Related papers: Binary Matrix Factorization via Dictionary Learnin…
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…
This paper describes a new approach, based on linear programming, for computing nonnegative matrix factorizations (NMFs). The key idea is a data-driven model for the factorization where the most salient features in the data are used to…
Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
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…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
For most problems in science and engineering we can obtain data sets that describe the observed system from various perspectives and record the behavior of its individual components. Heterogeneous data sets can be collectively mined by data…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. Leveraging variational inference (VI) and unitary approximate message passing (UAMP), we develop a Bayesian approach to MF with…
Quantization is widely applied in machine learning to reduce computational and storage costs for both data and models. Considering that classification tasks are fundamental to the field, it is crucial to investigate how quantization impacts…
Many predictive tasks of web applications need to model categorical variables, such as user IDs and demographics like genders and occupations. To apply standard machine learning techniques, these categorical predictors are always converted…
Binary, or one-bit, representations of data arise naturally in many applications, and are appealing in both hardware implementations and algorithm design. In this work, we study the problem of data classification from binary data and…
We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping from a finite dimensional Banach space into another finite dimensional Banach space. We provide transition formulas, and represent them…
The behavior of many Bayesian models used in machine learning critically depends on the choice of prior distributions, controlled by some hyperparameters that are typically selected by Bayesian optimization or cross-validation. This…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
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 continuation to our recent work on noncommutative polynomial factorization, we consider the factorization problem for matrices of polynomials and show the following results. (1) Given as input a full rank $d\times d$ matrix $M$ whose…
Matrix factorization is a fundamental method in statistics and machine learning for inferring and summarizing structure in multivariate data. Modern data sets often come with "side information" of various forms (images, text, graphs) that…