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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,…
Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different…
Learning approaches rely on hyperparameters that impact the algorithm's performance and affect the knowledge extraction process from data. Recently, Nonnegative Matrix Factorization (NMF) has attracted a growing interest as a learning…
Non-Negative Matrix Factorization (NMF) is a widely used dimension reduction method that factorizes a non-negative data matrix into two lower dimensional non-negative matrices: One is the basis or feature matrix which consists of the…
Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in…
Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
Binary data matrices can represent many types of data such as social networks, votes, or gene expression. In some cases, the analysis of binary matrices can be tackled with nonnegative matrix factorization (NMF), where the observed data…
We propose several new models for semi-supervised nonnegative matrix factorization (SSNMF) and provide motivation for SSNMF models as maximum likelihood estimators given specific distributions of uncertainty. We present multiplicative…
Nonnegative Matrix Factorization (NMF) is an unsupervised learning algorithm that produces a linear, parts-based approximation of a data matrix. NMF constructs a nonnegative low rank basis matrix and a nonnegative low rank matrix of weights…
Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization…
We propose a new variant of nonnegative matrix factorization (NMF), combining separability and sparsity assumptions. Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity…
Topic models have been extensively used to organize and interpret the contents of large, unstructured corpora of text documents. Although topic models often perform well on traditional training vs. test set evaluations, it is often the case…
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…
Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to…
Nonnegative Matrix Factorization (NMF) has been continuously evolving in several areas like pattern recognition and information retrieval methods. It factorizes a matrix into a product of 2 low-rank non-negative matrices that will define…
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…
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…
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,…
Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…