Related papers: Singular value decomposition based matrix surgery

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…

Vanishing and exploding gradients are two of the main obstacles in training deep neural networks, especially in capturing long range dependencies in recurrent neural networks~(RNNs). In this paper, we present an efficient parametrization of…

Singular Value Decomposition (SVD) has recently emerged as a new paradigm for processing different types of images. SVD is an attractive algebraic transform for image processing applications. The paper proposes an experimental survey for…

Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…

In high-dimensional data processing and data analysis related to dual quaternion statistics, generalized singular value decomposition (GSVD) of a dual quaternion matrix pair is an essential numerical linear algebra tool for an elegant…

With the tremendous success of Graph Convolutional Networks (GCNs), they have been widely applied to recommender systems and have shown promising performance. However, most GCN-based methods rigorously stick to a common GCN learning…

Aiming to provide a faster and convenient truncated SVD algorithm for large sparse matrices from real applications (i.e. for computing a few of largest singular values and the corresponding singular vectors), a dynamically shifted power…

Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…

Convergence of a matrix decomposition technique, the multi-field singular value decomposition (MFSVD) which efficiently analyzes nonlinear correlations by simultaneously decomposing multiple fields, is investigated. Toward applications in…

The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the…

Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM Review A. Barnett has provided new bounds on the rate of ill-conditioning of the discrete Fourier submatrices. In this paper we focus on…

We tackle the challenging problem of single-source domain generalization (DG) for medical image segmentation, where we train a network on one domain (e.g., CT) and directly apply it to a different domain (e.g., MR) without adapting the…

We propose a new hypermatrix singular value decomposition based upon the spectral decomposition of the symmetric products of transposes.

Matrix decompositions are ubiquitous in machine learning, including applications in dimensionality reduction, data compression and deep learning algorithms. Typical solutions for matrix decompositions have polynomial complexity which…

Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated singular values occur,…

An enhanced Kogbetliantz method for the singular value decomposition (SVD) of general matrices of order two is proposed. The method consists of three phases: an almost exact prescaling, that can be beneficial to the LAPACK's xLASV2 routine…

Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…

While transfer learning is an effective strategy, it often overlooks the opportunity to leverage knowledge from numerous available models online. Addressing this multi-source transfer learning problem is a promising path to boost…

We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD. Both of our generalisations are motivated by applications,…

The soft SVD is a robust matrix decomposition algorithm and a key component of matrix completion methods. However, computing the soft SVD for large sparse matrices is often impractical using conventional numerical methods for the SVD due to…