Discovering speech phones using convolutive non-negative matrix factorisation with a sparseness constraint

Discovering a representation that allows auditory data to be parsimoniously represented is useful for many machine learning and signal processing tasks. Such a representation can be constructed by Non-negative Matrix Factorisation (NMF), a method for finding parts-based representations of non-negative data. Here, we present an extension to convolutive NMF that includes a sparseness constraint, where the resultant algorithm has multiplicative updates and utilises the beta divergence as its reconstruction objective. In combination with a spectral magnitude transform of speech, this method discovers auditory objects that resemble speech phones along with their associated sparse activation patterns. We use these in a supervised separation scheme for monophonic mixtures, finding improved separation performance in comparison to classic convolutive NMF

The Diagonalized Newton Algorithm for Nonnegative Matrix Factorization

Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative data is approximated by the low-rank product of two matrices with non-negative entries. In this paper, the approximation quality is measured by the Kullback-Leibler divergence between the data and its low-rank reconstruction. The existence of the simple multiplicative update (MU) algorithm for computing the matrix factors has contributed to the success of NMF. Despite the availability of algorithms showing faster convergence, MU remains popular due to its simplicity. In this paper, a diagonalized Newton algorithm (DNA) is proposed showing faster convergence while the implementation remains simple and suitable for high-rank problems. The DNA algorithm is applied to various publicly available data sets, showing a substantial speed-up on modern hardware.Comment: 8 pages + references; International Conference on Learning Representations, 201

Robust speech recognition with spectrogram factorisation

Communication by speech is intrinsic for humans. Since the breakthrough of mobile devices and wireless communication, digital transmission of speech has become ubiquitous. Similarly distribution and storage of audio and video data has increased rapidly. However, despite being technically capable to record and process audio signals, only a fraction of digital systems and services are actually able to work with spoken input, that is, to operate on the lexical content of speech. One persistent obstacle for practical deployment of automatic speech recognition systems is inadequate robustness against noise and other interferences, which regularly corrupt signals recorded in real-world environments. Speech and diverse noises are both complex signals, which are not trivially separable. Despite decades of research and a multitude of different approaches, the problem has not been solved to a sufficient extent. Especially the mathematically ill-posed problem of separating multiple sources from a single-channel input requires advanced models and algorithms to be solvable. One promising path is using a composite model of long-context atoms to represent a mixture of non-stationary sources based on their spectro-temporal behaviour. Algorithms derived from the family of non-negative matrix factorisations have been applied to such problems to separate and recognise individual sources like speech. This thesis describes a set of tools developed for non-negative modelling of audio spectrograms, especially involving speech and real-world noise sources. An overview is provided to the complete framework starting from model and feature definitions, advancing to factorisation algorithms, and finally describing different routes for separation, enhancement, and recognition tasks. Current issues and their potential solutions are discussed both theoretically and from a practical point of view. The included publications describe factorisation-based recognition systems, which have been evaluated on publicly available speech corpora in order to determine the efficiency of various separation and recognition algorithms. Several variants and system combinations that have been proposed in literature are also discussed. The work covers a broad span of factorisation-based system components, which together aim at providing a practically viable solution to robust processing and recognition of speech in everyday situations

Underdetermined convolutive source separation using two dimensional non-negative factorization techniques

PhD ThesisIn this thesis the underdetermined audio source separation has been considered, that is, estimating the original audio sources from the observed mixture when the number of audio sources is greater than the number of channels. The separation has been carried out using two approaches; the blind audio source separation and the informed audio source separation. The blind audio source separation approach depends on the mixture signal only and it assumes that the separation has been accomplished without any prior information (or as little as possible) about the sources. The informed audio source separation uses the exemplar in addition to the mixture signal to emulate the targeted speech signal to be separated. Both approaches are based on the two dimensional factorization techniques that decompose the signal into two tensors that are convolved in both the temporal and spectral directions. Both approaches are applied on the convolutive mixture and the high-reverberant convolutive mixture which are more realistic than the instantaneous mixture. In this work a novel algorithm based on the nonnegative matrix factor two dimensional deconvolution (NMF2D) with adaptive sparsity has been proposed to separate the audio sources that have been mixed in an underdetermined convolutive mixture. Additionally, a novel Gamma Exponential Process has been proposed for estimating the convolutive parameters and number of components of the NMF2D/ NTF2D, and to initialize the NMF2D parameters. In addition, the effects of different window length have been investigated to determine the best fit model that suit the characteristics of the audio signal. Furthermore, a novel algorithm, namely the fusion K models of full-rank weighted nonnegative tensor factor two dimensional deconvolution (K-wNTF2D) has been proposed. The K-wNTF2D is developed for its ability in modelling both the spectral and temporal changes, and the spatial covariance matrix that addresses the high reverberation problem. Variable sparsity that derived from the Gibbs distribution is optimized under the Itakura-Saito divergence and adapted into the K-wNTF2D model. The tensors of this algorithm have been initialized by a novel initialization method, namely the SVD two-dimensional deconvolution (SVD2D). Finally, two novel informed source separation algorithms, namely, the semi-exemplar based algorithm and the exemplar-based algorithm, have been proposed. These algorithms based on the NMF2D model and the proposed two dimensional nonnegative matrix partial co-factorization (2DNMPCF) model. The idea of incorporating the exemplar is to inform the proposed separation algorithms about the targeted signal to be separated by initializing its parameters and guide the proposed separation algorithms. The adaptive sparsity is derived for both ii of the proposed algorithms. Also, a multistage of the proposed exemplar based algorithm has been proposed in order to further enhance the separation performance. Results have shown that the proposed separation algorithms are very promising, more flexible, and offer an alternative model to the conventional methods

Ghostbusters: A Parts-based NMF Algorithm

An exact nonnegative matrix decomposition algorithm is proposed. This is achieved by 1) Taking a nonlinear approximation of a sparse real-valued dataset at a given tolerance-to-error constraint, e; 2) Choosing an arbitrary lectic ordering on the rows or column entries; And, then 3) systematically applying a closure operator, so that all closures are selected. Assuming a nonnegative hierarchical closure structure (a Galois lattice) ensures the data has a unique ordered overcomplete dictionary representation. Parts-based constraints on these closures can then be used to specify and supervise the form of the solution. We illustrate that this approach outperforms NMF on two standard NMF datasets: it exhibits the properties described above; It is correct and exact

Real-time detection of overlapping sound events with non-negative matrix factorization

International audienceIn this paper, we investigate the problem of real-time detection of overlapping sound events by employing non-negative matrix factorization techniques. We consider a setup where audio streams arrive in real-time to the system and are decomposed onto a dictionary of event templates learned off-line prior to the decomposition. An important drawback of existing approaches in this context is the lack of controls on the decomposition. We propose and compare two provably convergent algorithms that address this issue, by controlling respectively the sparsity of the decomposition and the trade-off of the decomposition between the different frequency components. Sparsity regularization is considered in the framework of convex quadratic programming, while frequency compromise is introduced by employing the beta-divergence as a cost function. The two algorithms are evaluated on the multi-source detection tasks of polyphonic music transcription, drum transcription and environmental sound recognition. The obtained results show how the proposed approaches can improve detection in such applications, while maintaining low computational costs that are suitable for real-time

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique