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We introduce a Bayesian perspective for the structured matrix factorization problem. The proposed framework provides a probabilistic interpretation for existing geometric methods based on determinant minimization. We model input data…
In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the…
In this article, we study algorithms for nonnegative matrix factorization (NMF) in various applications involving streaming data. Utilizing the continual nature of the data, we develop a fast two-stage algorithm for highly efficient and…
Nowadays, nonnegative matrix factorization (NMF) based methods have been widely applied to blind spectral unmixing. Introducing proper regularizers to NMF is crucial for mathematically constraining the solutions and physically exploiting…
We consider the probabilistic analogue to neural network matrix factorization (Dziugaite & Roy, 2015), which we construct with Bayesian neural networks and fit with variational inference. We find that a linear model fit with variational…
We are interested in learning customers' video preferences from their historic viewing patterns and geographical location. We consider a Bayesian latent factor modeling approach for this task. In order to tune the complexity of the model to…
We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation…
Non-negative Matrix Factorization (NMF) is a key kernel for unsupervised dimension reduction used in a wide range of applications, including topic modeling, recommender systems and bioinformatics. Due to the compute-intensive nature of…
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and…
Motivated by the reconstruction and the prediction of electricity consumption, we extend Nonnegative Matrix Factorization~(NMF) to take into account side information (column or row features). We consider general linear measurement settings,…
The establishment of robust target appearance model over time is an overriding concern in visual tracking. In this paper, we propose an inverse nonnegative matrix factorization (NMF) method for robust appearance modeling. Rather than using…
Mutational signatures are patterns of somatic mutations in tumor genomes that provide insights into underlying mutagenic processes and cancer origin. Developing reliable methods for their estimation is of growing importance in cancer…
Nonnegative matrix factorization (NMF) has become a prominent technique for the analysis of image databases, text databases and other information retrieval and clustering applications. In this report, we define an exact version of NMF. Then…
The goal of this presentation is to build an efficient non-parametric Bayes classifier in the presence of large numbers of predictors. When analyzing such data, parametric models are often too inflexible while non-parametric procedures tend…
The electromagnetic nucleon form-factors data are studied with artificial feed forward neural networks. As a result the unbiased model-independent form-factor parametrizations are evaluated together with uncertainties. The Bayesian approach…
Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that…
Factors models are routinely used to analyze high-dimensional data in both single-study and multi-study settings. Bayesian inference for such models relies on Markov Chain Monte Carlo (MCMC) methods which scale poorly as the number of…
We introduce a new non-negative matrix factorization (NMF) method for ordinal data, called OrdNMF. Ordinal data are categorical data which exhibit a natural ordering between the categories. In particular, they can be found in recommender…
Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…