相关论文: Multiobjective decomposition of integer matrices: …

Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying…

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…

This paper studies the problem of decomposing a low-rank positive-semidefinite matrix into symmetric factors with binary entries, either $\{\pm 1\}$ or $\{0,1\}$. This research answers fundamental questions about the existence and…

We present two new algorithms for the computation of the q-integer linear decomposition of a multivariate polynomial. Such a decomposition is essential for the treatment of q-hypergeometric symbolic summation via creative telescoping and…

The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…

This paper proposes a novel framework of resource allocation in multi-cell intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) networks, where an IRS is deployed to enhance the wireless service. The problem of…

We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the…

We present a motivating example for matrix multiplication based on factoring a data matrix. Traditionally, matrix multiplication is motivated by applications in physics: composing rigid transformations, scaling, sheering, etc. We present an…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…

This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…

Processing sentence constituency trees in binarised form is a common and popular approach in literature. However, constituency trees are non-binary by nature. The binarisation procedure changes deeply the structure, furthering constituents…

The seriation problem seeks to reorder a set of elements given pairwise similarity information, so that elements with higher similarity are closer in the resulting sequence. When a global ordering consistent with the similarity information…

Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components each with its own property. Usually each component is described by its own subspace or dictionary.…

We present an iterative algorithm, called the symmetric tensor eigen-rank-one iterative decomposition (STEROID), for decomposing a symmetric tensor into a real linear combination of symmetric rank-1 unit-norm outer factors using only…

Unlike matrix completion, tensor completion does not have an algorithm that is known to achieve the information-theoretic sample complexity rate. This paper develops a new algorithm for the special case of completion for nonnegative…

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…

We propose a novel approach to iterated sparse matrix dense matrix multiplication, a fundamental computational kernel in scientific computing and graph neural network training. In cases where matrix sizes exceed the memory of a single…

Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…