping, ecological nets and neuro-fuzziness. From this discussion an equivalence between the concepts of fuzzy clustering and soft competitive learning in clustering algorithms is proposed as a unifying framework in the comparison of clustering systems. Moreover, a set of functional attributes is selected for use as dictionary entries in the comparison of clustering algorithms, which is the subject of Part II of this paper [1].

International Journal of Computer Applications, 2014

Fuzzy logic is an organized and mathematical method of handling inherently imprecise concepts through the use of membership functions, which allows membership with a certain degree. It has found application in numerous problem domains. It has been used in the interval [0, 1] fuzzy clustering, in pattern recognition and in other domains. In this paper, we introduce fuzzy logic, fuzzy clustering and an application and benefits. A case analysis has been done for various clustering algorithms in Fuzzy Clustering. It has been proved that some of the defined and available algorithms have difficulties at the borders in handling the challenges posed in collection of natural data. An analysis of two fuzzy clustering algorithms namely fuzzy c-means and Gustafson-Kessel fuzzy clustering algorithm has been analyzed.

Studies in Fuzziness and Soft Computing, 2006

2012

Abstract Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure.

International journal of performability engineering, 2006

Performance testing of an algorithm is necessary to ascertain its applicability in real data and to evolve software. Clustering of a data set could be either fuzzy (having vague boundaries among the clusters) or crisp (having welldefined fixed boundaries) in nature. The present work is focused on the performance measure of some similarity-based fuzzy clustering algorithms, where three methods and each method having three different approaches are developed. In the first method, cluster centers are decided based on the minimum of entropy (probability) values of different data points [10]. In the second method, cluster centers are selected based on the maximum of total similarity values of data points and in the third method, a ratio of dissimilarity to similarity is considered to determine the cluster centers. Performances of these methods and approaches are compared on three standard data sets, such as IRIS, WINES, and OLITOS. Experimental results show that entropy-based method is able to generate better quality clusters but at the cost of little more computations. Finally, the best sets of clusters are mapped to 2-D using a self-organizing map (SOM) for visualization.

Data Science, 2017

Usually, the aim of cluster analysis is to build prototypes, i.e., typologies of units that present similar characteristics. In this paper, an alternative approach based on consensus clustering between two different clustering methods is proposed to obtain homogeneous prototypes. The clustering methods used are fuzzy c-means (that minimizes the objective function with respect to centers of the groups) and archetypal analysis (that minimizes the objective function with respect to extremes of the groups). The consensus clustering is used to assess the correspondence between the clustering solutions obtained and to find the prototypes as a compromise between the two clustering methods.