Convolutive Non-negative Matrix Factorization Research Articles

Alternating Direction Method of Multipliers for Convolutive Non-Negative Matrix Factorization.

Non-negative matrix factorization (NMF) has become a popular method for learning interpretable patterns from data. As one of the variants of standard NMF, convolutive NMF (CNMF) incorporates an extra time dimension to each basis, known as convolutive bases, which is well suited for representing sequential patterns. Previously proposed algorithms for solving CNMF use multiplicative updates which can be derived by either heuristic or majorization-minimization (MM) methods. However, these algorithms suffer from problems, such as low convergence rates, difficulty to reach exact zeroes during iterations and prone to poor local optima. Inspired by the success of alternating direction method of multipliers (ADMMs) on solving NMF, we explore variable splitting (i.e., the core idea of ADMM) for CNMF in this article. New closed-form algorithms of CNMF are derived with the commonly used β -divergences as optimization objectives. Experimental results have demonstrated the efficacy of the proposed algorithms on their faster convergence, better optima, and sparser results than state-of-the-art baselines.

Layered Convolutive Nonnegative Matrix Factorization for Speech Separation

Abstract Nonnegative matrix factorization (NMF) has attracted significant attention for its good performance in single-channel speech separation. The improved algorithms of NMF have become research hotspots. Layered NMF (LNMF), an improved algorithm, can express the source signal more accurately for its multilayer structure. However, LNMF sometimes performs poorly because it ignores the short-term correlation of speech signals. Based on LNMF and the advantages of Convolutive NMF (CNMF), we proposed a Layered Convolutive NMF(LCNMF) algorithm for single-channel speech separation. The LCNMF corporates the multilayer structure into the NMF and expands the convolution of the top-level NMF model. During the training, NMF is used to learn the non-top-level basis matrices, and CNMF is used to learn the top-level basis matrix, then combined with each single-layer of basis matrix. During the prediction, CNMF is used to separate mixed signals. The results on the dataset MIK-1K showed that LCNMF outperformed NMF and LNMF for separating the mixture of single-channel speech signals. LCNMF improved by 0.019, 1.049dB, 1.305dB, and 0.851dB on average compared with NMF, and improved by 0.007, 0.172dB, 0.090dB, and 0.366dB on average compared with LNMF in sort-term objective intelligibility (STOI), Source to Distortion Ratio (SDR), Source to Interference Ratio (SIR) and Source to Artifacts Ratio (SAR)

Orthogonality-Constrained CNMF-Based Noise Reduction with Reduced Degradation of Biological Sound.

The number of deaths due to cardiovascular and respiratory diseases is increasing annually. Cardiovascular diseases with high mortality rates, such as strokes, are frequently caused by atrial fibrillation without subjective symptoms. Chronic obstructive pulmonary disease is another condition in which early detection is difficult owing to the slow progression of the disease. Hence, a device that enables the early diagnosis of both diseases is necessary. In our previous study, a sensor for monitoring biological sounds such as vascular and respiratory sounds was developed and a noise reduction method based on semi-supervised convolutive non-negative matrix factorization (SCNMF) was proposed for the noisy environments of users. However, SCNMF attenuated part of the biological sound in addition to the noise. Therefore, this paper proposes a novel noise reduction method that achieves less distortion by imposing orthogonality constraints on the SCNMF. The effectiveness of the proposed method was verified experimentally using the biological sounds of 21 subjects. The experimental results showed an average improvement of 1.4 dB in the signal-to-noise ratio and 2.1 dB in the signal-to-distortion ratio over the conventional method. These results demonstrate the capability of the proposed approach to measure biological sounds even in noisy environments.

An Improved Unsupervised Single-Channel Speech Separation Algorithm for Processing Speech Sensor Signals

As network supporting devices and sensors in the Internet of Things are leaping forward, countless real-world data will be generated for human intelligent applications. Speech sensor networks, an important part of the Internet of Things, have numerous application needs. Indeed, the sensor data can further help intelligent applications to provide higher quality services, whereas this data may involve considerable noise data. Accordingly, speech signal processing method should be urgently implemented to acquire low-noise and effective speech data. Blind source separation and enhancement technique refer to one of the representative methods. However, in the unsupervised complex environment, in the only presence of a single-channel signal, many technical challenges are imposed on achieving single-channel and multiperson mixed speech separation. For this reason, this study develops an unsupervised speech separation method CNMF+JADE, i.e., a hybrid method combined with Convolutional Non-Negative Matrix Factorization and Joint Approximative Diagonalization of Eigenmatrix. Moreover, an adaptive wavelet transform-based speech enhancement technique is proposed, capable of adaptively and effectively enhancing the separated speech signal. The proposed method is aimed at yielding a general and efficient speech processing algorithm for the data acquired by speech sensors. As revealed from the experimental results, in the TIMIT speech sources, the proposed method can effectively extract the target speaker from the mixed speech with a tiny training sample. The algorithm is highly general and robust, capable of technically supporting the processing of speech signal acquired by most speech sensors.

