Independent Component Analysis and its Extensions as Models of
	 Natural Image Statistics and the Visual Cortex
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			 Aapo Hyvarinen
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		 Neural Networks Research Centre
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		Helsinki University of Technology
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		       3pm, Friday, July 5
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		    CNS classroom (Meyer 815)
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Abstract: A fundamental approach in computional visual neuroscience is to
design a statistical generative model of the observed signals.  Such a
model can be used to explain properties of neurons in primary sensory
areas.  A recently developed generative model is independent component
analysis (ICA) in which statistically independent components generate the
signals by linear superposition. The coefficients in the linear
superposition are unknown, and so are the values of the independent
components.  Both of these are to be estimated from the observed signals.  
When ICA is applied to image windows, the independent components are given
by the outputs of filters that resemble wavelets or Gabor filters. In
other words, the filters are oriented, localized and band-pass.  ICA of
images is thus closely related to wavelet methods, but it has the
important benefit that the transformation is determined solely by the
statistical properties of the data. From a neurophysiological viewpoint,
ICA filters closely resemble simple cells in the primary visual cortex.
More recently, I have introduced extensions of ICA that lead to emergence
of further properties of visual neurons: topography and complex cell
receptive fields. These are based on modelling dependencies of the
"independent" components estimated by ICA; in fact they are not
independent but only as independent as possible by a linear
transformation. Thus, the approach shows promise to be able to model
neural properties even higher then V1 on the visual pathway.