Localized LRR on Grassmann Manifold: An Extrinsic View

Abstract

Subspace data representation has recently become a common practice in many computer vision tasks. Low-rank representation (LRR) is one of the most successful models for clustering vectorial data according to their subspace structures. This paper explores the possibility of extending LRR for subspace data on Grassmann manifold. Rather than directly embedding the Grassmann manifold into the symmetric matrix space, an extrinsic view is taken to build the self-representation in the local area of the tangent space at each Grassmannian point, resulting in a localized LRR method on Grassmann manifold. A novel algorithm for solving the proposed model is investigated and implemented. The performance of the new clustering algorithm is assessed through experiments on several real-world data sets including MNIST handwritten digits, ballet video clips, SKIG action clips, and DynTex++ data set and highway traffic video clips. The experimental results show that the new method outperforms a number of state-of-the-art clustering methods.