Bayesian Non-negative Matrix Factorization Research Articles

Correction: Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization

Correction: Uncovering Community Structures with Initialized Bayesian Nonnegative Matrix Factorization

Uncovering community structures with initialized Bayesian nonnegative matrix factorization.

Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian nonnegative matrix factorization model for determining community membership is proposed. First, based on singular value decomposition, we obtain simple initialized matrix factorizations from approximate decompositions of the complex network’s adjacency matrix. Then, within a few iterations, the final matrix factorizations are achieved by the Bayesian nonnegative matrix factorization method with the initialized matrix factorizations. Thus, the network’s community structure can be determined by judging the classification of nodes with a final matrix factor. Experimental results show that the proposed method is highly accurate and offers competitive performance to that of the state-of-the-art methods even though it is not designed for the purpose of modularity maximization.

Non-informative hierarchical Bayesian inference for non-negative matrix factorization

Non-negative matrix factorization (NMF) is an intuitive, non-negative, and interpretable approximation method. Canonical NMF approach could derive some basic components to represent original data, while probabilistic NMF approaches try to introduce some reasonable constraints to optimize the canonical NMF model. However, both of them cannot handle ground-truth bases discovering and model order determination problems. In general, the model order of basis matrix needs to be pre-defined. The model order determines the capability and accuracy of data structure discovering. However, how to accurately infer the model order of basis matrix has not been well investigated. In this paper, we propose a method called non-informative hierarchical Bayesian non-negative matrix factorization (NHBNMF) to automatically determine the model order and discover the data structure. They are achieved through hierarchical Bayesian inference model, maximum a posteriori (MAP) criterion, and non-informative parameters. In NHBNMF method, we first introduce a structure with two-level parameters to enable the entire model to approach the distributions of ground-truth bases. Then we use non-informative parameter scheme to eliminate the hyper-parameter to enable automatic searching. Finally, the model order and ground-truth bases are discovered by using MAP criterion and L2-norm selection. The experiments are conducted based on both synthetic and real-world datasets to show the effectiveness of our algorithm. The results demonstrate that our algorithm can accurately estimate the model order and discover the ground-truth bases. Even for the complicated FERET facial dataset, our algorithm still obtained interpretable bases and achieved satisfactory accuracy of the model order estimation.

DrugComboRanker: drug combination discovery based on target network analysis.

Motivation: Currently there are no curative anticancer drugs, and drug resistance is often acquired after drug treatment. One of the reasons is that cancers are complex diseases, regulated by multiple signaling pathways and cross talks among the pathways. It is expected that drug combinations can reduce drug resistance and improve patients’ outcomes. In clinical practice, the ideal and feasible drug combinations are combinations of existing Food and Drug Administration-approved drugs or bioactive compounds that are already used on patients or have entered clinical trials and passed safety tests. These drug combinations could directly be used on patients with less concern of toxic effects. However, there is so far no effective computational approach to search effective drug combinations from the enormous number of possibilities.Results: In this study, we propose a novel systematic computational tool DrugComboRanker to prioritize synergistic drug combinations and uncover their mechanisms of action. We first build a drug functional network based on their genomic profiles, and partition the network into numerous drug network communities by using a Bayesian non-negative matrix factorization approach. As drugs within overlapping community share common mechanisms of action, we next uncover potential targets of drugs by applying a recommendation system on drug communities. We meanwhile build disease-specific signaling networks based on patients’ genomic profiles and interactome data. We then identify drug combinations by searching drugs whose targets are enriched in the complementary signaling modules of the disease signaling network. The novel method was evaluated on lung adenocarcinoma and endocrine receptor positive breast cancer, and compared with other drug combination approaches. These case studies discovered a set of effective drug combinations top ranked in our prediction list, and mapped the drug targets on the disease signaling network to highlight the mechanisms of action of the drug combinations.Availability and implementation: The program is available on request.Contact: stwong@tmhs.org

Bayesian group sparse learning for music source separation

Nonnegative matrix factorization (NMF) is developed for parts-based representation of nonnegative signals with the sparseness constraint. The signals are adequately represented by a set of basis vectors and the corresponding weight parameters. NMF has been successfully applied for blind source separation and many other signal processing systems. Typically, controlling the degree of sparseness and characterizing the uncertainty of model parameters are two critical issues for model regularization using NMF. This paper presents the Bayesian group sparse learning for NMF and applies it for single-channel music source separation. This method reconstructs the rhythmic or repetitive signal from a common subspace spanned by the shared bases for the whole signal and simultaneously decodes the harmonic or residual signal from an individual subspace consisting of separate bases for different signal segments. A Laplacian scale mixture distribution is introduced for sparse coding given a sparseness control parameter. The relevance of basis vectors for reconstructing two groups of music signals is automatically determined. A Markov chain Monte Carlo procedure is presented to infer two sets of model parameters and hyperparameters through a sampling procedure based on the conditional posterior distributions. Experiments on separating single-channel audio signals into rhythmic and harmonic source signals show that the proposed method outperforms baseline NMF, Bayesian NMF, and other group-based NMF in terms of signal-to-interference ratio.

