Paper available on exploritory projection pursuit.

[Roland Baddeley]

The following paper is available on the web at

http://www.mrc-bbc.ox.ac.uk/~rjb/

It has been accepted for publication in Network.	

TITLE: Searching for filters with ``interesting'' output
distributions: an uninteresting direction to explore?

Abstract

It has been proposed that the receptive fields of neurons in V1 are
optimised to generate ``sparse'', Kurtotic, or ``interesting'' output
probability distributions
\cite{Barlow92,Barlow94,Field94,Intrator91,Intrator92d}.  We
investigate the empirical evidence for this further and argue that
filters can produce ``interesting'' output distributions simply
because natural images have variable local intensity variance. If the
proposed filters have zero D.C., then the probability distribution of
filter outputs (and hence the output Kurtosis) is well predicted
simply from these effects of variable local variance. This suggests
that finding filters with high output Kurtosis does not necessarily
signal interesting image structure.

It is then argued that finding filters that maximise output Kurtosis
generates filters that are incompatible with observed physiology. In
particular the optimal difference--of--Gaussian (DOG) filter should
have the smallest possible scale, an on--centre off--surround cell
should have a negative D.C., and that the ratio of centre width to
surround width should approach unity. This is incompatible with the
physiology. Further, it is also predicted that oriented filters should
always be oriented in the vertical direction, and of all the filters
tested, the filter with the highest output Kurtosis has the lowest
signal to noise (the filter is simply the difference of two
neighbouring pixels). Whilst these observations are not incompatible
with the brain using a sparse representation, it does argue that
little significance should be placed on finding filters with highly
Kurtotic output distributions. It is therefore argued that other
constraints are required in order to understand the development of
visual receptive fields.

FILE: http://www.mrc-bbc.ox.ac.uk/ftp/users/rjb/rjb_kur.ps.Z

	
-- 
Roland Baddeley
Research Fellow, MRC Centre for Cognitive Neuroscience
University of Oxford
 
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