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

Abstract

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.

Learning convolutive features for storage and transmission between networked sensors

“…For example, multiple observations of speech over nearby intervals of time have temporal relationships. These temporal relationships motivate the use of a convolutive generative model to extend ICA and NMF mixing models for speech [20], [16] and [21]. NMF models the sensed magnitude spectrogram V as the combination of a set of objects (single spectral features) and the activations of the each of these features in time.…”

Ghostbusters: A Parts-based NMF algorithm

“…The statistical interpretation of the first approach is maximum likelihood estimation, given linear measurements corrupted by noise -regularization may also be considered. Regularization is often used by the NMF community to encourage a parts-based decomposition [17]. For this swimmers dataset, regularization is required.…”

“…It is challenging for NMF as an overcomplete dictionary is required from a mixture of parts. Regularization is used to address this challenge: the choice of a suitable weighting term for the regularization parameter is difficult [17]. A second challenge lies in the fact that whilst the parts are binary, they are mixed synthetically with nonnegative values.…”

“…The relationship between the inter-formant frequency distances, though well-understood by the community, is not used in NMF decompositions [17]. As a result speech phones are sometimes separated into high frequency features and low frequency features, as the appropriate rank is not known, and the solution is not parts-based.…”

Non-negative matrix deconvolution in noise robust speech recognition

“…NMD has already been used successfully for sound source separation in music and speech applications [10,11].…”