Constructing an informative and discriminative graph plays an important role in various pattern recognition tasks such as clustering and classification. Among the existing graph-based learning models, low-rank representation (LRR) is a very competitive one, which has been extensively employed in spectral clustering and semi-supervised learning (SSL). In SSL, the graph is composed of both labele...

An n×n matrix X is called completely positive semidefinite (cpsd) if there exist d×d Hermitian positive semidefinite matrices {Pi}i=1 (for some d ≥ 1) such that Xij = Tr(PiPj), for all i, j ∈ {1, . . . , n}. The cpsd-rank of a cpsd matrix is the smallest d ≥ 1 for which such a representation is possible. In this work we initiate the study of the cpsd-rank which we motivate twofold. First, the c...

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model where we assume instead that the matrix is only locally of low-rank, leading t...

Accurate tumor classification is crucial to the proper treatment of cancer. To now, sparse representation (SR) has shown its great performance for tumor classification. This paper conceives a new SR-based method for tumor classification by using gene expression data. In the proposed method, we firstly use latent low-rank representation for extracting salient features and removing noise from the...

In this paper we introduce a Givens-weight representation for rank structured matrices, where the rank structure is defined by certain low rank submatrices starting from the bottom left matrix corner. This representation will be compared to the (block) quasiseparable representations occurring in the literature. We will then provide some basic algorithms for the Givens-weight representation, in ...

Under today’s big data environment, with the rapid development of computer network technology and information technology, data mining is becoming more and more important in computer science. Classification is one of the most important aspects in data mining research Field. Recently, representation methods, such as sparse representation and low rank representation, have been much concerned. They...

Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems and eigenvalue problems on Hilbert spaces. Although this question is central to the success of all existing solvers based on low-rank tensor techniques, very...

We hypothesize that optimal deep neural networks (DNN) class-conditional posterior probabilities live in a union of lowdimensional subspaces. In real test conditions, DNN posteriors encode uncertainties which can be regarded as a superposition of unstructured sparse noise over the optimal posteriors. We aim to investigate different ways to structure the DNN outputs by exploiting low-rank repres...

Patch-based sparse representation and low-rank approximation for image processing attract much attention in recent years. The minimization of the matrix rank coupled with the Frobenius norm data fidelity can be solved by the hard thresholding filter with principle component analysis (PCA) or singular value decomposition (SVD). Based on this idea, we propose a patch-based low-rank minimization m...

Video segmentation is to partition the video into several semantically consistent spatio-temporal regions. It is a fundamental computer vision problem in many applications, such as object tracking, activity recognition, video analytics, summarization and indexing. However, there exists several remaining issues to be addressed. First, most of video segmentation methods have worse segmentation qu...