1 research outputs found
Partial Sum Minimization of Singular Values Representation on Grassmann Manifolds
As a significant subspace clustering method, low rank representation (LRR)
has attracted great attention in recent years. To further improve the
performance of LRR and extend its applications, there are several issues to be
resolved. The nuclear norm in LRR does not sufficiently use the prior knowledge
of the rank which is known in many practical problems. The LRR is designed for
vectorial data from linear spaces, thus not suitable for high dimensional data
with intrinsic non-linear manifold structure. This paper proposes an extended
LRR model for manifold-valued Grassmann data which incorporates prior knowledge
by minimizing partial sum of singular values instead of the nuclear norm,
namely Partial Sum minimization of Singular Values Representation (GPSSVR). The
new model not only enforces the global structure of data in low rank, but also
retains important information by minimizing only smaller singular values. To
further maintain the local structures among Grassmann points, we also integrate
the Laplacian penalty with GPSSVR. An effective algorithm is proposed to solve
the optimization problem based on the GPSSVR model. The proposed model and
algorithms are assessed on some widely used human action video datasets and a
real scenery dataset. The experimental results show that the proposed methods
obviously outperform other state-of-the-art methods.Comment: Submitting to ACM Transactions on Knowledge Discovery from Data with
minor revisio