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Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…
We introduce a new kind of linear transform named Deformable Butterfly (DeBut) that generalizes the conventional butterfly matrices and can be adapted to various input-output dimensions. It inherits the fine-to-coarse-grained learnable…
In this paper we study the problem of deterministic factorization of sparse polynomials. We show that if $f \in \mathbb{F}[x_{1},x_{2},\ldots ,x_{n}]$ is a polynomial with $s$ monomials, with individual degrees of its variables bounded by…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…
In this paper, we study sparse factorization of the (scaled) square all-ones matrix $J$ of arbitrary order. We introduce the concept of hierarchically banded matrices and propose two types of hierarchically banded factorization of $J$: the…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…
This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the…
In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) model, under mild conditions. Specifically, using the proposed criterion, it…
In this paper we extend the deterministic sublinear FFT algorithm in Plonka et al. (2018) for fast reconstruction of $M$-sparse vectors ${\mathbf x}$ of length $N= 2^J$, where we assume that all components of the discrete Fourier transform…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive…
We study the problem of large-scale network embedding, which aims to learn latent representations for network mining applications. Previous research shows that 1) popular network embedding benchmarks, such as DeepWalk, are in essence…
We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method…
We present a class of fast subspace tracking algorithms based on orthogonal iterations for structured matrices/pencils that can be represented as small rank perturbations of unitary matrices. The algorithms rely upon an updated data sparse…
Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing…