Speech Dereverberation Using Non-Negative Convolutive Transfer Function and Spectro-Temporal Modeling

Spectral un mixing has been an important technique for hyperspectral imagery processing. In spectral unmixing methods that are based on the original non-negative matrix factorization (NMF) model, unmixing accuracy is limited by the lack of appropriate constraints that derived from the inherent properties of hyperspectral images. It was shown that the correlation analysis can be extended for NMF-based spectral unmixing model, based on the advantage that the spatial and spectral correlation features can provide necessary constraints for NMF to overcome related problems and obtain better performance. However, many correlation constrained NMF models prefer adopting only spatial correlation, the neglect of spectral correlation may limit the accuracy and application scope. This letter presents a novel method of imposing spatial and spectral correlation constraints simultaneously on the NMF-based unmixing model by adopting Markov Random Field (MRF) and complexity pursuit respectively. The related issues, including reducing the deviation of endmembers' spatial energy distribution and substituting the predictability of signal for piecewise smoothness of spectra, were studied together. Experiments showed that the new proposed NMF model was superior to some existing NMF models with only spatial correlation constraint in terms of estimation accuracy of endmember spectra and fractional abundances.

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as the product of two smaller nonnegative matrices, $W$ and $H$. In this paper, we introduce a general framework to design multiplicative updates (MU) for NMF based on $\beta$-divergences ($\beta$-NMF) with disjoint equality constraints, and with penalty terms in the objective function. By disjoint, we mean that each variable appears in at most one equality constraint. Our MU satisfy the set of constraints after each update of the variables during the optimization process, while guaranteeing that the objective function decreases monotonically. We showcase this framework on three NMF models, and show that it competes favorably the state of the art: (1)~$\beta$-NMF with sum-to-one constraints on the columns of $H$, (2) minimum-volume $\beta$-NMF with sum-to-one constraints on the columns of $W$, and (3) sparse $\beta$-NMF with $\ell_2$-norm constraints on the columns of $W$.

Label consistency-based deep semisupervised NMF for tumor recognition

Feature analysis is a fundamental research area in computer graphics; meanwhile, meaningful and part-aware feature bases are always demanding. This paper proposes a framework for conducting feature analysis on a three-dimensional (3D) model by introducing modified Non-negative Matrix Factorization (NMF) model into the graphical feature space and push forward further applications. By analyzing and utilizing the intrinsic ideas behind NMF, we propose conducting the factorization on feature matrices constructed based on descriptors or graphs, which provides a simple but effective way to raise compressed and scale-aware descriptors. In order to enable part-aware model analysis, we modify the NMF model to be sparse and constrained regarding to both bases and encodings, which gives rise to Sparse and Constrained Non-negative Matrix Factorization (SAC-NMF). Subsequently, by adapting the analytical components (including hidden variables, bases, and encodings) to design descriptors, several applications have been easily but effectively realized. The extensive experimental results demonstrate that the proposed framework has many attractive advantages, such as being efficient, extendable, and so forth.

Object representation in the inferior temporal cortex (IT), an area of visual cortex critical for object recognition in the primate, exhibits two prominent properties: (1) objects are represented by the combined activity of columnar clusters of neurons, with each cluster representing component features or parts of objects, and (2) closely related features are continuously represented along the tangential direction of individual columnar clusters. Here we propose a learning model that reflects these properties of parts-based representation and topographic organization in a unified framework. This model is based on a nonnegative matrix factorization (NMF) basis decomposition method. NMF alone provides a parts-based representation where nonnegative inputs are approximated by additive combinations of nonnegative basis functions. Our proposed model of topographic NMF (TNMF) incorporates neighborhood connections between NMF basis functions arranged on a topographic map and attains the topographic property without losing the parts-based property of the NMF. The TNMF represents an input by multiple activity peaks to describe diverse information, whereas conventional topographic models, such as the self-organizing map (SOM), represent an input by a single activity peak in a topographic map. We demonstrate the parts-based and topographic properties of the TNMF by constructing a hierarchical model for object recognition where the TNMF is at the top tier for learning high-level object features. The TNMF showed better generalization performance over NMF for a data set of continuous view change of an image and more robustly preserving the continuity of the view change in its object representation. Comparison of the outputs of our model with actual neural responses recorded in the IT indicates that the TNMF reconstructs the neuronal responses better than the SOM, giving plausibility to the parts-based learning of the model.

Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due to its good adaptability for mixed data with different degrees. The majority of existing NMF-based unmixing methods are developed by incorporating additional constraints into the standard NMF based on the spectral and spatial information of hyperspectral images. However, they neglect to exploit the nature of imbalanced pixels included in the data, which may cause the pixels mixed with imbalanced endmembers to be ignored, and thus the imbalanced endmembers generally cannot be accurately estimated due to the statistical property of NMF. To exploit the information of imbalanced samples in hyperspectral data during the unmixing procedure, in this paper, a cluster-wise weighted NMF (CW-NMF) method for the unmixing of hyperspectral images with imbalanced data is proposed. Specifically, based on the result of clustering conducted on the hyperspectral image, we construct a weight matrix and introduce it into the model of standard NMF. The proposed weight matrix can provide an appropriate weight value to the reconstruction error between each original pixel and the reconstructed pixel in the unmixing procedure. In this way, the adverse effect of imbalanced samples on the statistical accuracy of NMF is expected to be reduced by assigning larger weight values to the pixels concerning imbalanced endmembers and giving smaller weight values to the pixels mixed by majority endmembers. Besides, we extend the proposed CW-NMF by introducing the sparsity constraints of abundance and graph-based regularization, respectively. The experimental results on both synthetic and real hyperspectral data have been reported, and the effectiveness of our proposed methods has been demonstrated by comparing them with several state-of-the-art methods.

