Beamspace-Domain Multichannel Nonnegative Matrix Factorization for Audio Source Separation

The Gaussian and Gaussian-sigmoidal primaries are introduced as initialization functions in the nonnegative matrix factorization (NNMF) method to achieve more consistent error statistics. The proposed NNMF method with multiplicative update algorithm is employed for reconstruction of spectral data of Munsell and Colorchecker DC datasets from the corresponding CIEXYZ tristimulus values and the resultant achievements are compared with those obtained from PCA and the classical NNMF techniques. Both colorimetric and spectrophotometric errors between the original and the reconstructed spectra are used for the evaluation of reconstruction methods. While run to run variability of the classical NNMF method with multiplicative update algorithm is significantly remarkable, the stability of the suggested technique is fairly high, similar to the PCA method. The ensuing findings show that the embedding of Gaussian initializing vectors in NNMF method provide the all positive bases that enhance both the accuracy of Gaussian method and the reliability of NNMF technique.

We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. We work in the short-time Fourier transform (STFT) domain, where convolution is routinely approximated as linear instantaneous mixing in each frequency band. Each source STFT is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura-Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization (EM) algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms are applied to stereo audio source separation in various settings, covering blind and supervised separation, music and speech sources, synthetic instantaneous and convolutive mixtures, as well as professionally produced music recordings. Our EM method produces competitive results with respect to state-of-the-art as illustrated on two tasks from the international Signal Separation Evaluation Campaign (SiSEC 2008).

Spatial gradients in the primary geomagnetic fields directly contribute to both the amplitudes and phases of inter-station transfer functions (IS-TFs). This suggests that, for the analysis of subsurface resistivity structures, IS-TFs should be carefully treated by checking the establishment of the plane-wave assumption. Geomagnetic time-series data include various and complicated characteristics and accordingly, time–frequency domain analysis is suitable for the discussion of spatial gradients of time-varying geomagnetic fields. However, such evaluations are complicated by the huge amount of information contained in the spectrograms from several stations. Therefore, we propose a Multi-Channel Nonnegative Matrix Factorization (MC-NMF) method that can decompose raw spectrograms into several components, allowing the spatial gradient of each geomagnetic temporal variation to be identified. We confirm that such components actually affect the estimation of IS-TFs using data acquired at the Kakioka and Memambetsu magnetic observatories in Japan. We derive the year-to-year changes in IS-TFs from each set of paired stations among Kakioka, Kanoya, and Memambetsu observatories. Although the IS-TFs should exhibit opposite polarities (a negative correlation) when the input and output observatories are swapped; surprisingly, some of them have “identical” polarities. The application of MC-NMF shows that the analyzed geomagnetic data include several components that have various spatial gradients. Although IS-TFs sometimes fail to give the expected implication regarding the spatial gradients of geomagnetic temporal variations, MC-NMF can verify whether the IS-TFs exhibit any spatial gradients. Thus, the use of IS-TFs with MC-NMF can yield better implications regarding subsurface resistivity information.

Non-negative matrix factorization for speech/music separation using source dependent decomposition rank, temporal continuity term and filtering

BackgroundIn-vivo single voxel proton magnetic resonance spectroscopy (SV 1H-MRS), coupled with supervised pattern recognition (PR) methods, has been widely used in clinical studies of discrimination of brain tumour types and follow-up of patients bearing abnormal brain masses. SV 1H-MRS provides useful biochemical information about the metabolic state of tumours and can be performed at short (< 45 ms) or long (> 45 ms) echo time (TE), each with particular advantages. Short-TE spectra are more adequate for detecting lipids, while the long-TE provides a much flatter signal baseline in between peaks but also negative signals for metabolites such as lactate. Both, lipids and lactate, are respectively indicative of specific metabolic processes taking place. Ideally, the information provided by both TE should be of use for clinical purposes. In this study, we characterise the performance of a range of Non-negative Matrix Factorisation (NMF) methods in two respects: first, to derive sources correlated with the mean spectra of known tissue types (tumours and normal tissue); second, taking the best performing NMF method for source separation, we compare its accuracy for class assignment when using the mixing matrix directly as a basis for classification, as against using the method for dimensionality reduction (DR). For this, we used SV 1H-MRS data with positive and negative peaks, from a widely tested SV 1H-MRS human brain tumour database.ResultsThe results reported in this paper reveal the advantage of using a recently described variant of NMF, namely Convex-NMF, as an unsupervised method of source extraction from SV1H-MRS. Most of the sources extracted in our experiments closely correspond to the mean spectra of some of the analysed tumour types. This similarity allows accurate diagnostic predictions to be made both in fully unsupervised mode and using Convex-NMF as a DR step previous to standard supervised classification. The obtained results are comparable to, or more accurate than those obtained with supervised techniques.ConclusionsThe unsupervised properties of Convex-NMF place this approach one step ahead of classical label-requiring supervised methods for the discrimination of brain tumour types, as it accounts for their increasingly recognised molecular subtype heterogeneity. The application of Convex-NMF in computer assisted decision support systems is expected to facilitate further improvements in the uptake of MRS-derived information by clinicians.

