Hybrid Fuzzy-Crisp Clustering Algorithm: Theory and Experiments
This addresses a specific issue in clustering for data with varying cluster sizes, but it is incremental as it builds on existing fuzzy methods.
The paper tackles the problem of imbalanced cluster influence in fuzzy c-means clustering by proposing a hybrid fuzzy-crisp algorithm that sets membership to zero for distant points, and it outperforms conventional methods on imbalanced datasets while being competitive on balanced ones.
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.