Quantifying Discriminability between NMF Bases

Non-negative matrix factorization (NMF) is a powerful approach to single channel audio source separation. In a supervised setting, NMF is first applied to train the basis spectra of each sound source. At test time, NMF is applied to the spectrogram of a mixture signal using the pretrained spectra. The source signals can then be separated out using a Wiener filter. A typical way to train the basis spectra of each source is to minimize the objective function of NMF. However, the basis spectra obtained in this way do not ensure that the separated signal will be optimal at test time due to the inconsistency between the objective functions for training and separation (Wiener filtering). To address this, a framework called discriminative NMF (DNMF) has recently been proposed. In in this work a multiplicative update algorithm was proposed for the basis training, however one drawback is that the convergence is not guaranteed. To overcome this drawback, this paper proposes using a majorization-minimization principle to develop a convergence-guaranteed algorithm for DNMF. Experimental results showed that the proposed algorithm outperformed standard NMF and DNMF using a multiplicative update algorithm as regards both the signal-to-distortion and signal-to-interference ratios.

The objective of single-channel source separation is to accurately recover source signals from mixtures. Non-negative matrix factorization (NMF) is a popular approach for this task, yet previous NMF approaches have not optimized directly this objective, despite some efforts in this direction. Our paper introduces discriminative training of the NMF basis functions such that, given the coefficients obtained on a mixture, a desired source is optimally recovered. We approach this optimization by generalizing the model to have separate analysis and reconstruction basis functions. This generalization frees us to optimize reconstruction objectives that incorporate the filtering step and SNR performance criteria. A novel multiplicative update algorithm is presented for the optimization of the reconstruction basis functions according to the proposed discriminative objective functions. Results on the 2nd CHiME Speech Separation and Recognition Challenge task indicate significant gains in source-to-distortion ratio with respect to sparse NMF, exemplar-based NMF, as well as a previously proposed discriminative NMF criterion.

Non-negative subspace feature representation for few-shot learning in medical imaging

Non-negative Matrix Factorization (NMF) is among the most popular subspace methods widely used in a variety of pattern recognition applications. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis criteria and achieves an efficient decomposition of the provided data to its salient parts has been proposed. An extension of this work specialized for classification, optimized using projected gradients in order to ensure converge to a stationary limit point, resulted in a more efficient method of the latter approach. Assuming multimodality of the underlying data samples distribution and incorporating clustering discriminant inspired constraints into the NMF decomposition cost function, resulted in the Subclass Discriminant NMF algorithm which found to outperform both approaches under real life settings. In this work we review all these methods in the context of various pattern recognition problems using facial images.

The methods introduced so far regarding discriminant non-negative matrix factorization (DNMF) do not guarantee convergence to a stationary limit point. In order to remedy this limitation, a novel DNMF method is presented that uses projected gradients. The proposed algorithm employs some extra modifications that make the method more suitable for classification tasks. The usefulness of the proposed technique to frontal face verification and facial expression recognition problems is demonstrated.

Discriminative nonnegative matrix factorization with autoencoder structure for unsupervised feature selection

Deep learning is a popular method for monaural source separation, and especially for extracting a singing voice from a single-channel song. However, deep learning-based source separation ignores the geometrical structure of the input data. This work develops a novel approach to source separation that is based on non-negative matrix factorization (NMF) and deep recurrent neural networks (DRNN) with a locality-preserving constraint. First, NMF was used to learn patterns from training data. The learned patterns are linearly combined with the output of DRNN. Second, a locality-preserving constraint is developed to exploit the inner-structure of the input data in the DRNN learning process. Experimental results obtained using the MIR-1K dataset reveal that the proposed algorithm outperforms the baselines.

Monaural speech separation is a very challenging task, for the limitation of information from only a single channel. After Deep Learning is introduced into the monaural speech separation, researchers have made great improvement on the separation performance with the progress of different network structure. Among various of separation methods, especially methods with masking-based training targets, the influence of phase were always neglected during the separation process. In this paper, the impact of phase on monaural speech separation is discussed and proved using theoretical explanations and examples. New training targets in complement of existing magnitude training targets were trained through neural network methods to compensate for phase of target in order to achieve better separation performance. Comparisons and evaluations show that using phase compensation in separation boosts separation effect to a certain degree.

In this paper, we present RT-GCC-NMF: a real-time (RT), two-channel blind speech enhancement algorithm that combines the non-negative matrix factorization (NMF) dictionary learning algorithm with the generalized cross-correlation (GCC) spatial localization method. Using a pre-learned universal NMF dictionary, RT-GCC-NMF operates in a frame-by-frame fashion by associating individual dictionary atoms to target speech or background interference based on their estimated time-delay of arrivals. We evaluate RT-GCC-NMF on two-channel mixtures of speech and real-world noise from the signal separation and evaluation campaign (SiSEC). We demonstrate that this approach generalizes to new speakers, acoustic environments, and recording setups from very little training data, and outperforms all but one of the algorithms from the SiSEC challenge in terms of overall perceptual evaluation methods for audio source separation (PEASS) scores and compares favourably to the ideal binary mask baseline. Over a wide range of input signal to noise ratios (SNRs), we show that this approach simultaneously improves the PEASS and SNR-based blind source separation eval objective quality metrics as well as the short-time objective intelligibility (STOI) and extended STOI objective speech intelligibility metrics. A flexible, soft masking function in the space of NMF activation coefficients offers real-time control of the tradeoff between interference suppression and target speaker fidelity. Finally, we use an asymmetric short-time Fourier transform to reduce the inherent algorithmic latency of RT-GCC-NMF from 64 ms to 2 ms with no loss in performance. We demonstrate that latencies within the tolerable range for hearing aids are possible on current hardware platforms.

