One-Step Clustering with Adaptively Local Kernels and a Neighborhood Kernel

Abstract

Among the methods of multiple kernel clustering (MKC), some adopt a neighborhood kernel as the optimal kernel, and some use local base kernels to generate an optimal kernel. However, these two methods are not synthetically combined together to leverage their advantages, which affects the quality of the optimal kernel. Furthermore, most existing MKC methods require a two-step strategy to cluster, i.e., first learn an indicator matrix, then executive clustering. This does not guarantee the optimality of the final results. To overcome the above drawbacks, a one-step clustering with adaptively local kernels and a neighborhood kernel (OSC-ALK-ONK) is proposed in this paper, where the two methods are combined together to produce an optimal kernel. In particular, the neighborhood kernel improves the expression capability of the optimal kernel and enlarges its search range, and local base kernels avoid the redundancy of base kernels and promote their variety. Accordingly, the quality of the optimal kernel is enhanced. Further, a soft block diagonal (BD) regularizer is utilized to encourage the indicator matrix to be BD. It is helpful to obtain explicit clustering results directly and achieve one-step clustering, then overcome the disadvantage of the two-step strategy. In addition, extensive experiments on eight data sets and comparisons with six clustering methods show that OSC-ALK-ONK is effective.