Related papers: Accelerated structured matrix factorization

Nonnegative matrix factorization (NMF) is a popular method used to reduce dimensionality in data sets whose elements are nonnegative. It does so by decomposing the data set of interest, $\mathbf{X}$, into two lower rank nonnegative matrices…

We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…

Factor models are widely used for dimension reduction. Bayesian approaches to these models often place a prior on the factor loadings that allows for infinitely many factors, with loadings increasingly shrunk toward zero as the column index…

Sparse matrix reordering can significantly reduce the fill-in during matrix factorization, thereby decreasing the computational and storage requirements in sparse matrix computations. Finding a minimal fill-in ordering is known to be an…

Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor…

Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…

Factor analysis models explain dependence among observed variables by a smaller number of unobserved factors. A main challenge in confirmatory factor analysis is determining whether the factor loading matrix is identifiable from the…

The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…

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…

What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…

Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

Matrix factorization methods - including Factor analysis (FA), and Principal Components Analysis (PCA) - are widely used for inferring and summarizing structure in multivariate data. Many matrix factorization methods exist, corresponding to…

Factorization Machines (FM) are powerful class of models that incorporate higher-order interaction among features to add more expressive power to linear models. They have been used successfully in several real-world tasks such as…

Matrix factorization, one of the most popular methods in machine learning, has recently benefited from introducing non-linearity in prediction tasks using tropical semiring. The non-linearity enables a better fit to extreme values and…

Despite the popularity of factor models with sparse loading matrices, little attention has been given to formally address identifiability of these models beyond standard rotation-based identification such as the positive lower triangular…

Matrix factorization (MF) is a simple collaborative filtering technique that achieves superior recommendation accuracy by decomposing the user-item interaction matrix into user and item latent matrices. Because the model typically learns…

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…

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of…

Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a…