Maximizing Schatten-p Norm Regularization Toward Balance

Abstract The Schatten-p norm, as a class of structure-inducing norms based on singular values, has been widely used to enhance model low-rankness and representation capability due to its flexibility in structural modeling and favorable mathematical properties. However, its potential in cluster distribution modeling has long been overlooked. Therefore, we explore the potential of maximizing the Schatten-p norm as a regularization strategy specifically designed to achieve balanced clustering. This work is the first to investigate its effectiveness in promoting cluster balance. To be specific, maximizing Schatten-p norm effectively guides the assignment of data points, ensuring a more balanced distribution of samples across clusters. We have conducted an in-depth theoretical analysis and validated its effectiveness through extensive clustering experiments. Experimental results demonstrate that, compared to existing methods, this regularization term significantly improves clustering quality and obtain reasonable clustering.