Blind separation of nonlinear mixtures by variational Bayesian learning

Authors:
Antti Honkela;Harri Valpola;Alexander Ilin;Juha Karhunen
Affiliations:
Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland;Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9203, FI-02015 TKK, Finland;Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland;Adaptive Informatics Research Centre, Helsinki University of Technology, P.O. Box 5400, FI-02015 TKK, Finland
Venue:
Digital Signal Processing
Year:
2007

Citing 21
Cited 2

Probabilistic reasoning in intelligent systems: networks of plausible inference

Probabilistic reasoning in intelligent systems: networks of plausible inference
Multilayer feedforward networks are universal approximators

Neural Networks
Nonlinear component analysis as a kernel eigenvalue problem

Neural Computation
Nonlinear independent component analysis: existence and uniqueness results

Neural Networks
Independent factor analysis

Neural Computation
Local minima and plateaus in hierarchical structures of multilayer perceptions

Neural Networks
Mean-field approaches to independent component analysis

Neural Computation
Variational mixture of Bayesian independent component analyzers

Neural Computation
Accelerating Cyclic Update Algorithms for Parameter Estimation by Pattern Searches

Neural Processing Letters
Variational Bayesian learning of ICA with missing data

Neural Computation
MISEP - Linear and nonlinear ICA based on mutual information

The Journal of Machine Learning Research
Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation

The Journal of Machine Learning Research
Variational Message Passing

The Journal of Machine Learning Research
Separating a Real-Life Nonlinear Image Mixture

The Journal of Machine Learning Research
On the Effect of the Form of the Posterior Approximation in Variational Learning of ICA Models

Neural Processing Letters
Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models

The Journal of Machine Learning Research
Neural Networks: A Comprehensive Foundation (3rd Edition)

Neural Networks: A Comprehensive Foundation (3rd Edition)
Building Blocks for Variational Bayesian Learning of Latent Variable Models

The Journal of Machine Learning Research
Separation of nonlinear image mixtures by denoising source separation

ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Source separation in post-nonlinear mixtures

IEEE Transactions on Signal Processing
Variational learning and bits-back coding: an information-theoretic view to Bayesian learning

IEEE Transactions on Neural Networks

Approximate Riemannian Conjugate Gradient Learning for Fixed-Form Variational Bayes

The Journal of Machine Learning Research
Recurrent networks for separating extractable-target nonlinear mixtures. Part II. Blind configurations

Signal Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Blind separation of sources from nonlinear mixtures is a challenging and often ill-posed problem. We present three methods for solving this problem: an improved nonlinear factor analysis (NFA) method using a multilayer perceptron (MLP) network to model the nonlinearity, a hierarchical NFA (HNFA) method suitable for larger problems and a post-nonlinear NFA (PNFA) method for more restricted post-nonlinear mixtures. The methods are based on variational Bayesian learning, which provides the needed regularisation and allows for easy handling of missing data. While the basic methods are incapable of recovering the correct rotation of the source space, they can discover the underlying nonlinear manifold and allow reconstruction of the original sources using standard linear independent component analysis (ICA) techniques.