BackgroundLung adenocarcinoma (LUAD) is a heterogeneous disease. However the inner sub‐groups of LUAD have not been fully studied. Markers predicted the sub‐groups and prognosis of LUAD are badly needed.AimsTo identify biomarkers associated with the sub‐groups and prognosis of LUAD.Materials and MethodsUsing nonnegative matrix factorization (NMF) clustering, LUAD patients from The Cancer Genome Atlas (TCGA), Gene Expression Omnibus (GEO) datasets and LUAD cell lines from Genomics of Drug Sensitivity in Cancer (GDSC) dataset were divided into different sub‐consensuses based on the gene expression profiling. The overall survival of LUAD patients in each sub‐consensus was determined by Kaplan‐Meier survival analysis. The common genes which were differentially expressed in each sub‐consensus of LUAD patients and LUAD cell lines were identified using TBtools. The predictive accuracy of TPX2 and SELENBP1 for theinner sub‐consensuses of LUAD was determined by Receiver operator characteristic (ROC) analysis. The Kaplan‐Meier survival analysis was also used to test the prognostic significance of TPX2 and SELENBP1 in LUAD patients.ResultsUsing nonnegative matrix factorization clustering, LUAD patients in The Cancer Genome Atlas (TCGA), GSE30219, GSE42127, GSE50081, GSE68465, and GSE72094 datasets were divided into three sub‐consensuses. Sub‐consensus3 LUAD patients were with low overall survival and were with high TP53 mutations. Similarly, LUAD cell lines were also divided into three sub‐consensuses by NMF method, and sub‐consensus2 cell lines were resistant to EGFR inhibitors. Identification of the common genes which were differentially expressed in different sub‐consensuses of LUAD patients and LUAD cell lines revealed that TPX2 was highly expressed in sub‐consensus3 LUAD patients and sub‐consensus2 LUAD cell lines. On the contrary, SELENBP1 was highly expressed in sub‐consensus1 LUAD patients and sub‐consensus1 LUAD cell lines. The expression levels of TPX2 and SELENBP1 could distinguish sub‐consensus3 LUAD patients or sub‐consensus2 LUAD cell lines from other sub‐consensuses of LUAD patients or cell lines. Moreover, compared with normal lung tissues, TPX2 was highly expressed, while, SELENBP1 was lowly expressed in LUAD tissues. Furthermore, the higher expression levels of TPX2 were associated with the lower relapse‐free survival and the lower overall survival of LUAD patients. While, the higher expression levels of SELENBP1 were associated with the higher relapse‐free survival and higher overall survival. At last, we showed that TP53 mutant LUAD patients were with higher TPX2 and lower SELENBP1 expressions.DiscussionBoth iCluster and NMF method are proved to be robust LUAD classification systems. However, the LUAD patients in different iclusters had no significant clinical overall survival, while, sub‐consensus3 LUAD patients from NMF classification were with lower overall survival than other sub‐consensuses.ConclusionsBy integrated analysis of 1765 LUAD patients and 64 LUAD cell lines, we showed that NMF was a robust inner sub‐consensuses classification method of LUAD. TPX2 and SELENBP1 were differentially expressed in different LUAD sub‐ consensuses, and predicted the inner sub‐consensuses of LUAD with high accuracy. TPX2 was an unfavorable prognostic biomarker of LUAD which was up‐regulated in LUAD tissues and associated with the low overall survival of LUAD. SELENBP1 was a favorable prognostic biomarker of LUAD which was down‐regulated in LUAD tissues and associated with the prolonged overall survival of LUAD.

