title: Constructing a Nonnegative Low-Rank and Sparse Graph With Data-Adaptive Features.
abstract: This paper aims at constructing a good graph to discover the intrinsic data structures under a semisupervised learning setting. First, we propose to build a nonnegative low-rank and sparse (referred to as NNLRS) graph for the given data representation. In particular, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse reconstruction coefficients matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph captures both the global mixture of subspaces structure (by the low-rankness) and the locally linear structure (by the sparseness) of the data, hence it is both generative and discriminative. Second, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph simultaneously within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive NNLRS experiments on three publicly available data sets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semisupervised classification and discriminative analysis, which verifies the effectiveness of our proposed method.
authors.forename: Liansheng
authors.initials: L
authors.lastname: Zhuang
authors.forename: Shenghua
authors.initials: S
authors.lastname: Gao
authors.forename: Jinhui
authors.initials: J
authors.lastname: Tang
authors.forename: Jingjing
authors.initials: J
authors.lastname: Wang
authors.forename: Zhouchen
authors.initials: Z
authors.lastname: Lin
authors.forename: Yi
authors.initials: Y
authors.lastname: Ma
authors.forename: Nenghai
authors.initials: N
authors.lastname: Yu