Non-negative Matrix Factorization NMF Research Articles

Dirichlet Latent Variable Model: A Dynamic Model Based on Dirichlet Prior for Audio Processing

We propose a dynamic latent variable model for learning latent bases from time varying, non-negative data. We take a probabilistic approach to modeling the temporal dependence in data by introducing a dynamic Dirichlet prior—a Dirichlet distribution with dynamic parameters. This new distribution allows us to assure non-negativity and avoid intractability when sequential updates are performed otherwise encountered in using Dirichlet prior. We refer to the proposed model as the Dirichlet latent variable model DLVM. We develop an expectation maximization algorithm for the proposed model, and also derive a maximum a posteriori estimate of the parameters. Furthermore, we connect the proposed DLVM to two popular latent basis learning methods—probabilistic latent component analysis PLCA and non-negative matrix factorization NMF. We show that 1 PLCA is a special case of our DLVM, and 2 DLVM can be interpreted as a dynamic version of NMF. The usefulness of DLVM is demonstrated for three audio processing applications—speaker source separation, denoising, and bandwidth expansion. To this end, a new algorithm for source separation is also proposed. Through extensive experiments on benchmark databases, we show that the proposed model outperforms several relevant existing methods in all three applications.

Blind Speech Separation and Enhancement With GCC-NMF

We present a blind source separation algorithm named GCC-NMF that combines unsupervised dictionary learning via non-negative matrix factorization NMF with spatial localization via the generalized cross correlation GCC method. Dictionary learning is performed on the mixture signal, with separation subsequently achieved by grouping dictionary atoms, at each point in time, according to their spatial origins. The resulting source separation algorithm is simple yet flexible, requiring no prior knowledge or information. Separation quality is evaluated for three tasks using stereo recordings from the publicly available SiSEC signal separation evaluation campaign: 3 and 4 concurrent speakers in reverberant environments, speech mixed with real-world background noise, and noisy recordings of a moving speaker. Performance is quantified using perceptually motivated and SNR-based measures with the PEASS and BSS Eval toolkits, respectively. We evaluate the effects of model parameters on separation quality, and compare our approach with other unsupervised and semi-supervised speech separation and enhancement approaches. We show that GCC-NMF is a flexible source separation algorithm, outperforming task-specific approaches in each of the three settings, including both blind as well as several informed approaches that require prior knowledge or information.

Clustering of Expression Data in Chronic Lymphocytic Leukemia Reveals New Molecular Subdivisions.

Although the identification of inherent structure in chronic lymphocytic leukemia (CLL) gene expression data using class discovery approaches has not been extensively explored, the natural clustering of patient samples can reveal molecular subdivisions that have biological and clinical implications. To explore this, we preprocessed raw gene expression data from two published studies, combined the data to increase the statistical power, and performed unsupervised clustering analysis. The clustering analysis was replicated in 4 independent cohorts. To assess the biological significance of the resultant clusters, we evaluated their prognostic value and identified cluster-specific markers. The clustering analysis revealed two robust and stable subgroups of CLL patients in the pooled dataset. The subgroups were confirmed by different methodological approaches (non-negative matrix factorization NMF clustering and hierarchical clustering) and validated in different cohorts. The subdivisions were related with differential clinical outcomes and markers associated with the microenvironment and the MAPK and BCR signaling pathways. It was also found that the cluster markers were independent of the immunoglobulin heavy chain variable (IGVH) genes mutational status. These findings suggest that the microenvironment can influence the clinical behavior of CLL, contributing to prognostic differences. The workflow followed here provides a new perspective on differences in prognosis and highlights new markers that should be explored in this context.

Statistical process monitoring based on modified nonnegative matrix factorization

As an effective feature extraction and dimension reduction method, nonnegative matrix factorization NMF can yield sparse, spatially localized, part-based subspace representations by finding a low-rank matrix approximation from the original data. However, one drawback it has to suffer is its failure to retain the statistical properties of data. In this paper, NMF is modified to take the variations of data into account. This modified NMF MNMF is aimed at not only extracting the latent signals which are added together to produce the observed signals, but also capturing the main variations of data. Then MNMF can be used to extract the latent variables in a process and combine them with process monitoring techniques for fault detection. The proposed method was applied to the Tennessee Eastman Process TEP to evaluate its monitoring performance, and the experiment results demonstrated its feasibility and availability for process monitoring.

Community discovery and importance analysis in social network

Social networks are widespread and important in our daily life. Finding communities and reveal node characteristics in community are crucial to understand the network structure and function. Many methods based on Nonnegative matrix factorization NMF are proposed to find communities, while these results appear uncertain with the initial condition especially in weighted directed network. In this paper, firstly we improve the nonnegative matrix factorization NMF method with modeling network as the weighted directed graph and using diagonally dominant matrix as constraint condition to obtain the community membership of each node as well as the interaction among communities. Furthermore, we raise methods to evaluate nodes importance and to discuss node characteristics in community to analyze the network structure. Some experiments on the Zachary club datasets and other real-world datasets have been did to demonstrate the superiority of our methods for community discovery over other related matrix factorization methods. The results demonstrate that our methods are useful and applicable both in weighted directed model and undirected model for community discovery, and the results are more reliable. Experiments also illustrate the meaningful results by discussing the node characteristics in community. All those provide a useful way for analyzing social network.

Rectifying the representation learned by Non-negative Matrix Factorization

This paper proposes a novel method to the problem of non-orthogonality of features obtained using the Non-negative Matrix Factorization NMF method. For any given non-negative data matrix, the NMF method provides a learned local representation by approximating the data matrix as a product of two non-negative matrices. However, the non-orthogonality of the features hinders the effective use of the learned representation from the NMF. To overcome this problem, we propose the following steps: calculate the metric in the feature space adapted to the features, apply the Cholesky decomposition to the metric and identify the upper triangular matrix, and use the upper triangular matrix as a linear mapping for the learned representation from the NMF. The proposed method is applied to current NMF-based clustering algorithms and evaluated over real-world datasets. The results indicate that the proposed method improves the performance of those algorithms, and that the method is very robust, even in the presence of a large number of features.