The design and adjustment of the divergence in audio applications using nonnegative matrix factorization (NMF) is still open problem. In this study, to deal with this problem, we explore a representation of the divergence using neural networks (NNs). Instead of the divergence, our approach extends the multiplicative update algorithm (MUA), which estimates the NMF parameters, using NNs. The design of the extended MUA incorporates NNs, and the new algorithm is referred to as the deep MUA (DeMUA) for NMF. While the DeMUA represents the algorithm for the NMF, interestingly, the divergence is obtained from the incorporated NN. In addition, we propose theoretical guides to design the incorporated NN such that it can be interpreted as a divergence. By appropriately designing the NN, MUAs based on existing divergences with a single hyper-parameter can be represented by the DeMUA. To train the DeMUA, we applied it to audio denoising and supervised signal separation. Our experimental results show that the proposed architecture can learn the MUA and the divergences in sparse denoising and speech separation tasks and that the MUA based on generalized divergences with multiple parameters shows favorable performances on these tasks.

In this study, we aim to improve the performance of audio source separation for monaural mixture signals. For monaural audio source separation, semisupervised nonnegative matrix factorization (SNMF) can achieve higher separation performance by employing small supervised signals. In particular, penalized SNMF (PSNMF) with orthogonality penalty is an effective method. PSNMF forces two basis matrices for target and nontarget sources to be orthogonal to each other and improves the separation accuracy. However, the conventional orthogonality penalty is based on an inner product and does not affect the estimation of the basis matrix properly because of the scale indeterminacy between the basis and activation matrices in NMF. To cope with this problem, a new PSNMF with cosine similarity between the basis matrices is proposed. The experimental comparison shows the efficacy of the proposed cosine similarity penalty in supervised audio source separation.

We studied an acoustic anomaly detection system for equipments, where the outlier detection method based on recorded sounds is used. In a real environment, the SNR of the target sound against background noise is low, and there is the problem that it is necessary to catch slight changes in sound buried in noise. In this paper, we propose a system in which a sound source extraction process is provided at the preliminary stage of the outlier detection process. In the proposed system, nonnegative matrix factorization based on generalized Gaussian distribution (GGD-NMF) is used as a sound source extraction process. We evaluated the improvement of the anomaly detection performance in a low-SNR environment. In this experiment, SNR capable of detecting an anomaly was greatly improved by providing GGD-NMF for preprocessing.

Detecting community structures and analyzing temporal evolution in dynamic networks are challenging tasks to explore the inherent characteristics of the complex networks. In this paper, we propose a semi-supervised evolutionary clustering model based on symmetric nonnegative matrix factorization to detect communities in dynamic networks, named sEC-SNMF. We use the results of community partition at the previous time step as the priori information to modify the current network topology, then smooth-out the evolution of the communities and reduce the impact of noise. Furthermore, we introduce a community transition probability matrix to track and analyze the temporal evolutions. Different from previous algorithms, our approach does not need to know the number of communities in advance and can deal with the situation in which the number of communities and nodes varies over time. Extensive experiments on synthetic datasets demonstrate that the proposed method is competitive and has a superior performance.

The estimation of the matrix rank of harmonic components of a music spectrogram provides some useful information, e.g., the determination of the number of basis vectors of the matrix-factorization-based algorithms, which is required for the automatic music transcription or in post-processing. In this work, we develop an algorithm based on Stein's unbiased risk estimator (SURE) algorithm with the matrix factorization model. The noise variance required for the SURE algorithm is estimated by suppressing the harmonic component via median filtering. An evaluation performed using the MIDI-aligned piano sounds (MAPS) database revealed an average estimation error of -0.26 (standard deviation: 4.4) for the proposed algorithm.

Due to the need to protect personal information and the impracticality of exhaustive data collection, there is increasing need to deal with datasets with various levels of granularity, such as user-individual data and user-group data. In this study, we propose a new method for jointly analyzing multiple datasets with different granularity. The proposed method is a probabilistic model based on nonnegative matrix factorization, which is derived by introducing latent variables that indicate the high-resolution data underlying the low-resolution data. Experiments on purchase logs show that the proposed method has a better performance than the existing methods. Furthermore, by deriving an extension of the proposed method, we show that the proposed method is a new fundamental approach for analyzing datasets with different granularity.

In this letter, we propose a new blind source separation method, independent low-rank matrix analysis based on generalized Kullback-Leibler divergence. This method assumes a time-frequency-varying complex Poisson distribution as the source generative model, which yields convex optimization in the spectrogram estimation. The experimental evaluation confirms the proposed method's efficacy.

In this work, two new proposed NMF models are developed for facial expression recognition. They are called maximum volume constrained nonnegative matrix factorization (MV_NMF) and maximum volume constrained graph nonnegative matrix factorization (MV_GNMF). They achieve sparseness from a larger simplicial cone constraint and the extracted features preserve the topological structure of the original images.

Nonnegative Matrix Factorization (NMF) with sparseness and smoothness constraints has attracted increasing attention. When these properties are considered, NMF is usually formulated as an optimization problem in which a linear combination of an approximation error term and some regularization terms must be minimized under the constraint that the factor matrices are nonnegative. In this paper, we focus our attention on the error measure based on the Euclidean distance and propose a new iterative method for solving those optimization problems. The proposed method is based on the Hierarchical Alternating Least Squares (HALS) algorithm developed by Cichocki et al. We first present an example to show that the original HALS algorithm can increase the objective value. We then propose a new algorithm called the Gauss-Seidel HALS algorithm that decreases the objective value monotonically. We also prove that it has the global convergence property in the sense of Zangwill. We finally verify the effectiveness of the proposed algorithm through numerical experiments using synthetic and real data.