A Provably Correct and Robust Algorithm for Convolutive Nonnegative Matrix Factorization

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an NMF with additional sequential structure. This model is useful in a number of applications, such as audio source separation and neural sequence identification. While a number of heuristic algorithms have been proposed to solve CNMF, to the best of our knowledge no provably correct algorithms have been developed. We present an algorithm that takes advantage of the NMF model underlying CNMF and exploits existing algorithms for separable NMF to provably find the unique solution (up to permutation and scaling) under separability-like conditions. Our approach guarantees the solution in low noise settings, and runs in polynomial time. We illustrate its effectiveness on synthetic datasets, and on a singing bird audio sequence.

Impulse Feature Extraction of Bearing Faults Based on Convolutive Nonnegative Matrix Factorization

The detection of bearing faults is of great significance for the stable operation of rotating machinery. Apart from detection by analysing the vibration response, another powerful strategy is to extract the periodic impulse excitation directly induced by faults, which efficiently eliminates the influence of the transmission path and noise. Typical methods of this strategy include maximum correlated kurtosis deconvolution (MCKD) and multipoint optimal minimum entropy deconvolution (MOMEDA). However, these deconvolution methods based on maximizing a certain measurement index are still insufficient at finding the correct fault period directly because of the interference of noise components. To effectively extract the periodic impulse excitation from the vibration response, a new impulse feature extraction method from the vibration spectrogram based on convex hull convolutive nonnegative matrix factorization (CH-CNMF) is proposed. As the spectrogram intuitively reveals the time and frequency information of the impulse response generated by the fault excitation, according to the decomposition characteristics of CH-CNMF, the time-frequency structure of the impulse response is represented by the basis tensor, while the weight matrix corresponds to the impulse excitation. Meanwhile, autocorrelation is adopted to enhance the periodic impulse excitation. Finally, based on power spectral entropy and first-order correlated kurtosis, the optimal periodic pulse can be selected from the autocorrelation curves of the weight matrix. Both numerical simulation and experimental verifications on bearings indicate that the proposed method can eliminate the influence of random shock excitations and directly attain the periodic impulse for the source of the bearing fault, and that its extraction effectiveness outperforms MOMEDA.

Feature Extraction Based on the Non-Negative Matrix Factorization of Convolutional Neural Networks for Monitoring Domestic Activity With Acoustic Signals

In this paper, a feature extraction method is proposed based on the non-negative matrix factorization (NMF) for classifiers for monitoring domestic activities with acoustic signals. Most of the classifiers of the acoustic signals use data-independent spectral features (e.g., log-Mel spectrum and Mel-frequency cepstral coefficients). Recently, some novel feature extraction methods have been researched, including convolution-NMF-based features combined with K-means clustering. This study proposes an enhanced NMF-based feature extraction method that is inspired by the NMF-based noise reduction algorithm. The proposed method independently estimates the frequency basis matrix for each class, and then cascades the basis matrices to form the entire frequency bases, where the acoustic signal is transformed to the proposed feature by estimating the temporal basis matrix with the trained frequency bases. In addition, this study proposes a data augmentation method for the proposed feature that is inspired by the “mix and shuffle” method for audio waveforms. In order to evaluate the proposed system, which consists of the proposed NMF-based feature and the convolutional-neural-network-based classifier, some evaluations were performed using the Detection and Classification of Acoustic Scenes and Events (DCASE) 2018 Task 5 - Monitoring of Domestic Activities Based on Multi-channel Acoustics - Database. The results showed that the proposed system has comparable performance to that of state-of-the-art algorithms and that it has enhanced the F1-score performance of 6%-12% in comparison with the conventional NMF-based feature extraction method that is based on convolutional NMF and K-means clustering.

