engleski

A new fast fuzzy partitioning algorithm

In this paper, a new fast incremental fuzzy partitioning algorithm able to find either a fuzzy globally optimal partition or a fuzzy locally optimal partition of the set A\subset\R^n close to the global one is proposed. This is the main impact of the paper, which could have an important role in applied research. Since fuzzy k-optimal partitions with k=2, 3, ..., k_{; ; max}; ; clusters are determined successively in the algorithm, it is possible to calculate corresponding validity indices for every obtained partition. The number k_{; ; max}; ; is defined in such a way that the objective function value of optimal partition with k_{; ; max}; ; clusters is relatively very close to the objective function value of optimal partition with (k_{; ; max}; ; -1) clusters. Before clustering, the data are normalized and afterwards several validity indices are applied to partitions of the normalized data. Very simple relationships between used validity indices on normalized and original data are given as well. Hence, the proposed algorithm is able to find optimal partitions with the most appropriate number of clusters. The algorithm is tested on numerous synthetic data sets and several real data sets from the UCI data repository.

Fuzzy clustering; Fuzzy c-means; Fuzzy locally optimal partition; Fuzzy globally optimal partition; DIRECT; Incremental algorithm

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