Centroid-based clustering algorithms, such as hard K-means (HKM) and fuzzy K-means (FKM), have suffered from learning bias towards large clusters. Their centroids tend to be crowded in large clusters, compromising performance when the true underlying data groups vary in size (i.e., imbalanced data). To address this, we propose a new clustering objective function based on the Boltzmann operator, which introduces a novel centroid repulsion mechanism, where data points surrounding the centroids repel other centroids. Larger clusters repel more, effectively mitigating the issue of large cluster learning bias. The proposed new algorithm, called equilibrium K-means (EKM), is simple, alternating between two steps; resource-saving, with the same time and space complexity as FKM; and scalable to large datasets via batch learning. We substantially evaluate the performance of EKM on synthetic and real-world datasets. The results show that EKM performs competitively on balanced data and significantly outperforms benchmark algorithms on imbalanced data. Deep clustering experiments demonstrate that EKM is a better alternative to HKM and FKM on imbalanced data as more discriminative representation can be obtained. Additionally, we reformulate HKM, FKM, and EKM in a general form of gradient descent and demonstrate how this general form facilitates a uniform study of K-means algorithms.

翻译：暂无翻译