Automatic liver tumour segmentation in CT combining FCN and NMF-based deformable model

ABSTRACT Automatic liver tumour segmentation is an important step towards digital medical research, clinical diagnosis and therapy planning. However, the existence of noise, low contrast and heterogeneity make the automatic liver tumour segmentation remaining an open challenge. In this work, we focus on a novel automatic method to segment liver tumour in abdomen images from CT scans using fully convolutional networks (FCN) and non-negative matrix factorization (NMF) based deformable model. We train the FCN for semantic liver and tumour segmentation using preprocessed training data by BM3D. The segmented liver and tumour regions of FCN are used as ROI and initialization for the NMF-based tumour refinement, respectively. We refine the surfaces of tumours using a 3D deformable model which derived from NMF and driven by local cumulative spectral histograms (LCSH). The refinement is designed to obtain a smoother, more accurate and natural liver tumour surface. Experiments on 11 clinical datasets demonstrated that the proposed segmentation method achieves satisfactory results.

Blind DOA Estimation in a Reverberant Environment Based on Hybrid Initialized Multichannel Deep 2-D Convolutional NMF With Feedback Mechanism

The accuracy performance of traditional direction of arrival (DOA) estimation algorithms is seriously affected by the reverberation. Considering the advantage of the sparse characteristic of speech signal in time-frequency (T-F) domain, this paper presents a new blind DOA estimation method based on integrated deep learning and convolutional non-negative matrix factorization (NMF). Firstly, mathematic models of microphone array and room impulse response are built. In addition, we extracted blindly initialization parameters of 2-D convolutional NMF using k-means clustering algorithm and singular value decomposition algorithm, which can be used to accurately estimate the main components of desired sound source in the reverberation environment of multi-path propagation. Moreover, the feedback mechanism is introduced into deep 2-D convolutional NMF and correlation coefficient between the signal decomposed by NMF and the signal to be decomposed is used to select the best separated signal for DOA estimation, which make the separation algorithm simpler and more efficient. Finally, test of orthogonality of projected subspaces (TOPS) algorithm is used to validate the DOA estimation capability of this algorithm. Compared with the unprocessed reverberation speech, the estimation error is reduced, which shows that the proposed algorithm can effectively improve the estimation accuracy of DOA estimation when the received signals are in a reverberant environment.

Unsupervised Learning of Spatiotemporal Interictal Discharges in Focal Epilepsy

Interictal epileptiform discharges are an important biomarker for localization of focal epilepsy, especially in patients who undergo chronic intracranial monitoring. Manual detection of these pathophysiological events is cumbersome, but is still superior to current rule-based approaches in most automated algorithms. To develop an unsupervised machine-learning algorithm for the improved, automated detection and localization of interictal epileptiform discharges based on spatiotemporal pattern recognition. We decomposed 24 h of intracranial electroencephalography signals into basis functions and activation vectors using non-negative matrix factorization (NNMF). Thresholding the activation vector and the basis function of interest detected interictal epileptiform discharges in time and space (specific electrodes), respectively. We used convolutive NNMF, a refined algorithm, to add a temporal dimension to basis functions. The receiver operating characteristics for NNMF-based detection are close to the gold standard of human visual-based detection and superior to currently available alternative automated approaches (93% sensitivity and 97% specificity). The algorithm successfully identified thousands of interictal epileptiform discharges across a full day of neurophysiological recording and accurately summarized their localization into a single map. Adding a temporal window allowed for visualization of the archetypal propagation network of these epileptiform discharges. Unsupervised learning offers a powerful approach towards automated identification of recurrent pathological neurophysiological signals, which may have important implications for precise, quantitative, and individualized evaluation of focal epilepsy.

A Bayesian approach to convolutive nonnegative matrix factorization for blind speech dereverberation

Abstract When a signal is recorded in an enclosed room, it typically gets affected by reverberation. This degradation represents a problem when dealing with audio signals, particularly in the field of speech signal processing, such as automatic speech recognition. Although there are some approaches to deal with this issue that are quite satisfactory under certain conditions, constructing a method that works well in a general context still poses a significant challenge. In this article, we propose a Bayesian approach based on convolutive nonnegative matrix factorization that uses prior distributions in order to impose certain characteristics over the time-frequency components of the restored signal and the reverberant components. An algorithm for implementing the method is described and tested. Comparisons of the results against those obtained with state-of-the-art methods are presented, showing significant improvement.

