Constructing a Non-Negative Low Rank and Sparse Graph with Data-Adaptive Features

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data representation. Specifically, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph can capture both the global mixture of subspaces structure (by the low rankness) and the locally linear structure (by the sparseness) of the data, hence is both generative and discriminative. Secondly, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph jointly within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive experiments on three publicly available datasets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semi-supervised classification and discriminative analysis, which verifies the effectiveness of our proposed method

Non-negative low rank and sparse graph for semi-supervised learning

Constructing a good graph to represent data structures is critical for many important machine learning tasks such as clustering and classification. This paper proposes a novel non-negative low-rank and sparse (NNLRS) graph for semi-supervised learning. The weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse ma-trix that represents each data sample as a linear combina-tion of others. The so-obtained NNLRS-graph can capture both the global mixture of subspaces structure (by the low rankness) and the locally linear structure (by the sparse-ness) of the data, hence is both generative and discrimina-tive. We demonstrate the effectiveness of NNLRS-graph in semi-supervised classification and discriminative analysis. Extensive experiments testify to the significant advantages of NNLRS-graph over graphs obtained through convention-al means. 1