This article describes a computationally-efficient blind source separation (BSS) method based on the independence, low-rankness, and directivity of the sources. A typical approach to BSS is unsupervised learning of a probabilistic model that consists of a source model representing the time-frequency structure of source images and a spatial model representing their inter-channel covariance structure. Building upon the low-rank source model based on nonnegative matrix factorization (NMF), which has been considered to be effective for inter-frequency source alignment, multichannel NMF (MNMF) assumes source images to follow multivariate complex Gaussian distributions with unconstrained full-rank spatial covariance matrices (SCMs). An effective way of reducing the computational cost and initialization sensitivity of MNMF is to restrict the degree of freedom of SCMs. While a variant of MNMF called independent low-rank matrix analysis (ILRMA) severely restricts SCMs to rank-1 matrices under an idealized condition that only directional and less-echoic sources exist, we restrict SCMs to jointly-diagonalizable yet full-rank matrices in a frequency-wise manner, resulting in FastMNMF1. To help inter-frequency source alignment, we then propose FastMNMF2 that shares the directional feature of each source over all frequency bins. To explicitly consider the directivity or diffuseness of each source, we also propose rank-constrained FastMNMF that enables us to individually specify the ranks of SCMs. Our experiments showed the superiority of FastMNMF over MNMF and ILRMA in speech separation and the effectiveness of the rank constraint in speech enhancement.

This paper presents a statistical method of audio source separation based on a nonparametric Bayesian extension of probabilistic latent component analysis (PLCA). A major approach to audio source separation is to use nonnegative matrix factorization (NMF) that approximates the magnitude spectrum of a mixture signal at each frame as the weighted sum of fewer source spectra. Another approach is to use PLCA that regards the magnitude spectrogram as a two-dimensional histogram of "sound quanta" and classifies each quantum into one of sources. While NMF has a physically-natural interpretation, PLCA has been used successfully for music signal analysis. To enable PLCA to estimate the number of sources, we propose Dirichlet process PLCA (DP-PLCA) and derive two kinds of learning methods based on variational Bayes and collapsed Gibbs sampling. Unlike existing learning methods for nonparametric Bayesian NMF based on the beta or gamma processes (BP-NMF and GaP-NMF), our sampling method can efficiently search for the optimal number of sources without truncating the number of sources to be considered. Experimental results showFed that DP-PLCA is superior to GaP-NMF in terms of source number estimation.

Upgrading Sparse NMF algorithm for blind source separation through Adaptive Parameterized Hybrid Kernel based approach

This paper presents a convex geometry (CG)-based method for blind separation of nonnegative sources. First, the unaccessible source matrix is normalized to be column-sum-to-one by mapping the available observation matrix. Then, its zero-samples are found by searching the facets of the convex hull spanned by the mapped observations. Considering these zero-samples, a quadratic cost function with respect to each row of the unmixing matrix, together with a linear constraint in relation to the involved variables, is proposed. Upon which, an algorithm is presented to estimate the unmixing matrix by solving a classical convex optimization problem. Unlike the traditional blind source separation (BSS) methods, the CG-based method does not require the independence assumption, nor the uncorrelation assumption. Compared with the BSS methods that are specifically designed to distinguish between nonnegative sources, the proposed method requires a weaker sparsity condition. Provided simulation results illustrate the performance of our method.

Nonnegative matrix factorization (NMF) is an effective speech separation approach of extracting discriminative components of different speaker. However, traditional NMF focuses only on the additive combination of the components and ignores the dependencies of speeches. Convolutive NMF (CNMF) captures the dependencies of speeches by overlapping components and achieves better separation performance. NMF and CNMF learn dictionaries for speakers in the absence of mixture, and thus they are unable to get enough information to learn dictionaries accurately when testing speeches are available. To handle this problem, transductive NMF (TNMF) is proposed which simultaneously utilizes speech of each speaker and mixture to learn more meaningful features of speakers, and significantly boost speech separation. CNMF addresses the dependencies of speech signals while it ignores the positive effect of mixtures in learning dictionaries. TNMF emphasizes the transductive learning of dictionaries while it fails to consider dependencies of speeches. This paper proposes transductive convolutive NMF (TCNMF) to overcome the deficiencies of both CNMF and TNMF. Experimental results show that our method makes significant improvement compared to aforementioned NMF-based methods.

In this paper, we propose a novel algorithm for monaural blind source separation based on non-negative matrix factorization (NMF). A shortcoming of most source separation methods is the need for training data for each individual source. The algorithm proposed in this paper is able separate sources even when there is no training data for the individual sources. The algorithm makes use of models trained on mixed signals and uses training data where more than one source is active at the time. This makes the algorithm applicable to situations where recordings of the individual sources are unavailable. The key idea is to construct a structure matrix that indicates where each source is active, and we prove that this structure matrix, combined with a uniqueness assumption, is sufficient to ensure that results are equivalent to training on isolated sources. Our theoretical findings is backed up by simulations on music data that show that the proposed algorithm trained on mixed recordings performs as well as existing NMF source separation methods trained on solo recordings.