Non-negative matrix factorization (NMF) has been one of the most popular methods for feature learning in the field of machine learning and computer vision. Most existing works directly apply NMF on high-dimensional image datasets for computing the effective representation of the raw images. However, in fact, the common essential information of a given class of images is hidden in their low rank parts. For obtaining an effective low-rank data representation, we in this paper propose a non-negative low-rank matrix factorization (NLMF) method for image clustering. For the purpose of improving its robustness for the data in a manifold structure, we further propose a graph regularized NLMF by incorporating the manifold structure information into our proposed objective function. Finally, we develop an efficient alternating iterative algorithm to learn the low-dimensional representation of low-rank parts of images for clustering. Alternatively, we also incorporate robust principal component analysis into our proposed scheme. Experimental results on four image datasets reveal that our proposed methods outperform four representative methods.

Non-negative matrix factorization (NMF) is a very popular dimensionality reduction method that has been widely used in computer vision and data clustering. However, NMF does not consider the intrinsic geometric information of a data set and also does not produce smooth and stable solutions. To resolve these problems, we propose a Graph regularized Lp Smooth Non-negative Matrix Factorization (GSNMF) method by incorporating graph regularization with Lp smooth constraint. The graph regularization can discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. The Lp smooth constraint can combine the merits of isotropic (L2-norm) and anisotropic (L1-norm) diffusion smoothing, and produce a smooth and more accurate solution to the optimization problem. Experimental results on some data sets demonstrate that the proposed method outperforms related state-of-the-art NMF methods.

Nonnegative Matrix Factorization (NMF), as a popular feature extraction technique, has recently attracted increasing attentions in high-dimensional data analysis, due to the strong ability of dimension reduction and semantic representation. In order to utilize the partial label information in practice, several semi-supervised NMF methods have been proposed. However, existing semi-supervised NMF variants only consider the global label constraint of data, but ignore the local label information embedded in geometric structure, which is very crucial for data representation. To address the above issue, we propose an improved NMF method, namely local and global regularized semi-supervised NMF (LGNMF), by considering the local and global label constraints simultaneously. Specifically, the local label constraint is depicted in a graph, which is pre-computed by metric learning. In addition, to explore the global label information, we construct an indicator matrix to restrict the coefficient matrix in LGNMF. For the formulated LGNMF, a multiplicative update rule (MUR) is developed. Extensive experiments on several real datasets demonstrate the superiority of the proposed method over the state-of-the-art methods in terms of clustering accuracy and normalized mutual information.

In this paper, we present a novel muscle synergy extraction method based on multivariate curve resolution–alternating least squares (MCR-ALS) to overcome the limitation of the nonnegative matrix factorization (NMF) method for extracting non-sparse muscle synergy, and we study its potential application for evaluating motor function of stroke survivors. Nonnegative matrix factorization (NMF) is the most widely used method for muscle synergy extraction. However, NMF is susceptible to components’ sparseness and usually provides inferior reliability, which significantly limits the promotion of muscle synergy. In this study, MCR-ALS was employed to extract muscle synergy from electromyography (EMG) data. Its performance was compared with two other matrix factorization algorithms, NMF and self-modeling mixture analysis (SMMA). Simulated data sets were utilized to explore the influences of the sparseness and noise on the extracted synergies. As a result, the synergies estimated by MCR-ALS were the most similar to true synergies as compared with SMMA and NMF. MCR-ALS was used to analyze the muscle synergy characteristics of upper limb movements performed by healthy (n = 11) and stroke (n = 5) subjects. The repeatability and intra-subject consistency were used to evaluate the performance of MCR-ALS. As a result, MCR-ALS provided much higher repeatability and intra-subject consistency as compared with NMF, which were important for the reliability of the motor function evaluation. The stroke subjects had lower intra-subject consistency and seemingly had more synergies as compared with the healthy subjects. Thus, MCR-ALS is a promising muscle synergy analysis method for motor function evaluation of stroke patients.

