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

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

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