Related papers: Butterfly factorization with error guarantees
Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
Bayesian matrix factorization (BMF) is a powerful tool for producing low-rank representations of matrices and for predicting missing values and providing confidence intervals. Scaling up the posterior inference for massive-scale matrices is…
In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…
The development of randomized algorithms for numerical linear algebra, e.g. for computing approximate QR and SVD factorizations, has recently become an intense area of research. This paper studies one of the most frequently discussed…
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…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…
Sparse coding is a core building block in many data analysis and machine learning pipelines. Typically it is solved by relying on generic optimization techniques, that are optimal in the class of first-order methods for non-smooth, convex…
Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Ensuring fairness in machine learning algorithms is a challenging and essential task. We consider the problem of clustering a set of points while satisfying fairness constraints. While there have been several attempts to capture group…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths…
We study the following problem: Given a variable of interest, we would like to find a best linear predictor for it by choosing a subset of $k$ relevant variables obeying a matroid constraint. This problem is a natural generalization of…
Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…