Skip Nav Destination
Close Modal
Update search
NARROW
Format
Journal
TocHeadingTitle
Date
Availability
1-2 of 2
H. Attias
Close
Follow your search
Access your saved searches in your account
Would you like to receive an alert when new items match your search?
Sort by
Journal Articles
Publisher: Journals Gateway
Neural Computation (1999) 11 (4): 803–851.
Published: 15 May 1999
Abstract
View article
PDF
We introduce the independent factor analysis (IFA) method for recovering independent hidden sources from their observed mixtures. IFA generalizes and unifies ordinary factor analysis (FA), principal component analysis (PCA), and independent component analysis (ICA), and can handle not only square noiseless mixing but also the general case where the number of mixtures differs from the number of sources and the data are noisy. IFA is a two-step procedure. In the first step, the source densities, mixing matrix, and noise covariance are estimated from the observed data by maximum likelihood. For this purpose we present an expectation-maximization (EM) algorithm, which performs unsupervised learning of an associated probabilistic model of the mixing situation. Each source in our model is described by a mixture of gaussians; thus, all the probabilistic calculations can be performed analytically. In the second step, the sources are reconstructed from the observed data by an optimal nonlinear estimator. A variational approximation of this algorithm is derived for cases with a large number of sources, where the exact algorithm becomes intractable. Our IFA algorithm reduces to the one for ordinary FA when the sources become gaussian, and to an EM algorithm for PCA in the zero-noise limit. We derive an additional EM algorithm specifically for noiseless IFA. This algorithm is shown to be superior to ICA since it can learn arbitrary source densities from the data. Beyond blind separation, IFA can be used for modeling multidimensional data by a highly constrained mixture of gaussians and as a tool for nonlinear signal encoding.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1998) 10 (6): 1373–1424.
Published: 15 August 1998
Abstract
View article
PDF
We derive a novel family of unsupervised learning algorithms for blind separation of mixed and convolved sources. Our approach is based on formulating the separation problem as a learning task of a spatiotemporal generative model, whose parameters are adapted iteratively to minimize suitable error functions, thus ensuring stability of the algorithms. The resulting learning rules achieve separation by exploiting high-order spatiotemporal statistics of the mixture data. Different rules are obtained by learning generative models in the frequency and time domains, whereas a hybrid frequency-time model leads to the best performance. These algorithms generalize independent component analysis to the case of convolutive mixtures and exhibit superior performance on instantaneous mixtures. An extension of the relative-gradient concept to the spatiotemporal case leads to fast and efficient learning rules with equivariant properties. Our approach can incorporate information about the mixing situation when available, resulting in a “semiblind” separation method. The spatiotemporal redundancy reduction performed by our algorithms is shown to be equivalent to information-rate maximization through a simple network. We illustrate the performance of these algorithms by successfully separating instantaneous and convolutive mixtures of speech and noise signals.