Hybrid Fuzzy-Crisp Clustering Algorithm: Theory and Experiments

TL;DR

This paper introduces a hybrid fuzzy-crisp clustering algorithm that effectively handles imbalanced datasets by combining fuzzy and crisp clustering principles, demonstrating superior performance on real-world and simulated data.

Contribution

The paper proposes a novel hybrid fuzzy-crisp clustering algorithm with a new target function, improving clustering accuracy on imbalanced datasets.

Findings

Outperforms conventional fuzzy and crisp clustering methods on imbalanced datasets

Demonstrates competitive results on balanced datasets

Provides geometric interpretation of the hybrid clustering approach

Abstract

With the membership function being strictly positive, the conventional fuzzy c-means clustering method sometimes causes imbalanced influence when clusters of vastly different sizes exist. That is, an outstandingly large cluster drags to its center all the other clusters, however far they are separated. To solve this problem, we propose a hybrid fuzzy-crisp clustering algorithm based on a target function combining linear and quadratic terms of the membership function. In this algorithm, the membership of a data point to a cluster is automatically set to exactly zero if the data point is ``sufficiently'' far from the cluster center. In this paper, we present a new algorithm for hybrid fuzzy-crisp clustering along with its geometric interpretation. The algorithm is tested on twenty simulated data generated and five real-world datasets from the UCI repository and compared with conventional fuzzy and crisp clustering methods. The proposed algorithm is demonstrated to outperform the conventional methods on imbalanced datasets and can be competitive on more balanced datasets.