In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between input and low-rank approximation, Kullback-Leibler (KL) divergence one of most widely used objective function NMF. It corresponds maximum likehood estimator when underlying statistics observed sample follows Poisson distribution, K...

Exposure of certain cell lines to the differentiation-inducing agent N-methylformamide (NMF) enhances their radiosensitivity. As part of an attempt to elucidate the mechanism of NMF-induced radiosensitization, we examined the effects of NMF on chromatin structure, as reflected by changes in DNA-protein cross-links (DPCs) and the chromatin protein/DNA ratio, in two cell lines, clone A and HCA-1....

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is to decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropria...

Non-negative matrix factorization (NMF, Nature 401 (1999) 788-791) is a method to derive non-negative basis functions for sets of data that are inherently non-negative, such as color spectra. We applied NMF to Munsell color spectra and investigated the color names associated with the non-negative basis functions. NMF yields basis functions compatible with established color naming categories.

In this paper, a class of algorithms for automatic classification of individual musical instrument sounds is presented. Several perceptual features used in general sound classification applications were measured for 300 sound recordings consisting of 6 different musical instrument classes (piano, violin, cello, flute, bassoon, and soprano saxophone). In addition, MPEG-7 basic spectral and spect...

Reverse-convex programming (RCP) concerns global optimization of a specific class of non-convex optimization problems. We show that a recently proposed model for sparse non-negative matrix factorization (NMF) belongs to this class. Based on this result, we design two algorithms for sparse NMF that solve sequences of convex secondorder cone programs (SOCP). We work out some well-defined modifica...

In this article, we integrate the spatial-spectral information of hyperspectral image (HSI) samples into nonnegative matrix factorization (NMF) for affinity learning to address issue HSI clustering. This technique consists three main components: 1) oversegmentation computing spectral-spatial matrix; 2) NMF with guidance obtained and 3) density-based spectral clustering on final matrix. First, i...

Abstract In this paper, we propose a supervised single-channel speech enhancement method that combines Kullback-Leibler (KL) divergence-based non-negative matrix factorization (NMF) and hidden Markov model (NMF-HMM). With the integration of HMM, temporal dynamics information signals can be taken into account. This includes training stage an stage. stage, sum Poisson distribution, leading to KL ...