The symmetric eigenvalue problem
The symmetric eigenvalue problem
Relationships between the FastICA algorithm and the rayleigh quotient iteration
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Local convergence analysis of FastICA
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Monotonic convergence of fixed-point algorithms for ICA
IEEE Transactions on Neural Networks
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In recent years, there has been an increasing interest in developing new algorithms for digital signal processing by applying and generalising existing numerical linear algebra tools. A recent result shows that the FastICA algorithm, a popular state-of-the-art method for linear Independent Component Analysis (ICA), shares a nice interpretation as a Newton type method with the Rayleigh Quotient Iteration (RQI), the latter method wellknown to the numerical linear algebra community. In this work, we develop an analogous theory of single vector iteration ICA methods. Two classes of methods are proposed for the one-unit linear ICA problem, namely, power ICA methods and inverse iteration ICA methods. By means of a scalar shift, scalar shifted versions of both power ICA method and inverse iteration ICA method are proposed and proven to be locally quadratically convergent to a correct demixing vector.