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

Discriminant non-negative graph embedding for face recognition

In this study, we describe a mixture model based single-channel speech-music separation method. Given a catalog of background music material, we propose a generative model for the superposed speech and music spectrograms. The background music signal is assumed to be generated by a jingle in the catalog. The background music component is modeled by a scaled conditional mixture model representing the jingle. The speech signal is modeled by a probabilistic model, which is similar to the probabilistic interpretation of Non-negative Matrix Factorization (NMF) model. The parameters of the speech model is estimated in a semi-supervised manner from the mixed signal. The approach is tested with Poisson and complex Gaussian observation models that correspond respectively to Kullback-Leibler (KL) and Itakura-Saito (IS) divergence measures. Our experiments show that the proposed mixture model outperforms a standard NMF method both in speech-music separation and automatic speech recognition (ASR) tasks. These results are further improved using Markovian prior structures for temporal continuity between the jingle frames. Our test results with real data show that our method increases the speech recognition performance.

Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have become popular in modern data analysis problems due to their computational efficiency. Even though they have proved useful for many statistical models, the application of SG-MCMC to non-negative matrix factorization (NMF) models has not yet been extensively explored. In this study, we develop two parallel SG-MCMC algorithms for a broad range of NMF models. We exploit the conditional independence structure of the NMF models and utilize a stratified sub-sampling approach for enabling parallelization. We illustrate the proposed algorithms on an image restoration task and report encouraging results.

As one of the most important characteristics of complex networks, community structure have been studied extensively in real cases. However, in signed networks that include both positive and negative edges, the development of community discovery is still limited now. Because the sign information on edges poses a challenge to modeling the signed network. Most existing methods are based on heuristics, so these methods tend to have high computational complexity and ignore the generation of the networks. Here, we propose a Double Non-negative Matrix Factorization (DouNMF) model from the perspective of generative model to detect communities in the signed network. This algorithm skillfully applies the Non-negative matrix Factorization algorithm to the signed network. In addition, the algorithm integrates indegree information into the process of matrix factorization. Large amounts of experiments on several artificial and real-world signed networks validate that the effectiveness and accuracy of our proposed approaches both in community discovery and link prediction.

Nonnegative Matrix Factorization (NMF) is valuable in many applications of blind source separation, signal processing and machine learning. A number of algorithms that can infer nonnegative latent factors have been developed, but most of these assume a specific noise kernel. This is insufficient to deal with complex noise in real scenarios. In this paper, we present a hierarchical Dirichlet process nonnegative matrix factorization (DPNMF) model in which the Gaussian mixture model is used to approximate the complex noise distribution. Moreover, the model is cast in the nonparametric Bayesian framework by using Dirichlet process mixture to infer the necessary number of Gaussian components. We derive a mean-field variational inference algorithm for the proposed nonparametric Bayesian model. We first test the model on synthetic data sets contaminated by Gaussian, sparse and mixed noise. We then apply it to extract muscle synergies from the electromyographic (EMG) signal and to select discriminative features for motor imagery single-trial electroencephalogram (EEG) classification. Experimental results demonstrate that DPNMF performs better in extracting the latent nonnegative factors in comparison with state-of-the-art methods.

Imaging genetics is an approach that explores the underlying mechanisms of brain disorders such as Alzheimer's disease (AD) by analyzing the correlation between neuroimaging and genetic data. Traditional non-negative matrix factorization (NMF) algorithms are based on linear assumptions, which limits the potential of nonlinear feature extraction among multi-omics data. This study proposes a novel joint-connectivity-based deep semi-supervised non-negative matrix factorization (JCB-DSNMF) model to overcome this limitation and incorporate prior knowledge from both within and between different modalities of data. The model effectively integrates physiological constraints such as connectivity to identify regions of interest (ROI), risk genes, and risk SNP loci associated with AD patients. JCB-DSNMF outperformed other NMF-based algorithms, such as JDSNMF and NMF, in identifying and predicting biologically relevant biomarkers closely related to AD from essential modules. The accuracy of the selected features was further validated by constructing a diagnostic model with high classification accuracy, achieving an AUC value of 0.8621 on the test set. In particular, the brain region Putamen_L and the gene RALGAPB achieved AUC values of 0.903 and 0.924, respectively, highlighting the importance of these features in early AD diagnosis.

Supervised single-channel speech dereverberation and denoising using a two-stage model based sparse representation

Text embedding plays a crucial role in natural language processing (NLP). Among various approaches, nonnegative matrix factorization (NMF) is an effective method for this purpose. However, the standard NMF approach, fundamentally based on the bag-of-words model, fails to utilize the contextual information of documents and may result in a significant loss of semantics. To address this issue, we propose a new NMF scheme incorporating a regularization term based on the Wasserstein metric, which quantifies an approximation of a word-context matrix to leverage semantic information. Since the word-context matrix is typically symmetric and positive definite (SPD), the Wasserstein metric used in the regularization is related to a natural SPD manifold structure. We then build upon this manifold structure to integrate an explicit expression of the Wasserstein metric into the NMF framework. Additionally, we introduce modifications to the gradient computation to adapt three fundamental classes of numerical algorithms from ordinary NMF to tackle the Wasserstein-regularized NMF (NMF-WR) problem. To demonstrate the effectiveness of the NMF-WR model and the proposed algorithms, we conduct experiments on popular datasets, focusing on topic modeling and document clustering. The results indicate that the NMF-WR model exhibits superior performance compared to other conventional NMF models in processing text embeddings. These findings suggest that this novel NMF-WR framework not only enhances semantic representation but also underscores a commitment to the model’s reliability and interpretability.