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Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…
Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…
Nonnegative matrix factorization (NMF) seeks a low-rank approximation $X \approx UV^T$ with nonnegative factors and is commonly solved using interior methods that enforce feasibility throughout optimization. We show that such…
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.…
$K$-means clustering is a widely used machine learning method for identifying patterns in large datasets. Recently, semidefinite programming (SDP) relaxations have been proposed for solving the $K$-means optimization problem, which enjoy…
Non-negative matrix factorisation (NMF) is a widely used tool for unsupervised learning and feature extraction, with applications ranging from genomics to text analysis and signal processing. Standard formulations of NMF are typically…
Nonnegative matrix factorization (NMF) often relies on the separability condition for tractable algorithm design. Separability-based NMF is mainly handled by two types of approaches, namely, greedy pursuit and convex programming. A notable…
Single-cell RNA sequencing (scRNA-seq) is a relatively new technology that has stimulated enormous interest in statistics, data science, and computational biology due to the high dimensionality, complexity, and large scale associated with…
Nonnegative matrix factorization (NMF) is a prominent technique for data dimensionality reduction that has been widely used for text mining, computer vision, pattern discovery, and bioinformatics. In this paper, a framework called ARkNLS…
Simplex-structured matrix factorization (SSMF) is a generalization of nonnegative matrix factorization, a fundamental interpretable data analysis model, and has applications in hyperspectral unmixing and topic modeling. To obtain…
Cancer, with its inherent heterogeneity, is commonly categorized into distinct subtypes based on unique traits, cellular origins, and molecular markers specific to each type. However, current studies primarily rely on complete multi-omics…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
The problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use non-negative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in…
This article presents a novel approach to solving the sparsity-constrained Orthogonal Nonnegative Matrix Factorization (SCONMF) problem, which requires decomposing a non-negative data matrix into the product of two lower-rank non-negative…
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…
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,…
We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification,…
Nonnegative matrix factorization (NMF) has been actively investigated and used in a wide range of problems in the past decade. A significant amount of attention has been given to develop NMF algorithms that are suitable to model time series…
Bayesian Matrix Factorization (BMF) is a powerful technique for recommender systems because it produces good results and is relatively robust against overfitting. Yet BMF is more computationally intensive and thus more challenging to…
Dimensionality Reduction plays a pivotal role in improving feature learning accuracy and reducing training time by eliminating redundant features, noise, and irrelevant data. Nonnegative Matrix Factorization (NMF) has emerged as a popular…