Sparse, complex-valued representations of natural sounds learned with phase and amplitude continuity priors
This work addresses a specific issue in auditory signal processing for researchers in computational neuroscience and machine learning, offering an incremental improvement by adapting existing methods with new priors.
The paper tackled the problem of learning phase-invariant sparse representations from natural sounds, which previously lacked this property, by introducing priors that bias basis functions towards phase invariance. The result showed that prior-based basis functions achieved performance comparable to unconstrained sparse coding while explicitly representing phase as a temporal shift.
Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns phase invariant features which closely resemble receptive fields of complex cells in the visual cortex. Features trained on natural sounds however, rarely reveal phase invariance and capture other aspects of the data. This observation is a starting point of the present work. As its first contribution, it provides an analysis of natural sound statistics by means of learning sparse, complex representations of short speech intervals. Secondly, it proposes priors over the basis function set, which bias them towards phase-invariant solutions. In this way, a dictionary of complex basis functions can be learned from the data statistics, while preserving the phase invariance property. Finally, representations trained on speech sounds with and without priors are compared. Prior-based basis functions reveal performance comparable to unconstrained sparse coding, while explicitely representing phase as a temporal shift. Such representations can find applications in many perceptual and machine learning tasks.