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, is able to combine hidden features to form more representative features for pattern recognition. In this paper, we proposed sparse deep nonnegative matrix fac...

In sparse nonnegative component analysis (sparse NMF) a given dataset is decomposed into a mixing matrix and a feature data set, which are both nonnegative and fulfill certain sparsity constraints. In this paper, we extend the sparse NMF algorithm to allow for varying sparsity in each feature and discuss the uniqueness of an involved projection step. Furthermore, the eligibility of the extended...

Nonnegative Matrix Factorization (NMF) has been widely used in computer vision and pattern recognition. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally leads to parts-based and non-subtractive representation. In this paper, we present a neighborhood preserving nonnegative matrix factorization (NPNMF) for dimensionality red...

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, complexity, algorithms, and its link with extended formulations of polyhedra. In order to put NMF into perspective, the more general problem class of constrained low-r...

Nonnegative Matrix Factorization (NMF) techniques has aroused considerable interests from the field of artificial intelligence in recent years because of its good interpretability and computational efficiency. However, in many real world applications, the data features usually evolve over time smoothly. In this case, it would be very expensive in both computation and storage to rerun the whole ...

T here has been a recent surge of interest in matrix and tensor factorization (decomposition), which provides meaningful latent (hidden) components or features with physical or physiological meaning and interpretation. Nonnegative matrix factorization (NMF) and its extension to three-dimensional (3-D) nonnegative tensor factorization (NTF) attempt to recover hidden nonnegative common structures...

We give a short combinatorial proof that the nonnegative matrix factorization is an NP-hard problem. Moreover, we prove that NMF remains NP-hard when restricted to 01-matrices, answering a recent question of Moitra. The (exact) nonnegative matrix factorization is the following problem. Given an integer k and a matrix A with nonnegative entries, do there exist k nonnegative rank-one matrices tha...

This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion, in the sense that it kills two birds w...