Survey on ICA . Technical Report, Aapo Hyvärinen, 1999. http://ww.icsi.berkeley.edu/~jagota/NCS. Outline. 2nd-order methods PCA / factor analysis Higher order methods Projection pursuit / Blind deconvolution ICA definitions criteria for identifiability relations to other methods
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Technical Report, Aapo Hyvärinen, 1999.
x = As + n
Latent variables, factors, independent components
s = f (x)
Consider only linear transformation:
s = Wx
Observe filtered version of s(t):
x(t) = s(t)*g(t)
Find filter h(t), such that
s(t) = h(t)*x(t)
Seismic: ”statistical deconvolution”
Definition 1 (General definition)
ICA of a random vector x consists of finding a linear transformation, s=Wx, so that the components, si, are as independent as possible, in the sense of maximizing some function F(s1,..,sm) that measure independence.
Definition 2 (Noisy ICA)
ICA of a random vector x consists of estimating the following model for the data:
x = As + n
where the latent variables si are assumed independent
Definition 3 (Noise-free ICA) x = As
ICA method = Objective function + Optimization algorithm