Double Nuclear Norm Based Low Rank Representation on Grassmann Manifolds for Clustering

Unsupervised clustering for high-dimension data (such as imageset or video) is a hard issue in data processing and data mining area since these data always lie on a manifold (such as Grassmann manifold). Inspired of Low Rank representation theory, researchers proposed a series of effective clustering methods for high-dimension data with non-linear metric. However, most of these methods adopt the traditional single nuclear norm as the relaxation of the rank function, which would lead to suboptimal solution deviated from the original one. In this paper, we propose a new low rank model for high-dimension data clustering task on Grassmann manifold based on the Double Nuclear norm which is used to better approximate the rank minimization of matrix. Further, to consider the inner geometry or structure of data space, we integrated the adaptive Laplacian regularization to construct the local relationship of data samples. The proposed models have been assessed on several public datasets for imageset clustering. The experimental results show that the proposed models outperform the state-of-the-art clustering ones.