Related papers: Robust Matrix Factorization with Grouping Effect
Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…
Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc). Despite having received extensive…
In the non-negative matrix factorization (NMF) problem, the input is an $m\times n$ matrix $M$ with non-negative entries and the goal is to factorize it as $M\approx AW$. The $m\times k$ matrix $A$ and the $k\times n$ matrix $W$ are both…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Matrix factorization (MF) has been widely used to discover the low-rank structure and to predict the missing entries of data matrix. In many real-world learning systems, the data matrix can be very high-dimensional but sparse. This poses an…
In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are…
Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals…
Non-negative Matrix Factorization (NMF) is a popular tool for data exploration. Bayesian NMF promises to also characterize uncertainty in the factorization. Unfortunately, current inference approaches such as MCMC mix slowly and tend to get…
There has been a recent critical need to study fairness and bias in machine learning (ML) algorithms. Since there is clearly no one-size-fits-all solution to fairness, ML methods should be developed alongside bias mitigation strategies that…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
Nonnegative matrix factorization (NMF) is a known unsupervised data-reduction method. The principle of the common cause (PCC) is a basic methodological approach in probabilistic causality, which seeks an independent mixture model for the…
We propose a new neural network framework, termed Neural Network Machine Regression (NNMR), which integrates trainable input gating and adaptive depth regularization to jointly perform feature selection and function estimation in an…
We present a novel game-theoretic formulation of Non-Negative Matrix Factorization (NNMF), a popular data-analysis method with many scientific and engineering applications. The game-theoretic formulation is shown to have favorable scaling…
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. We interpret the factorization in a new way and use it to generate missing attributes from test data. We provide a joint…
In this work we perform some mathematical analysis on non-negative matrix factorizations (NMF) and apply NMF to some imaging and inverse problems. We will propose a sparse low-rank approximation of big positive data and images in terms of…
We propose a geometric assumption on nonnegative data matrices such that under this assumption, we are able to provide upper bounds (both deterministic and probabilistic) on the relative error of nonnegative matrix factorization (NMF). The…
Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts. However, this decompostion is not generally identifiable (even up to permutation and…
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,…