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.

A Survey of Sparse Representation: Algorithms and Applications

“…Zhang et al [198] proposed a discriminative tensor sparse coding (RTSC) method for robust image classification. Recently, low-rank based sparse representation became a popular topic such as non-negative low-rank and sparse graph [199]. Some sparse representation methods in face recognition can be found in a review [83] and other more image classification methods can be found in a more recent review [200].…”

Low-rank double dictionary learning from corrupted data for robust image classification

“…Same as [40], [41], [42], the image samples used in this paper are normalized to unit length (i.e., the ℓ2-norm of each image vector equals to one). As the accuracy of our method is not sensitive to and , we fix = 0.1, = 1 for all the experiments in this paper.…”

“…Similar to [39], [40], [41], [52], the proposed objective function (5) of LRD 2 L is nonconvex to the unknown variables. Since the proposed LRD 2 L algorithm can only converge to a local minimum, the initialization of each dictionary is important for achieving a desirable solution.…”

Semi-Supervised Sparse Representation Based Classification for Face Recognition With Insufficient Labeled Samples

“…He et al [28] proposed a nonnegative sparse algorithm to derive the graph weights for graph-based SSL. Besides the sparsity property, Zhuang et al [29], [30] also imposed low-rank constraints to estimate the weight matrix of the pairwise relationship graph for SSL. The main difference between them and our proposed method S 3 RC is that the previous works used sparse/low-rank technologies to learn the weight matrix for graph-based SSL, which are essentially SSL methods.…”