Related papers: Min-plus algebraic low rank matrix approximation: …

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

This paper proposes a novel approach to pattern classification using a probabilistic neural network model. The strategy is based on a compact-sized probabilistic neural network capable of continuous incremental learning and unlearning…

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they…

Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Low rank approximation of a matrix (LRA) is a highly important area of Numerical Linear and Multilinear Algebra and Data Mining and Analysis. One can operate with an LRA superfast -- by using much fewer memory cells and flops than an input…

Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…

We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as…

A multimodal network encodes relationships between the same set of nodes in multiple settings, and network alignment is a powerful tool for transferring information and insight between a pair of networks. We propose a method for multimodal…

The rank of neural networks measures information flowing across layers. It is an instance of a key structural condition that applies across broad domains of machine learning. In particular, the assumption of low-rank feature representations…

Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal…

Subspace inference for neural networks assumes that a subspace of their parameter space suffices to produce a reliable uncertainty quantification. In this work, we underpin the validity of this assumption by using low rank techniques. We…

We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a…

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…

Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…