相关论文: Low Rank Pure Quaternion Approximation for Pure Qu…

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks, but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR…

Regression analysis-based approaches have been widely studied for face recognition (FR) in the past several years. More recently, to better deal with some difficult conditions such as occlusions and illumination, nuclear norm based matrix…

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function…

Low rank tensor ring model is powerful for image completion which recovers missing entries in data acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization…

One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current…

Matrix completion is a modern missing data problem where both the missing structure and the underlying parameter are high dimensional. Although missing structure is a key component to any missing data problems, existing matrix completion…

Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…

We study the problem of learning a partially observed matrix under the low rank assumption in the presence of fully observed side information that depends linearly on the true underlying matrix. This problem consists of an important…

The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…

The low-rank matrix approximation problems within a threshold are widely applied in information retrieval, image processing, background estimation of the video sequence problems and so on. This paper presents an adaptive randomized…

Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. This…

Low-rank approximation with zeros aims to find a matrix of fixed rank and with a fixed zero pattern that minimizes the Euclidean distance to a given data matrix. We study the critical points of this optimization problem using algebraic…

In this work, we address the challenging problem of blind deconvolution for color images. Existing methods often convert color images to grayscale or process each color channel separately, which overlooking the relationships between color…

In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…

Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation…

In this paper a quaternion approach of enhancement method is proposed in which color in the image is considered as a single entity. This new method is referred as the alpha-rooting method of color image enhancement by the two-dimensional…

This paper discusses the left and right ranks of quaternion matrices with Hankel structure. While they are in general different for arbitrary quaternion matrices, we show that the left and right ranks of quaternion Hankel matrices are…

The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…

Matrix completion is a problem that arises in many data-analysis settings where the input consists of a partially-observed matrix (e.g., recommender systems, traffic matrix analysis etc.). Classical approaches to matrix completion assume…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…