GTM: the generative topographic mapping
Neural Computation
Modern mathematical methods for physicists and engineers
Modern mathematical methods for physicists and engineers
A Maximum Likelihood Approach to Nonlinear Blind Source Separation
ICANN '97 Proceedings of the 7th International Conference on Artificial Neural Networks
Learning Overcomplete Representations
Neural Computation
A post nonlinear geometric algorithm for independent component analysis
Digital Signal Processing
Source separation in post-nonlinear mixtures
IEEE Transactions on Signal Processing
Sparse Bayesian learning for basis selection
IEEE Transactions on Signal Processing
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
Subset selection in noise based on diversity measure minimization
IEEE Transactions on Signal Processing
Nonlinear blind source separation using a radial basis function network
IEEE Transactions on Neural Networks
Nonlinear blind source separation using kernels
IEEE Transactions on Neural Networks
Variational learning and bits-back coding: an information-theoretic view to Bayesian learning
IEEE Transactions on Neural Networks
Blind source separation with dynamic source number using adaptive neural algorithm
Expert Systems with Applications: An International Journal
Underdetermined blind separation of non-sparse sources using spatial time-frequency distributions
Digital Signal Processing
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Nonlinear signal separation and underdetermined signal separation have received much attention in blind signal separation literature. However, neither of them can solve the situation where both nonlinear and underdetermined characteristics exist at the same time. In this paper, a new learning algorithm based on Bayesian statistics is proposed to solve the separation problem of the blind nonlinear underdetermined mixtures. We suppose that the observations are post-nonlinear mixtures of the sources and the number of observations is less than the number of sources. Due to the characteristics of Bayesian statistics, the generalized Gaussian distribution model is utilized to approximate the prior probability distribution of the source signals and the mixing variables. Formal derivation shows that the source signals, mixing matrix and nonlinear functions can be estimated through an iterative technique based on alternate optimization. The nonlinear mismatch problem is also considered by applying a multilayer perceptron with a typical least square error problem. Simulations have been given to demonstrate the effectiveness in separating signals under nonlinear and underdetermined conditions.