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Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…

Rational-function simplification is key bottlenecks in integration-by-parts (IBP) reduction of Feynman integrals. We study denominator factorization patterns appearing in IBP coefficients and develop practical algorithms for extracting and…

We construct cubature methods on scattered data via resampling on the support of known algebraic cubature formulas, by different kinds of adaptive interpolation (polynomial, RBF, PUM). This approach gives a promising alternative to other…

The factorization of skew-symmetric matrices is a critically understudied area of dense linear algebra, particularly in comparison to that of general and symmetric matrices. While some algorithms can be adapted from the symmetric case, the…

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major…

Referring back to the original text in the course of hierarchical learning is a common human trait that ensures the right direction of learning. The models developed based on the concept of Non-negative Matrix Factorization (NMF), in this…

Traditional NMF-based signal decomposition relies on the factorization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn…

A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced…

We consider the problem of interpolating a sparse multivariate polynomial over a finite field, represented with a black box. Building on the algorithm of Ben-Or and Tiwari for interpolating polynomials over rings with characteristic zero,…

Non-negative matrix factorization (NMF) is widely used as a feature extraction technique for matrices with non-negative entries, such as image data, purchase histories, and other types of count data. In NMF, a non-negative matrix is…

Most communications systems tend to achieve bandwidth, power and cost efficiencies to capable to describe modulation scheme. Hence for signal modulation, orthogonal frequency division multiplexing (OFDM) transceiver is introduced to cover…

Accurate and fast treatment of electron-electron interactions remains a central challenge in electronic structure theory because post-Hartree-Fock methods often suffered from the computational cost for 4-index electron repulsion integrals…

In this paper, a novel decomposition method for non-stationary and nonlinear signals is proposed. This method is inspired by the adaptive wavelet filter bank of the empirical wavelet transform (EWT) and Fourier intrinsic band functions…

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…

In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian $(-\Delta)^\frac{\alpha}{2}$ for $\alpha \in (0, 2)$. The main advantage of our method is to easily increase numerical…

Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…

In this paper, we propose a new low-rank matrix factorization model dubbed bounded simplex-structured matrix factorization (BSSMF). Given an input matrix $X$ and a factorization rank $r$, BSSMF looks for a matrix $W$ with $r$ columns and a…

Bayesian Matrix Factorization (BMF) is a powerful technique for recommender systems because it produces good results and is relatively robust against overfitting. Yet BMF is more computationally intensive and thus more challenging to…

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…