A Unified Framework for Discrete Multi-kernel k-means with Kernel Diversity Regularization

Multiple kernel clustering seeks to combine several kernels for boosting the clustering performance. However, most existing MKKM methods fail to evaluate kernel correlation adequately, which may inevitably select highly correlated kernels resulting in kernel redundancy. Besides, most existing methods solve the NP-hard cluster labels assignment task in two stages: first learning the relaxed labels with continuous values and then obtaining the discrete labels via other discretization methods like k-means. This two-stage strategy may result in the loss of information owing to the deviation between the genuine solution and the approximated one. In this work, we present a unified framework for Discrete Multi-kernel k-means with Kernel Diversity Regularization (DMK-KDR). It is capable of penalizing highly correlated kernels through a well-designed matrix-induced regularization, thus allowing for improved diversity and reduced redundancy in kernel fusion. Additionally, it learns both discrete and continuous clustering indicator matrices simultaneously, thereby ensuring the integrity of the discrete solution without over-reliance on k-means or the loss of information. The efficacy of our model has been evaluated in a number of experiments using real-world datasets.