Kernel Clustering on Symmetric Positive Definite Manifolds via Double Approximated Low Rank Representation

As an effective descriptor, Symmetric Positive Definite (SPD) matrix is widely used in several areas such as image clustering. Recently, researchers proposed some effective methods based on low rank theory for SPD data clustering with nonlinear metric. However, single nuclear norm is always adopted to formulate the low rank model in these methods, which would lead to suboptimal solution. In this paper, we proposed a novel double low rank representation method for SPD clustering problem, in which matrix factorization and non-convex rank constraint are combined to reveal the intrinsic property of the data instead of employing the nuclear norm. Meanwhile, kernel method and Log-Euclidean metric are combined to better explore the intrinsic geometry within SPD data. The proposed method has been evaluated on several public datasets and the experimental results demonstrate that the proposed method outperforms the state-of-the-art ones.