A general soft-balanced clustering framework based on a novel balance regularizer

In the past few decades, clustering algorithms have been extensively explored. Conventional clustering methods such as k-means and spectral clustering have achieved excellent clustering performance, however they pay less attention on the balanced distribution of many real-world data, which is significant to some practical applications. In this paper, we present a soft-balanced clustering framework, and the degree of balance can be flexibly adjusted by setting the parameter. The core of the framework is a novel regularizer, by optimizing which the clustering becomes more balanced. The framework can be combined with many clustering methods in a concise way. Taking k-means as an example, we extend k-means to a Balanced k-means with a Novel Constraint (BKNC) model with the help of this framework. Then an alternative iterative optimization algorithm is proposed to solve it. Comprehensive experiments on several benchmark datasets demonstrate the superior balance and clustering performance of the BKNC method than other k-means based hard- and soft-balanced methods.