Microorganisms play a significant role in the evolutionary process of the Earth and are closely related to the modification and evolution of the Earth’s surface circles at different spatial and temporal scales. Given geological microbiology in the self-potential signal data can be represented with non-negative matrix, which makes use of non-negative matrix factorization method to deal with the data become possible. This paper introduces the basic principle of non-negative matrix factorization method, based on non-negative matrix factorization method is discussed to isolate the self-potential signal data in geological microbes may and effect. By separating two natural potential signals containing noise with blind sources, the separation effect is good and the non-negative matrix factorization method is found to be an effective method for extracting their self-potential signal data. Although this numerical simulation is the self-potential signal is introduced in the work of geological microbiology, but this method also has reference significance for other signal data processing, can also be used to other geophysical data processing, the implementation of the research on environmental protection, to improve the cognitive complex biological geological process of shallow earth environment has important significance.

In this work we present a modified Nonnegative Matrix Factorization (NMF) method for learning a mixture of local SOM models. The proposed method approximates a data point with a linear combination of its k-nearest neighbor prototypes. This allows obtaining a low quantization error and at the same time keeping the interpretability of the prototypes. The results of the new method are compared with those obtained using non-negative least squares, NMF and SOM, using four benchmark data sets. Two metrics are used to assess the performance of the different approaches. The proposed k-nn NMF method obtained the lowest relative local quantization error, while keeping a global quantization error similar to the best alternative methods.KeywordsSelf Organizing MapNonnegative Matrix Factorizationk-Nearest NeighborsLinear MixtureRelative Quantization Error

Even though Nonnegative Matrix Factorization (NMF) in its original form performs rank reduction and signal compaction implicitly, it does not explicitly consider storage or transmission constraints. We propose a Frobenius-norm Quantized Nonnegative Matrix Factorization algorithm that is 1) almost as precise as traditional NMF for decomposition ranks of interest (with in 1-4dB), 2) admits to practical encoding techniques by learning a factorization which is simpler than NMF's (by a factor of 20-70) and 3) exhibits a complexity which is comparable with state-of-the-art NMF methods. These properties are achieved by considering the quantization residual via an outer quantization optimization step, in an extended NMF iteration, namely QNMF. This approach comes in two forms: QNMF with 1) quasi-fixed and 2) adaptive quantization levels. Quantized NMF considers element-wise quantization constraints in the learning algorithm to eliminate defects due to post factorization quantization. We demonstrate significant reduction in the cardinality of the factor signal values set for comparable Signal-to-Noise-Ratios in a matrix decomposition task.

We apply the vectorized non-negative matrix factorization (NMF) method to the post-processing of the direct imaging data of exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a nonorthogonal and non-negative basis of components using the given reference images and then models a target with the components. The constructed model is then rescaled with a factor to compensate for the contribution from the disks. We compare NMF with existing methods (classical reference differential imaging method, and the Karhunen–Loève image projection algorithm) using synthetic circumstellar disks and demonstrate the superiority of NMF: with no need of prior selection of references, NMF not only can detect fainter circumstellar disks but also better preserves their morphology and does not require forward modeling. As an application to a well-known disk example, we process the archival Hubble Space Telescope STIS coronagraphic observations of HD 181327 with different methods and compare them, and NMF is able to extract some circumstellar materials inside the primary ring for the first time. In an appendix, we mathematically investigate the stability of NMF components during the iteration and the linearity of NMF modeling.

There is currently an unprecedented demand for large-scale temporal data analysis due to the explosive growth of data. Dynamic topic modeling has been widely used in social and data sciences with the goal of learning latent topics that emerge, evolve, and fade over time. Previous work on dynamic topic modeling primarily employ the method of nonnegative matrix factorization (NMF), where slices of the data tensor are each factorized into the product of lower-dimensional nonnegative matrices. With this approach, however, information contained in the temporal dimension of the data is often neglected or underutilized. To overcome this issue, we propose instead adopting the method of nonnegative CANDECOMP/PARAPAC (CP) tensor decomposition (NNCPD), where the data tensor is directly decomposed into a minimal sum of outer products of nonnegative vectors, thereby preserving the temporal information. The viability of NNCPD is demonstrated through application to both synthetic and real data, where significantly improved results are obtained compared to those of typical NMF-based methods. The advantages of NNCPD over such approaches are studied and discussed. To the best of our knowledge, this is the first time that NNCPD has been utilized for the purpose of dynamic topic modeling, and our findings will be transformative for both applications and further developments.