Optimization and expansion of non-negative matrix factorization

Statistical Optimization of Non-Negative Matrix Factorization

Non-Negative Matrix Factorization (NMF) is a dimensionality reduction method that has been shown to be very useful for a variety of tasks in machine learning and data mining. One of the fastest algorithms for NMF is the Block Principal Pivoting method (BPP) of [6], which follows a block coordinate descent approach. The optimization in each iteration involves solving a large number of expensive ...

Bandwidth expansion of narrowband speech using non-negative matrix factorization

In this paper, we present a novel technique for the estimation of the high frequency components (4-8kHz) of speech signals from narrow-band (0-4 kHz) signals using convolutive Non-Negative Matrix Factorisation (NMF). The proposed technique utilizes a brief recording of simultaneous broad band and narrow band signals from a target speaker to learn a set of broad-band non-negative "bases" for the...

Non-negative matrix factorization

Non-negative Matrix Factorization with Quasi-Newton Optimization

Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most applications use relative simple multiplicative NMF learning algorithms which were proposed by Lee and Seung, and are based on minimization of the Kullback-Leibler divergence and Frobenius norm. Unfortunately...

Bayesian Non-negative Matrix Factorization

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 ...