A deterministic annealing approach to clustering
Pattern Recognition Letters
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Validity-guided (re)clustering with applications to image segmentation
IEEE Transactions on Fuzzy Systems
The possibilistic C-means algorithm: insights and recommendations
IEEE Transactions on Fuzzy Systems
Robust clustering methods: a unified view
IEEE Transactions on Fuzzy Systems
Optimization of clustering criteria by reformulation
IEEE Transactions on Fuzzy Systems
Interpretation of clusters in the framework of shadowed sets
Pattern Recognition Letters
Computational Statistics & Data Analysis
Granular computing with shadowed sets
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
Liver tumor segmentation using kernel-based FGCM and PGCM
MICCAI'11 Proceedings of the Third international conference on Abdominal Imaging: computational and Clinical Applications
Clustering quality evaluation based on fuzzy FCA
DEXA'07 Proceedings of the 18th international conference on Database and Expert Systems Applications
Hi-index | 0.00 |
Fuzzy clustering algorithms have been widely studied and applied in a variety of areas. They become the major techniques in cluster analysis. In this paper, we focus on objective function models whose aim is to assign the data to clusters so that a given objective function is optimized. We propose a new approach in fuzzy clustering and show how it can be used to obtain a systematic method deriving objective functions. This approach is based on a unifying principle of physics, that of extreme physical information (EPI) defined by Frieden (Physics from Fisher Information: A Unification, 1999). The information in question is the trace of the Fisher information matrix for the estimation procedure; this information is shown to be a physical measure of disorder. We use the EPI approach for finding the effective and minimal constraint terms in objective functions. With the proposed approach we justify the constraint terms defined a priori in the Fuzzy c-means (FcM) algorithm and Possibilistic and Maximum Entropy Inference approaches. Indeed, these algorithms, by contrast, offer no such systematic method of finding its constraints. Moreover, in this context, the EPI approach derives the "reason" for the extremization of objective functions. The resulting formulae have a clearer physical meaning than those obtained by means of classical algorithms. The updated equations of our algorithm are identical to those of the possibilistic, MEI and FcM with regularization approaches.