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The fixed-point algorithm and the underlying contrast functions have a
number of desirable properties when
compared with existing methods for ICA.
-
The convergence is cubic (or at least quadratic), under the assumption
of the ICA data model (for a proof, see the convergence proof in the
Appendix). This is in contrast
to gradient descent methods, where the convergence is only linear. This
means a very fast convergence, as has been confirmed by simulations
and experiments on
real data (see Section 5).
-
Contrary to gradient-based algorithms, there are no step size
parameters to choose (in the original fixed-point algorithm). This
means that the algorithm is easy to use. Even in the
stabilized version, reasonable values for the step size parameter are
very easy to choose.
-
The algorithm finds directly independent components of (practically) any
non-Gaussian distribution using any nonlinearity g. This is in
contrast to many algorithms,
where some estimate of the probability distribution function has to be
first available, and the nonlinearity must be chosen accordingly.
- The performance of the method can be optimized by choosing a
suitable nonlinearity g. In particular, one can obtain algorithms
that are robust and/or of minimum variance.
- The independent
components can be estimated one by one, which is roughly equivalent to
doing projection pursuit.
-
The fixed-point algorithm inherits most of the advantages of neural
algorithms: It is parallel, distributed,
computationally simple, and requires little memory space. Stochastic
gradient methods seem to be preferable only if fast
adaptivity in a changing environment is required.
Next: Simulation and experimental results
Up: Fixed-point algorithms for ICA
Previous: Fixed-point algorithm for several
Aapo Hyvarinen
1999-04-23