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

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…

For a given symmetric tensor, we aim at finding a new one whose symmetric rank is small and that is close to the given one. There exist linear relations among the entries of low rank symmetric tensors. Such linear relations can be expressed…

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…

Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…

We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…

In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…

We revisit a formula that connects the minimal ranks of triangular parts of a matrix and its inverse and relate the result to structured rank matrices. We also address the generic minimal rank problem.

Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen…

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In…

This paper presents a hierarchical low-rank decomposition algorithm assuming any matrix element can be computed in $O(1)$ time. The proposed algorithm computes rank-revealing decompositions of sub-matrices with a blocked adaptive cross…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

A simple but efficient spectral approach for analyzing the community structure of complex networks is introduced. It works the same way for all types of networks, by spectrally splitting the adjacency matrix into a "unipartite" and a…

Given a matrix $M\in \mathbb{R}^{m\times n}$, the low rank matrix completion problem asks us to find a rank-$k$ approximation of $M$ as $UV^\top$ for $U\in \mathbb{R}^{m\times k}$ and $V\in \mathbb{R}^{n\times k}$ by only observing a few…

To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…

The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have…

We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools from matrix theory, (analytic) optimization theory and…

Networks are a useful representation for data on connections between units of interests, but the observed connections are often noisy and/or include missing values. One common approach to network analysis is to treat the network as a…

Matrix completion and approximation are popular tools to capture a user's preferences for recommendation and to approximate missing data. Instead of using low-rank factorization we take a drastically different approach, based on the simple…

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

In the well-known Minimum Linear Arrangement problem (MinLA), the goal is to arrange the nodes of an undirected graph into a permutation so that the total stretch of the edges is minimized. This paper studies an online (learning) variant of…