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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…
Continuous symmetries are fundamental to many scientific and learning problems, yet they are often unknown a priori. Existing symmetry discovery approaches typically search directly in the space of transformation generators or rely on…
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear…
We study the relation between the boxed skew plane partition and the integrable phase model. We introduce a generalization of a scalar product of the phase model and calculate it in two ways; the first one in terms of the skew Schur…
A novel method for the extraction of form factors of unstable particles on the lattice is proposed. The approach is based on the study of two-particle scattering in a static, spatially periodic external field by using a generalization of…
Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking by special graphs. Signless formulas…
The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in…
Stacking polarized radio emission in SKA surveys provides statistical information on large samples that is not accessible otherwise due to limitations in sensitivity, source statistics in small fields, and averaging over frequency…
Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization…
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…
In this paper, we consider an arbitrary matrix-valued, rational spectral density $\Phi(z)$. We show with a constructive proof that $\Phi(z)$ admits a factorization of the form $\Phi(z)=W^\top (z^{-1})W(z)$, where $W(z)$ is stochastically…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…
Recently, convex formulations of low-rank matrix factorization problems have received considerable attention in machine learning. However, such formulations often require solving for a matrix of the size of the data matrix, making it…
Factor analysis is a statistical technique employed to evaluate how observed variables correlate through common factors and unique variables. While it is often used to analyze price movement in the unstable stock market, it does not always…
Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…
Let G be a piecewise constant $n\times n$ matrix function which is defined on a smooth closed curve $\Gamma$ in the complex sphere and which has m jumps. We consider the problem of determining the partial indices of the factorization of the…
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive…