Non-negative matrix factorization (NMF) has proven to be a useful decomposition technique for multivariate data, where the non-negativity constraint is necessary to have a meaningful physical interpretation. NMF reduces the dimensionality of non-negative data by decomposing it into two smaller non-negative factors with physical interpretation for class discovery. The NMF algorithm, however, ass...

Non-negative matrix factorization has been used as an effective approach for document clustering lately. One advantage of this method is that clustering results can be directly concluded from the factor matrices. This project gives parallel implementation of three algorithms for Non-negative matrix factorization. Experiments of these parallel algorithms for large datasets shows good speedup for...

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden dat...

MOTIVATION Identifying different cancer classes or subclasses with similar morphological appearances presents a challenging problem and has important implication in cancer diagnosis and treatment. Clustering based on gene-expression data has been shown to be a powerful method in cancer class discovery. Non-negative matrix factorization is one such method and was shown to be advantageous over ot...

In this chapter, I briefly introduce a multivariate analysis technique called non-negative matrix factorization (NMF), which has attracted a lot of attention in the field of audio signal processing in recent years. I will mention some basic properties of NMF, effects induced by the non-negative constraints, how to derive an iterative algorithm for NMF, and some attempts that have been made to a...

The multiplicative update (MU) algorithm has been used extensively to estimate the basis and coefficient matrices in nonnegative matrix factorization (NMF) problems under a wide range of divergences and regularizations. However, theoretical convergence guarantees have only been derived for a few special divergences and without regularizers. We provide a conceptually simple, self-contained, and ...

Hyperspectral remote sensing has been used in many fields, such as agriculture, military detection and mineral exploration. Hyperspectral image (HSI), despite its high spectral resolution, has lower spatial resolution than panchromatic image (PI). Therefore, it is useful yet still challenging to effectively fuse HSI and PI to obtain images with both high spectral resolution and high spatial res...

Audio understanding and classification tasks are often aided by a reduced dimensionality representation of the source observations. For example, a supervised learning system trained to detect the genre or artist of a piece of music performs better if the input nodes are statistically de-correlated, either to prevent overfitting in the learning process or to ‘anchor’ similar observations to clus...

Scalable and robust nonnegative matrix factorization (NMF) algorithms and software are needed for the generation of feature vectors from text corpora. By preserving nonnegativity, the NMF facilitates a sum-of-parts representation of the underlying term usage patterns in textual data. Both training and test sets of documents can be parsed and then factored by the NMF to produce a reduced-rank re...

Clustering of class labels can be generated automatically, which is much lower quality than labels specified by human. In this paper, we propose a new enhancing document clustering method using terms of class label and term weights. The terms of class label can well represent the inherent structure of document clusters by non-negative matrix factorization (NMF). It can also improve the quality ...