Phase‐Mapper: Accelerating Materials Discovery with AI

From the stone age to the bronze, iron, and modern silicon ages, the discovery and characterization of new materials has always been instrumental to humanity's development and progress. With the current pressing need to address sustainability challenges and find alternatives to fossil fuels, we look for solutions in the development of new materials that will allow for renewable energy. To discover materials with the required properties, materials scientists can perform high‐throughput materials discovery, which includes rapid synthesis and characterization via X‐ray diffraction (XRD) of thousands of materials. A central problem in materials discovery, the phase map identification problem, involves the determination of the crystal structure of materials from materials composition and structural characterization data. This analysis is traditionally performed mainly by hand, which can take days for a single material system. In this work we present Phase‐Mapper, a solution platform that tightly integrates XRD experimentation, AI problem solving, and human intelligence for interpreting XRD patterns and inferring the crystal structures of the underlying materials. Phase‐Mapper is compatible with any spectral demixing algorithm, including our novel solver, AgileFD, which is based on convolutive nonnegative matrix factorization (NMF). AgileFD allows materials scientists to rapidly interpret XRD patterns, and incorporates constraints to capture prior knowledge about the physics of the materials as well as human feedback. With our system, materials scientists have been able to interpret previously unsolvable systems of XRD data at the Department of Energy's Joint Center for Artificial Photosynthesis, including the Nb‐Mn‐V oxide system, which led to the discovery of new solar light absorbers and is provided as an illustrative example of AI‐enabled high‐throughput materials discovery.

Improving the evaluation of soundscape variability via blind source separation

Evaluation of soundscape variability is essential for acoustic-based biodiversity monitoring. To study biodiversity change, many researchers tried to quantify the complexity of biological sound. However, the analysis of biological sound remains difficult because the soundscape is made up of multiple sound sources. To facilitate the acoustic analysis, we have applied non-negative matrix factorization (NMF) to separate different sound sources in an unsupervised manner. NMF is a self-learning algorithm which factorizes a non-negative matrix as a basis matrix and an encoding matrix. Based on the periodicity information learned from the encoding matrix, biological chorus and the other noise sources can be efficiently separated. Besides, vocalizations of different species can also be separated by using the encoding information learned from multiple layers of NMF and convolutive NMF. In this presentation, we will demonstrate the application of NMF-based blind source separation in the analysis of long-duration field recordings. Our preliminary results suggest that NMF-based blind source separation can effectively recognize biological and non-biological sounds without any learning database. It can also accurately separate different vocalizing animals and improve acoustic-based biodiversity monitoring in a noisy environment.

Phase-Mapper: An AI Platform to Accelerate High Throughput Materials Discovery

High-throughput materials discovery involves the rapid synthesis, measurement, and characterization of many different but structurally related materials. A central problem in materials discovery, the phase map identification problem, involves the determination of the crystal structure of materials from materials composition and structural characterization data. We present Phase-Mapper, a novel solution platform that allows humans to interact with both the data and products of AI algorithms, including the incorporation of human feedback to constrain or initialize solutions. Phase-Mapper is compatible with any spectral demixing algorithm, including our novel solver, AgileFD, which is based on convolutive non-negative matrix factorization. AgileFD allows materials scientists to rapidly interpret XRD patterns, and can incorporate constraints to capture the physics of the materials as well as human feedback. We compare three solver variants with previously proposed methods in a large-scale experiment involving 20 synthetic systems, demonstrating the efficacy of imposing physical constraints using AgileFD. Since the deployment of Phase-Mapper at the Department of Energy’s Joint Center for Artificial Photosynthesis (JCAP), thousands of X-ray diffraction patterns have been processed and the results are yielding discovery of new materials for energy applications, as exemplified by the discovery of a new family of metal oxide solar light absorbers, among the previously unsolved Nb-Mn-V oxide system, which is provided here as an illustrative example. Phase-Mapper is also being deployed at the Stanford Synchrotron Radiation Lightsource (SSRL) to enable phase mapping on datasets in real time.

Automated Phase Mapping with AgileFD and its Application to Light Absorber Discovery in the V-Mn-Nb Oxide System.

Rapid construction of phase diagrams is a central tenet of combinatorial materials science with accelerated materials discovery efforts often hampered by challenges in interpreting combinatorial X-ray diffraction data sets, which we address by developing AgileFD, an artificial intelligence algorithm that enables rapid phase mapping from a combinatorial library of X-ray diffraction patterns. AgileFD models alloying-based peak shifting through a novel expansion of convolutional nonnegative matrix factorization, which not only improves the identification of constituent phases but also maps their concentration and lattice parameter as a function of composition. By incorporating Gibbs' phase rule into the algorithm, physically meaningful phase maps are obtained with unsupervised operation, and more refined solutions are attained by injecting expert knowledge of the system. The algorithm is demonstrated through investigation of the V-Mn-Nb oxide system where decomposition of eight oxide phases, including two with substantial alloying, provides the first phase map for this pseudoternary system. This phase map enables interpretation of high-throughput band gap data, leading to the discovery of new solar light absorbers and the alloying-based tuning of the direct-allowed band gap energy of MnV2O6. The open-source family of AgileFD algorithms can be implemented into a broad range of high throughput workflows to accelerate materials discovery.

