First and Second Order Similarity Learning for Clustering on Grassmann Manifolds

Abstract

It is challenging to cluster multidimensional data (such as image sets or videos) with complex intrinsic relationships and nonlinear manifolds structure. Inspired by the self-expression models for clustering in the linear space, researchers proposed several effective clustering methods in Grassmann manifolds space. However, these methods in the manifolds space obtain the affinity matrix by the self-expression coefficient, which may fail to fully consider the local structural relationships of data points on Grassmann manifolds. To address these issues, a first and second order similarity learning model for clustering on Grassmann manifolds (GFSOSL) is proposed. To consider the local structural relationships of data points and their neighborhood structural relationships, we learn the first order similarity (FOS) and second order similarity (SOS) simultaneously. Further, to constrain the rank of affinity matrix properly, the nuclear norm and Frobenius norm simultaneous constraint is proposed. The experiments have been constructed on some common image datasets and video datasets and the results demonstrate that the performance of our proposed algorithm outperforms the state-of-the-art baselines.