Reweighted Non-convex Non-smooth Rank Minimization Based Spectral Clustering on Grassmann Manifold

Abstract

Low Rank Representation (LRR) based unsupervised clustering methods have achieved great success since these methods could explore low-dimensional subspace structure embedded in original data effectively. The conventional LRR methods generally treat the data as the points in Euclidean space. However, it is no longer suitable for high-dimension data (such as video or imageset). That is because high-dimension data are always considered as non-linear manifold data such as Grassmann manifold. Besides, the typical LRR methods always adopt the traditional single nuclear norm based low rank constraint which can not fully reveal the low rank property of the data representation and often leads to suboptimal solution. In this paper, a new LRR based clustering model is constructed on Grassmann manifold for high-dimension data. In the proposed method, each high-dimension data is formed as a sample on Grassmann manifold with non-linear metric. Meanwhile, a non-convex low rank representation is adopt to reveal the intrinsic property of these high-dimension data and reweighted rank minimization constraint is introduced. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.