Title :
Gaussian Processes for Underdetermined Source Separation
Author :
Liutkus, Antoine ; Badeau, Roland ; Richard, Gäel
Author_Institution :
CNRS LTCI, Telecom ParisTech, Paris, France
fDate :
7/1/2011 12:00:00 AM
Abstract :
Gaussian process (GP) models are very popular for machine learning and regression and they are widely used to account for spatial or temporal relationships between multivariate random variables. In this paper, we propose a general formulation of underdetermined source separation as a problem involving GP regression. The advantage of the proposed unified view is first to describe the different underdetermined source separation problems as particular cases of a more general framework. Second, it provides a flexible means to include a variety of prior information concerning the sources such as smoothness, local stationarity or periodicity through the use of adequate covariance functions. Third, given the model, it provides an optimal solution in the minimum mean squared error (MMSE) sense to the source separation problem. In order to make the GP models tractable for very large signals, we introduce framing as a GP approximation and we show that computations for regularly sampled and locally stationary GPs can be done very efficiently in the frequency domain. These findings establish a deep connection between GP and nonnegative tensor factorizations (NTF) with the Itakura-Saito distance and lead to effective methods to learn GP hyperparameters for very large and regularly sampled signals.
Keywords :
Gaussian processes; covariance matrices; frequency-domain analysis; matrix decomposition; mean square error methods; regression analysis; source separation; tensors; GP approximation; GP hyperparameter; GP model; GP regression; Gaussian process; Itakura-Saito distance; MMSE; covariance function; frequency domain; minimum mean squared error; nonnegative tensor factorization; optimal solution; source separation; Approximation methods; Computational modeling; Covariance matrix; Frequency modulation; Gaussian processes; Source separation; Cokriging; Gaussian processes (GP); kriging; nonnegative matrix factorization (NMF); nonnegative tensor factorizations (NTF); probability theory; regression; source separation;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2011.2119315