Community detection is an important task in the social network analysis field. Many detection methods have been developed; however, they provide little semantic interpretation for the discovered communities. We develop a framework based on joint matrix factorization to integrate network topology and node content information, such that the communities and their semantic labels are derived simultaneously. Moreover, to improve the detection accuracy, we attempt to make the community relationships derived from two types of information consistent. Experimental results on real-world networks show the superior performance of the proposed method and demonstrate its ability to semantically annotate communities.

In multi-view social networks field, a flexible Nonnegative Matrix Factorization (NMF) based framework is proposed which integrates multi-view relation data and feature data for community discovery. Benefit with a relaxed pairwise regularization and a novel orthogonal regularization, it outperforms the-state-of-art algorithms on five real-world datasets in terms of accuracy and NMI.

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm is developed to approximate the RLS-based online NMF algorithm with low complexity. The proposed algorithm is evaluated in terms of audio source separation, and the results show that the performance of the proposed algorithms are superior to that of the conventional online NMF algorithm with significantly reduced complexity.

Nonnegative component representation (NCR) is a mid-level representation based on nonnegative matrix factorization (NMF). Recently, it has attached much attention and achieved encouraging result for action recognition. In this paper, we propose a novel hierarchical dictionary learning strategy (HDLS) for NMF to improve the performance of NCR. Considering the variability of action classes, HDLS clusters the similar classes into groups and forms a two-layer hierarchical class model. The groups in the first layer are disjoint, while in the second layer, the classes in each group are correlated. HDLS takes account of the differences between two layers and proposes to use different dictionary learning methods for this two layers, including the discriminant class-specific NMF for the first layer and the discriminant joint dictionary NMF for the second layer. The proposed approach is extensively tested on three public datasets and the experimental results demonstrate the effectiveness and superiority of NCR with HDLS for large-scale action recognition.

Unsupervised spoken unit discovery or zero-source speech recognition is an emerging research topic which is important for spoken document analysis of languages or dialects with little human annotation. In this paper, we extend our earlier joint training framework for unsupervised learning of discrete density HMM to continuous density HMM (CDHMM) and apply it to spoken unit discovery. In the proposed recipe, we first cluster a group of Gaussians which then act as initializations to the joint training framework of nonnegative matrix factorization and semi-continuous density HMM (SCDHMM). In SCDHMM, all the hidden states share the same group of Gaussians but with different mixture weights. A CDHMM is subsequently constructed by tying the top-N activated Gaussians to each hidden state. Baum-Welch training is finally conducted to update the parameters of the Gaussians, mixture weights and HMM transition probabilities. Experiments were conducted on word discovery from TIDIGITS and phone discovery from TIMIT. For TIDIGITS, units were modeled by 10 states which turn out to be strongly related to words; while for TIMIT, units were modeled by 3 states which are likely to be phonemes.

Nonnegative matrix factorization (NMF) is an unsupervised technique to represent nonnegative data as linear combinations of nonnegative bases, which has shown impressive performance for source separation. However, its source separation performance degrades when one signal can also be described well with the bases for the interfering source signals. In this paper, we propose a discriminative NMF (DNMF) algorithm which exploits the reconstruction error for the interfering signals as well as the target signal based on target bases. The objective function for training the bases is constructed so as to yield high reconstruction error for the interfering source signals while guaranteeing low reconstruction error for the target source signals. Experiments show that the proposed method outperformed the standard NMF and another DNMF method in terms of both the perceptual evaluation of speech quality score and signal-to-distortion ratio in various noisy environments.

In this letter, we address monaural source separation based on supervised nonnegative matrix factorization (SNMF) and propose a new penalized SNMF. Conventional SNMF often degrades the separation performance owing to the basis-sharing problem. Our penalized SNMF forces nontarget bases to become different from the target bases, which increases the separated sound quality.

This paper presents a method for learning an overcomplete, nonnegative dictionary and for obtaining the corresponding coefficients so that a group of nonnegative signals can be sparsely represented by them. This is accomplished by posing the learning as a problem of nonnegative matrix factorization (NMF) with maximization of the incoherence of the dictionary and of the sparsity of coefficients. By incorporating a dictionary-incoherence penalty and a sparsity penalty in the NMF formulation and then adopting a hierarchically alternating optimization strategy, we show that the problem can be cast as two sequential optimal problems of quadratic functions. Each optimal problem can be solved explicitly so that the whole problem can be efficiently solved, which leads to the proposed algorithm, i.e., sparse hierarchical alternating least squares (SHALS). The SHALS algorithm is structured by iteratively solving the two optimal problems, corresponding to the learning process of the dictionary and to the estimating process of the coefficients for reconstructing the signals. Numerical experiments demonstrate that the new algorithm performs better than the nonnegative K-SVD (NN-KSVD) algorithm and several other famous algorithms, and its computational cost is remarkably lower than the compared algorithms.

In this paper, a geometric source separation system using nonnegative matrix factorization (NMF) is proposed. The adaptive beamformer is the best method for geometric source separation, but it suffers from a “target signal cancellation” problem in multi-path situations. We modified the HALS-NMF algorithm for decomposition into bases, and developed an interference suppression module in order to cancel the interference bases. A performance comparison between the proposed and subband GSC-RLS algorithm using a MATLAB® simulation was executed; the results show that the proposed system is robust in multi-path situations.

Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multi-sensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the alpha and beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-determined (over-complete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for N-th order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multi-layer hierarchical NMF approach [3].