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Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…

We present a necessary and sufficient condition for a 3 by 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3 by 3 matrix can be tested. This test generalizes to a…

Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…

Completing a data matrix X has become an ubiquitous problem in modern data science, with applications in recommender systems, computer vision, and networks inference, to name a few. One typical assumption is that X is low-rank. A more…

We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…

One may identify the general properties of the neutrino mass matrix by generating many random mass matrices and testing them against the results of the neutrino experiments.

Combining multiple machine learning models has long been a technique for enhancing performance, particularly in distributed settings. Traditional approaches, such as model ensembles, work well, but are expensive in terms of memory and…

Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…

Revealing the functional sites of biological sequences, such as evolutionary conserved, structurally interacting or co-evolving protein sites, is a fundamental, and yet challenging task. Different frameworks and models were developed to…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

In this work, we prove that any symplectic matrix can be factored into no more than 9 unit triangular symplectic matrices. This structure-preserving factorization of the symplectic matrices immediately reveals two well-known features that,…

Formal methods apply algorithms based on mathematical principles to enhance the reliability of systems. It would only be natural to try to progress from verification, model checking or testing a system against its formal specification into…

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…

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…