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Matrix factorization (MF) is a classical collaborative filtering algorithm for recommender systems. It decomposes the user-item interaction matrix into a product of low-dimensional user representation matrix and item representation matrix.…

Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…

A key goal of computational personalized medicine is to systematically utilize genomic and other molecular features of samples to predict drug responses for a previously unseen sample. Such predictions are valuable for developing hypotheses…

Recommendation from implicit feedback is a highly challenging task due to the lack of the reliable observed negative data. A popular and effective approach for implicit recommendation is to treat unobserved data as negative but downweight…

Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…

In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions,…

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…

The relationships between objects in a network are typically diverse and complex, leading to the heterogeneous edges with different semantic information. In this paper, we focus on exploring the heterogeneous edges for network…

Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…

Nonnegative matrix factorization (NMF) has become a workhorse for signal and data analytics, triggered by its model parsimony and interpretability. Perhaps a bit surprisingly, the understanding to its model identifiability---the major…

Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…

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…

Community is a fundamental and critical characteristic of an undirected social network, making community detection be a vital yet thorny issue in network representation learning. A symmetric and non-negative matrix factorization (SNMF)…

Multimodal data arise in various applications where information about the same phenomenon is acquired from multiple sensors and across different imaging modalities. Learning from multimodal data is of great interest in machine learning and…

Non-Negative Matrix Factorization (NMF) is an unsupervised learning method offering low-rank representations across various domains such as audio processing, biomedical signal analysis, and image recognition. The incorporation of…

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates…

Matrix factorization models are the core of current commercial collaborative filtering Recommender Systems. This paper tested six representative matrix factorization models, using four collaborative filtering datasets. Experiments have…

We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior…

Non-negative Matrix Factorization (NMF) is an intensively used technique for obtaining parts-based, lower dimensional and non-negative representation. Researchers in biology, medicine, pharmacy and other fields often prefer NMF over other…

We propose the convex factorization machine (CFM), which is a convex variant of the widely used Factorization Machines (FMs). Specifically, we employ a linear+quadratic model and regularize the linear term with the $\ell_2$-regularizer and…