In this paper, we propose multi-layer non-negative matrix factorization (NMF) network for classification task, which provides intuitively understandable hierarchical feature learning process. The layer-by-layer learning strategy was adopted through stacked NMF layers, which enforced non-negativity of both features and their coefficients. With the non-negativity constraint, the learning process ...

We present a Bayesian treatment of non-negative matrix factorization (NMF), based on a normal likelihood and exponential priors, and derive an efficient Gibbs sampler to approximate the posterior density of the NMF factors. On a chemical brain imaging data set, we show that this improves interpretability by providing uncertainty estimates. We discuss how the Gibbs sampler can be used for model ...

This paper proposes an acoustic event detection (AED) method using semi-supervised non-negative matrix factorization (NMF) with a mixture of local dictionaries (MLD). The proposed method based on semi-supervised NMF newly introduces a noise dictionary and a noise activation matrix both dedicated to unknown acoustic atoms which are not included in the MLD. Because unknown acoustic atoms are bett...

Non-negative matrix factorization (NMF) is a method for dimensionality reduction and simplification of large data sets. Unlike tools such as principle components analysis (PCA) and factor analysis , NMF produces basis vectors that correspond to perceptible features in the original data. This is particularly useful when working with data where visual interpretation of the simplified representati...

Non-negative matrix factorization (NMF), as a useful decomposition method for multivariate data, has been widely used in pattern recognition, information retrieval and computer vision. NMF is an effective algorithm to find the latent structure of the data and leads to a parts-based representation. However, NMF is essentially an unsupervised method and can not make use of label information. In t...

In statistical practice, rectangular tables of numeric data are commonplace, and are often analyzed using dimension reduction methods like the singular value decomposition (SVD) and its close cousin, principal component analysis (PCA). This analysis produces score and loading matrices representing the rows and the columns of the original table and these matrices may be used for both prediction ...

introduction non-invasive fluorescent reflectance imaging (fri) is used for accessing physiological and molecular processes in biological media. the aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using svd, jacobi svd, and nmf methods in the fri mode. materials and methods in this article, a tissue-like phantom and an optical...

Non-negative matrix factorization (NMF) is a widely used tool for exploratory data analysis in many disciplines. In this paper, we describe an approach to NMF based on random projections and give a geometric analysis of a prototypical algorithm. Our main result shows the proto-algorithm requires κ̄k log k optimizations to find all the extreme columns of the matrix, where k is the number of extre...

A local-knowledge method for masquerade detection that uses a Non-negative Matrix Factorization (NMF) algorithm is here proposed. This method does not consider training data from other users to build a specific user profile but his own. It is used a normalization phase that helps improve a previous NMF-based method by Wang et.al. Comparisons with other local-knowledge methods like Wang’s, Hidde...

Non-negative matrix factorization (NMF) has become a well-established class of methods for the analysis non-negative data. In particular, lot effort been devoted to probabilistic NMF, namely estimation or inference tasks in models describing data, based example on Poisson exponential likelihoods. When dealing with time series several works have proposed model evolution activation coefficients a...