Protein complex detection via weighted ensemble clustering based on Bayesian nonnegative matrix factorization.

Detecting protein complexes from protein-protein interaction (PPI) networks is a challenging task in computational biology. A vast number of computational methods have been proposed to undertake this task. However, each computational method is developed to capture one aspect of the network. The performance of different methods on the same network can differ substantially, even the same method may have different performance on networks with different topological characteristic. The clustering result of each computational method can be regarded as a feature that describes the PPI network from one aspect. It is therefore desirable to utilize these features to produce a more accurate and reliable clustering. In this paper, a novel Bayesian Nonnegative Matrix Factorization(NMF)-based weighted Ensemble Clustering algorithm (EC-BNMF) is proposed to detect protein complexes from PPI networks. We first apply different computational algorithms on a PPI network to generate some base clustering results. Then we integrate these base clustering results into an ensemble PPI network, in the form of weighted combination. Finally, we identify overlapping protein complexes from this network by employing Bayesian NMF model. When generating an ensemble PPI network, EC-BNMF can automatically optimize the values of weights such that the ensemble algorithm can deliver better results. Experimental results on four PPI networks of Saccharomyces cerevisiae well verify the effectiveness of EC-BNMF in detecting protein complexes. EC-BNMF provides an effective way to integrate different clustering results for more accurate and reliable complex detection. Furthermore, EC-BNMF has a high degree of flexibility in the choice of base clustering results. It can be coupled with existing clustering methods to identify protein complexes.

Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

Overlapping community detection using Bayesian non-negative matrix factorization

Identifying overlapping communities in networks is a challenging task. In this work we present a probabilistic approach to community detection that utilizes a Bayesian non-negative matrix factorization model to extract overlapping modules from a network. The scheme has the advantage of soft-partitioning solutions, assignment of node participation scores to modules, and an intuitive foundation. We present the performance of the method against a variety of benchmark problems and compare and contrast it to several other algorithms for community detection.

Unmixing of Hyperspectral Images using Bayesian Non-negative Matrix Factorization with Volume Prior

Hyperspectral imaging can be used in assessing the quality of foods by decomposing the image into constituents such as protein, starch, and water. Observed data can be considered a mixture of underlying characteristic spectra (endmembers), and estimating the constituents and their abundances requires efficient algorithms for spectral unmixing. We present a Bayesian spectral unmixing algorithm employing a volume constraint and propose an inference procedure based on Gibbs sampling. We evaluate the method on synthetic and real hyperspectral data of wheat kernels. Results show that our method perform as good or better than existing volume constrained methods. Further, our method gives credible intervals for the endmembers and abundances, which allows us to asses the confidence of the results.

Enforcing Harmonicity and Smoothness in Bayesian Non-Negative Matrix Factorization Applied to Polyphonic Music Transcription

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) in a Bayesian framework. A model of superimposed Gaussian components including harmonicity is proposed, while temporal continuity is enforced through an inverse-Gamma Markov chain prior. We then exhibit a space-alternating generalized expectation-maximization (SAGE) algorithm to estimate the parameters. Computational time is reduced by initializing the system with an original variant of multiplicative harmonic NMF, which is described as well. The algorithm is then applied to perform polyphonic piano music transcription. It is compared to other state-of-the-art algorithms, especially NMF-based. Convergence issues are also discussed on a theoretical and experimental point of view. Bayesian NMF with harmonicity and temporal continuity constraints is shown to outperform other standard NMF-based transcription systems, providing a meaningful mid-level representation of the data. However, temporal smoothness has its drawbacks, as far as transients are concerned in particular, and can be detrimental to transcription performance when it is the only constraint used. Possible improvements of the temporal prior are discussed. </para>

Enforcing Harmonicity and Smoothness in Bayesian Non-Negative Matrix Factorization Applied to Polyphonic Music Transcription

This paper presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) in a Bayesian framework. A model of superimposed Gaussian components including har...

Enforcing Harmonicity and Smoothness in Bayesian Non-negative Matrix Factorization Applied to Polyphonic Music Transcription.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents theoretical and experimental results about constrained non-negative matrix factorization (NMF) in a Bayesian framework. A model of superimposed Gaussian components including harmonicity is proposed, while temporal continuity is enforced through an inverse-Gamma Markov chain prior. We then exhibit a space-alternating generalized expectation-maximization (SAGE) algorithm to estimate the parameters. Computational time is reduced by initializing the system with an original variant of multiplicative harmonic NMF, which is described as well. The algorithm is then applied to perform polyphonic piano music transcription. It is compared to other state-of-the-art algorithms, especially NMF-based. Convergence issues are also discussed on a theoretical and experimental point of view. Bayesian NMF with harmonicity and temporal continuity constraints is shown to outperform other standard NMF-based transcription systems, providing a meaningful mid-level representation of the data. However, temporal smoothness has its drawbacks, as far as transients are concerned in particular, and can be detrimental to transcription performance when it is the only constraint used. Possible improvements of the temporal prior are discussed. </para>