A Centroid Auto-Fused Hierarchical Fuzzy c-Means Clustering

Abstract: Like k-means and Gaussian Mixture Model (GMM), fuzzy c-means (FCM) with soft partition has also become a popular clustering algorithm and still is extensively studied. However, these algorithms and their variants still suffer from some difficulties such as determination of the optimal number of clusters which is a key factor for clustering quality. A common approach for overcoming this difficulty is to use the trial-and-validation strategy, i.e., traversing every integer from large number like $\sqrt{n}$ to 2 until finding the optimal number corresponding to the peak value of some cluster validity index. But it is scarcely possible to naturally construct an adaptively agglomerative hierarchical cluster structure as using the trial-and-validation strategy. Even possible, existing different validity indices also lead to different number of clusters. To effectively mitigate the problems while motivated by convex clustering, in this paper we present a Centroid Auto-Fused Hierarchical Fuzzy c-means method (CAF-HFCM) whose optimization procedure can automatically agglomerate to form a cluster hierarchy, more importantly, yielding an optimal number of clusters without resorting to any validity index. Although a recently-proposed robust-learning fuzzy c-means (RL-FCM) can also automatically obtain the best number of clusters without the help of any validity index, so-involved 3 hyper-parameters need to adjust expensively, conversely, our CAF-HFCM involves just 1 hyper-parameter which makes the corresponding adjustment is relatively easier and more operational. Further, as an additional benefit from our optimization objective, the CAF-HFCM effectively reduces the sensitivity to the initialization of clustering performance. Moreover, our proposed CAF-HFCM method is able to be straightforwardly extended to various variants of FCM.