A Spectral Clustering on Grassmann Manifold via Double Low Rank Constraint

Abstract

Data clustering is a fundamental topic in machine learning and data mining areas. In recent years, researchers have proposed a series of effective methods based on Low Rank Representation (LRR) which could explore low-dimension subspace structure embedded in original data effectively. The traditional LRR methods are usually designed for vectorial data from linear spaces with Euclidean distance. However, high-dimension data (such as video clip or imageset) are always considered as non-linear manifold data such as Grassmann manifold with non-linear metric. In addition, traditional LRR clustering method always adopt single nuclear norm as low rank constraint which would lead to suboptimal solution and decrease the clustering accuracy. In this paper, we proposed a new low rank method on Grassmann manifold for video or imageset data clustering task. In the proposed method, video or imageset data are formulated as sample data on Grassmann manifold first. And then a double low rank constraint is proposed by combining the nuclear norm and bilinear representation to better construct the representation matrix. The experimental results on several public datasets show that the proposed method outperforms the state-of-the-art clustering methods.