Related papers: Accelerating Nonnegative Matrix Factorization Algo…

In this paper, we design a hierarchical clustering algorithm for high-resolution hyperspectral images. At the core of the algorithm, a new rank-two nonnegative matrix factorizations (NMF) algorithm is used to split the clusters, which is…

Random projections have been recently implemented in Nonnegative Matrix Factorization (NMF) to speed-up the NMF computations, with a negligible loss of performance. In this paper, we investigate the effects of such projections when the NMF…

Dimensionality reduction and matrix factorization techniques are important and useful machine-learning techniques in many fields. Nonnegative matrix factorization (NMF) is particularly useful for spectral analysis and image processing in…

Non-negative matrix factorization (NMF) is a prob- lem with many applications, ranging from facial recognition to document clustering. However, due to the variety of algorithms that solve NMF, the randomness involved in these algorithms,…

We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…

We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS occurs naturally in a wide variety of applications where an unknown, non-negative quantity must be recovered from linear measurements. We present a unified framework…

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…

Nonnegative Matrix Factorization (NMF) has been a popular representation method for pattern classification problem. It tries to decompose a nonnegative matrix of data samples as the product of a nonnegative basic matrix and a nonnegative…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices and has been widely used for unsupervised learning tasks such as product recommendation based on a rating matrix. However, although…

Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. Generally, existing NMF methods represent each sample with several centroids, and find the optimal…

We propose a Block Majorization Minimization method with Extrapolation (BMMe) for solving a class of multi-convex optimization problems. The extrapolation parameters of BMMe are updated using a novel adaptive update rule. By showing that…

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…

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…

Matrix decomposition is ubiquitous and has applications in various fields like speech processing, data mining and image processing to name a few. Under matrix decomposition, nonnegative matrix factorization is used to decompose a…

Non-negative matrix factorization (NMF) is widely used for dimensionality reduction and interpretable analysis, but standard formulations are unsupervised and cannot directly exploit class labels. Existing supervised or semi-supervised…

We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving…

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) 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…

Symmetric nonnegative matrix factorization (SNMF) has demonstrated to be a powerful method for data clustering. However, SNMF is mathematically formulated as a non-convex optimization problem, making it sensitive to the initialization of…

Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs.…