Related papers: A Nonlinear Orthogonal Non-Negative Matrix Factori…
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…
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…
Nonnegative matrix factorization (NMF) is widely used for clustering with strong interpretability. Among general NMF problems, symmetric NMF is a special one that plays an important role in graph clustering where each element measures the…
This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still…
By combining related objects, unsupervised machine learning techniques aim to reveal the underlying patterns in a data set. Non-negative Matrix Factorization (NMF) is a data mining technique that splits data matrices by imposing…
Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for…
Non-negative matrix factorization (NMF) is a popular unsupervised learning approach widely used in image clustering. However, in real-world clustering scenarios, most existing NMF methods are highly sensitive to noise corruption and are…
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…
Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are $l_2$ distance or Kullback-Leibler (KL)…
The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called the orthogonal NMF (ONMF), has been found a promising clustering model and can outperform the classical…
Nonnegative matrix factorization (NMF) is a powerful class of feature extraction techniques that has been successfully applied in many fields, namely in signal and image processing. Current NMF techniques have been limited to a…
Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not…
This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering…
Symmetric nonnegative matrix factorization (symNMF) is a variant of nonnegative matrix factorization (NMF) that allows to handle symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper,…
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,…
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…
The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve…
Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Symmetric nonnegative matrix factorization (SNMF) is equivalent to computing a symmetric nonnegative low rank approximation of a data similarity matrix. It inherits the good data interpretability of the well-known nonnegative matrix…