Related papers: Matrix taxonomy and Bourn localization
Machine learning algorithms play an important role in a variety of important decision-making processes, including targeted advertisement displays, home loan approvals, and criminal behavior predictions. Given the far-reaching impact of…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…
Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds…
Multiplication of a sparse matrix with another (dense or sparse) matrix is a fundamental operation that captures the computational patterns of many data science applications, including but not limited to graph algorithms, sparsely connected…
Given labeled data represented by a binary matrix, we consider the task to derive a Boolean matrix factorization which identifies commonalities and specifications among the classes. While existing works focus on rank-one factorizations…
In this paper, we propose an online algorithm to compute matrix factorizations. Proposed algorithm updates the dictionary matrix and associated coefficients using a single observation at each time. The algorithm performs low-rank updates to…
The goal of Boolean Matrix Factorization (BMF) is to approximate a given binary matrix as the product of two low-rank binary factor matrices, where the product of the factor matrices is computed under the Boolean algebra. While the problem…
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary $R$-matrix and to a simple object in a unitary braided fusion category. Unitary $R$-matrices, namely unitary solutions to the…
Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an…
The matrix product representation provides a useful formalism to study not only entangled states, but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
Matrix seriation, the problem of permuting the rows and columns of a matrix to uncover latent structure, is a fundamental technique in data science, particularly in the visualization and analysis of relational data. Applications span…
Complexity is an interdisciplinary concept which, first of all, addresses the question of how order emerges out of randomness. For many reasons matrices provide a very practical and powerful tool in approaching and quantifying the related…
An approach to the classification problem of machine learning, based on building local classification rules, is developed. The local rules are considered as projections of the global classification rules to the event we want to classify. A…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
Often multiple instances of an object occur in the same scene, for example in a warehouse. Unsupervised multi-instance object discovery algorithms are able to detect and identify such objects. We use such an algorithm to provide object…
Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…