Nonnegative Matrix Factorization (NMF) is a popular decomposition technique in pattern analysis, document clustering, image processing and related fields. In this paper, we propose a fast NMF algorithm via Projected Newton Method (PNM). First, we propose PNM to efficiently solve a nonnegative least squares problem, which achieves a quadratic convergence rate under appropriate assumptions. Secon...

MOTIVATION Many practical pattern recognition problems require non-negativity constraints. For example, pixels in digital images and chemical concentrations in bioinformatics are non-negative. Sparse non-negative matrix factorizations (NMFs) are useful when the degree of sparseness in the non-negative basis matrix or the non-negative coefficient matrix in an NMF needs to be controlled in approx...

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm...

Non-negative matrix factorization (NMF) has been a popular method for modeling audio signals, in particular for single-channel source separation. An important factor in the success of NMF-based algorithms is the “quality” of the basis functions that are obtained from training data. In order to model rich signals such as speech or wide ranges of non-stationary noises, NMF typically requires usin...

Non-negative matrix factorization (NMF), with the constraints of non-negativity, has been recently proposed for multi-variate data analysis. Because it allows only additive, not subtractive, combinations of the original data, NMF is capable of producing region or parts-based representation of objects. It has been used for image analysis and text processing. Unlike PCA, the resolutions of NMF ar...

Searching and mining biomedical literature databases are common ways of generating scientific hypotheses by biomedical researchers. Clustering can assist researchers to form hypotheses by seeking valuable information from grouped documents effectively. Although a large number of clustering algorithms are available, this paper attempts to answer the question as to which algorithm is best suited ...

In essence, the network is a way of encoding information underlying social management system. Ubiquitous systems rarely exist alone and have dynamic complexity. For complex systems, it difficult to extract represent multi-angle features data only by using non-negative matrix factorization. Existing deep NMF models integrating multi-layer struggle explain results obtained after mid-layer NMF. th...

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 linear inverse problems than the conventional LS. Because an NMF problem can be decomposed into LS subproblems, it can be expected that Tikhonov regularized...

Non-negative Matrix Factorization (NMF) and Probabilistic Latent Semantic Indexing (PLSI) have been successfully applied to document clustering recently. In this paper, we show that PLSI and NMF (with the I-divergence objective function) optimize the same objective function, although PLSI and NMF are different algorithms as verified by experiments. This provides a theoretical basis for a new hy...

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...