Related papers: Matrix taxonomy and Bourn localization

Recent advancements in machine learning and deep learning have brought algorithmic fairness into sharp focus, illuminating concerns over discriminatory decision making that negatively impacts certain individuals or groups. These concerns…

The paper deals with a new sharp criterion ensuring the Aubin property of solution maps to a class of parameterized variational systems. This class includes parameter-dependent variational inequalities with non-polyhedral constraint sets…

We develop a fixed-point iterative algorithm that computes the matrix projection with respect to the Bures distance on the set of positive definite matrices that are invariant under some symmetry. We prove that the fixed-point iteration…

A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…

Matrix factorization (MF) has become a common approach to collaborative filtering, due to ease of implementation and scalability to large data sets. Two existing drawbacks of the basic model is that it does not incorporate side information…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

It is shown that, in certain circumstances, systems of cultural rules may be represented by doubly stochastic matrices denoted called possibility transforms, and by certain real valued possibility densities with inner product. Using such…

We summarize some aspects of matrix models from the approaches directly based on their properties at finite N.

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…

Covariance matrices of amino acid displacements, commonly used to characterize the large-scale movements of proteins, are investigated through the prism of Random Matrix Theory. Bulk universality is detected in the local spacing statistics…

Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of unfolding a tensor into matrices, commonly known as tensor…

Recommender system is currently widely used in many e-commerce systems, such as Amazon, eBay, and so on. It aims to help users to find items which they may be interested in. In literature, neighborhood-based collaborative filtering and…

We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.

As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates…

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and…

Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…

The area related to M. Liv\v{s}ic's characteristic matrix functions is too vast to be discussed in one paper and we selected for this article the problems which are close to our scientific interests. We discuss M.Liv\v{s}ic's results…

Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…

Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…

Matrix factorization is a key component of collaborative filtering-based recommendation systems because it allows us to complete sparse user-by-item ratings matrices under a low-rank assumption that encodes the belief that similar users…