Related papers: Fast Rank-1 NMF for Missing Data with KL Divergenc…

We consider the problem of regularized Poisson Non-negative Matrix Factorization (NMF) problem, encompassing various regularization terms such as Lipschitz and relatively smooth functions, alongside linear constraints. This problem holds…

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…

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,…

A well-known method for completing low-rank matrices based on convex optimization has been established by Cand{\`e}s and Recht. Although theoretically complete, the method may not entirely solve the low-rank matrix completion problem. This…

Nonnegative matrix factorization is a powerful technique to realize dimension reduction and pattern recognition through single-layer data representation learning. Deep learning, however, with its carefully designed hierarchical structure,…

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,…

Robust matrix factorization (RMF), which uses the $\ell_1$-loss, often outperforms standard matrix factorization using the $\ell_2$-loss, particularly when outliers are present. The state-of-the-art RMF solver is the RMF-MM algorithm,…

Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing regularly-sampled data, i.e., data that can be stored in a matrix. For audio, this has led to numerous applications using time-frequency (TF) representations like…

This paper investigates a non-negative matrix factorization (NMF)-based approach to the semi-supervised single-channel speech enhancement problem where only non-stationary additive noise signals are given. The proposed method relies on…

We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a…

We present here an original application of the non-negative matrix factorization (NMF) method, for the case of extra-financial data. These data are subject to high correlations between co-variables, as well as between observations. NMF…

While the matrix completion problem has attracted considerable attention over the decades, few works address the nonignorable missing issue and all have their limitations. In this article, we propose a nuclear norm regularized row- and…

Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute.…

We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

We present a new probabilistic model to address semi-nonnegative matrix factorization (SNMF), called Skellam-SNMF. It is a hierarchical generative model consisting of prior components, Skellam-distributed hidden variables and observed data.…

Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for clustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to construct similarity matrix. However, $k$-NN may mislead clustering since the neighbors…

In this paper, we introduce a probabilistic model for learning nonnegative matrix factorization (NMF) that is commonly used for predicting missing values and finding hidden patterns in the data, in which the matrix factors are latent…

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent…

Due to the iterative nature of most nonnegative matrix factorization (\textsc{NMF}) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes…