38,609 research outputs found
Stochastic trapping in a solvable model of on-line independent component analysis
Previous analytical studies of on-line Independent Component Analysis (ICA)
learning rules have focussed on asymptotic stability and efficiency. In
practice the transient stages of learning will often be more significant in
determining the success of an algorithm. This is demonstrated here with an
analysis of a Hebbian ICA algorithm which can find a small number of
non-Gaussian components given data composed of a linear mixture of independent
source signals. An idealised data model is considered in which the sources
comprise a number of non-Gaussian and Gaussian sources and a solution to the
dynamics is obtained in the limit where the number of Gaussian sources is
infinite. Previous stability results are confirmed by expanding around optimal
fixed points, where a closed form solution to the learning dynamics is
obtained. However, stochastic effects are shown to stabilise otherwise unstable
sub-optimal fixed points. Conditions required to destabilise one such fixed
point are obtained for the case of a single non-Gaussian component, indicating
that the initial learning rate \eta required to successfully escape is very low
(\eta = O(N^{-2}) where N is the data dimension) resulting in very slow
learning typically requiring O(N^3) iterations. Simulations confirm that this
picture holds for a finite system.Comment: 17 pages, 3 figures. To appear in Neural Computatio
Dynamical Component Analysis (DyCA) and its application on epileptic EEG
Dynamical Component Analysis (DyCA) is a recently-proposed method to detect
projection vectors to reduce the dimensionality of multi-variate deterministic
datasets. It is based on the solution of a generalized eigenvalue problem and
therefore straight forward to implement. DyCA is introduced and applied to EEG
data of epileptic seizures. The obtained eigenvectors are used to project the
signal and the corresponding trajectories in phase space are compared with PCA
and ICA-projections. The eigenvalues of DyCA are utilized for seizure detection
and the obtained results in terms of specificity, false discovery rate and miss
rate are compared to other seizure detection algorithms.Comment: 5 pages, 4 figures, accepted for IEEE International Conference on
Acoustics, Speech and Signal Processing (ICASSP) 201
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