Automatic Model Order Selection for Convolutive Non-Negative Matrix Factorization

Automatic Model Order Selection for Convolutive Non-Negative Matrix Factorization

Speech Enhancement Under Low SNR Conditions Via Noise Estimation Using Sparse and Low-Rank NMF with Kullback–Leibler Divergence

A key stage in speech enhancement is noise estimation which usually requires prior models for speech or noise or both. However, prior models can sometimes be difficult to obtain. In this paper, without any prior knowledge of speech and noise, sparse and low-rank nonnegative matrix factorization (NMF) with Kullback-Leibler divergence is proposed to noise and speech estimation by decomposing the input noisy magnitude spectrogram into a low-rank noise part and a sparse speech-like part. This initial unsupervised speech-noise estimation allows us to set a subsequent regularized version of NMF or convolutional NMF to reconstruct the noise and speech spectrogram, either by estimating a speech dictionary on the fly (categorized as unsupervised approaches) or by using a pre-trained speech dictionary on utterances with disjoint speakers (categorized as semi-supervised approaches). Information fusion was investigated by taking the geometric mean of the outputs from multiple enhancement algorithms. The performance of the algorithms were evaluated on five metrics (PESQ, SDR, SNR, STOI, and OVERALL) by making experiments on TIMIT with 15 noise types. The geometric means of the proposed unsupervised approaches outperformed spectral subtraction (SS), minimum mean square estimation (MMSE) under low input SNR conditions. All the proposed semi-supervised approaches showed superiority over SS and MMSE and also obtained better performance than the state-of-the-art algorithms which utilized a prior noise or speech dictionary under low SNR conditions.

Speech Intelligibility Enhancement Using Convolutive Non-negative Matrix Factorization with Noise Prior

We propose a convolutive non-negative matrix factorization method to improve the intelligibility of speech signal in the context of adverse noise environment. The noise bases are prior learned with Non-negative Matrix Factorization (NMF) algorithm. A modified convolutive NMF with sparse constraint is then derived to extract speech bases from noisy speech. The divergence function is selected as an objective function to get a multiplicative update of speech base and its corresponding weight. The weights of prior learned noise bases are also updated in the update rule. Listening experiments are conducted to assess the intelligibility performance of speech synthesized using the proposed algorithm. Experimental results indicate that the proposed method is very effective to improve the intelligibility of the noisy speech in various noise contexts and it outperforms conventional algorithms.

Motor control primitives arising from a dynamical systems model of vocal tract articulation

We have previously presented a computational approach to derive interpretable movement primitives from speech articulation data using a convolutive Nonnegative Matrix Factorization with sparseness constraints (cNMFsc) technique (Ramanarayanan et al., Interspeech 2011; Ramanarayanan et al., J. Acoust. Soc. Am. 134(2), in press). However, it is not clear whether finding such a dictionary of primitives can be useful for speech motor control, particularly in finding a low-dimensional subspace for such control. In this paper, we examine this possibility in two steps. First, we use the iterative Linear Quadratic Gaussian (iLQG) algorithm to derive a set of control inputs to a dynamical systems model of the vocal tract that produces a desired movement sequence. Second, we use the cNMFsc algorithm to find a small dictionary of control input “primitives'' that can be used to drive said dynamical systems model of the vocal tract to produce the desired range of articulatory movement. We show, using both qualitative ...

Unsupervised learning of phonemes of whispered speech in a noisy environment based on convolutive non-negative matrix factorization

This paper focuses on the development of an algorithm that can be optimized for a specific acoustic environment to improve the intelligibility of whispered speech. A new convolutive non-negative matrix factorization (NMF) algorithm is proposed to extract phoneme bases from noisy whispered speech with the noise bases from prior learning; these noise bases are obtained from training using the conventional non-negative matrix factorization. The divergence function with a sparseness constraint term is selected as the objective function in the developed algorithm to obtain multiplicative update rules of the phoneme base matrix and the corresponding weight matrix. The weights of the noise bases from prior learning are also updated in the phoneme learning stage. Listening experiments were conducted to assess the intelligibility performance of speech synthesized using the proposed algorithm. The experimental results indicate that the proposed algorithm is very effective for improving the intelligibility of whispers in various noise contexts, and it outperforms conventional algorithms.