Non-negative matrix factorization (NMF) is a fundamental theory that has received much attention and widely used in image engineering, pattern recognition other fields. However, the classical NMF limitations such as only focusing on local information, sensitivity to noise small sample size (SSS) problems. Therefore, how develop improve performance robustness of algorithm worthy challenge. Based...

In this paper, based on low-rank representation and eigenface extraction, we present an improvement to the well known Sparse Representation based Classification (SRC). Firstly, the low-rank images of the face images of each individual in training subset are extracted by the Robust Principal Component Analysis (Robust PCA) to alleviate the influence of noises (e.g., illumination difference and o...

(a) (b) (c) Figure: (a) In a simple blocked low rank approximation the diagonal blocks are dense (gray), whereas the off-diagonal blocks are low rank. (b) In an HODLR matrix the low rank off-diagonal blocks form a hierarchical structure leading to a much more compact representation. (c) H2 matrices are a refinement of this idea. (a) In simple blocked low rank approximation the diagonal blocks a...

Low Rank Representation (LRR) intends to find the representation with lowest-rank of a given data set, which can be formulated as a rank minimization problem. Since the rank operator is non-convex and discontinuous, most of the recent works use the nuclear norm as a convex relaxation. This letter theoretically shows that under some conditions, Frobenius-norm-based optimization problem has an un...

In this paper, we propose three new tensor decompositions for even-order tensors corresponding respectively to the rank-one decompositions of some unfolded matrices. Consequently such new decompositions lead to three new notions of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly symmetric M-rank in this paper. We discuss the bounds between these new te...

Environmental perception and information processing are two key steps of active safety for vehicle reversing. Single-sensor environmental perception cannot meet the need for vehicle reversing safety due to its low reliability. In this paper, we present a novel multi-sensor environmental perception method using low-rank representation and a particle filter for vehicle reversing safety. The propo...

We will determine the structure of the modular standard modules of association schemes of class two. In the process, we will give the theoretical interpretation for the p-rank theory for strongly regular graphs, and understand the p-rank as the dimension of a submodule of the modular standard module. Considering the modular standard module, we can obtain the detailed classification more than th...

Graph-based semi-supervised classification uses a graph to capture the relationship between samples and exploits label propagation techniques on the graph to predict the labels of unlabeled samples. However, it is difficult to construct a graph that faithfully describes the relationship between high-dimensional samples. Recently, low-rank representation has been introduced to construct a graph,...