Multiple Kernel Subspace Clustering Based on Consensus Hilbert Space and Second-Order Neighbors

Abstract

How to deal with data sets in high-dimensional space is the focus of image processing. At present, subspace clustering method is one of the most commonly used methods for processing high-dimensional data sets. Traditional subspace clustering assumes that the data comes from different linear subspaces, and the different subspace regions do not overlap. However, the real data often does not satisfy these two constraints, which affects the effect of subspace clustering. In order to deal with these two problems, we first introduce the consensus Hilbert space to solve the nonlinear problem of subspace data, that is, a method that can learn the best consensus Hilbert space from a given set of kernel space; The second-order neighbors of the subspace coefficient matrix are used to deal with overlapping subspace problems. The second-order neighbors can effectively optimize the sparseness and connectivity of the self-representation. Subsequently, in order to effectively handle the above complex iterative optimization steps, an alternating direction multiplier method was developed. Finally, the designed multiple kernel subspace clustering algorithm is tested on a total of sixteen real data sets of four types, including face, handwritten, UCI and biomedical data sets. It can be seen from the experimental results that our proposed method has improved clustering accuracy, normalized mutual information and adjusted rand index compared to the latest algorithms.

Keywords

• Alternating direction method of multipliers
• consensus Hilbert space
• multiple kernel learning
• subspace clustering
• second-order neighbors