Research Project (2001-2003)
Slow feature analysis yields a rich repertoire of complex cell
properties
Pietro Berkes and Laurenz Wiskott
In the project Slow feature Analysis:
Unsupervised learning of invariances I have shown that the slowness
principle can be used to learn translation and other invariances for whole
objects in a hierarchical network model. However, the retina was only
one-dimensional and the stimuli were very artificial. In this project we
wanted to move to more natural stimuli, but for simplicity we first
considered only one layer rather than a whole hierarchical network. Thus
we applied slow feature analysis (SFA) to quasi-natural image sequences
(derived from static
natural images) and obtained units that were (inhomogeneous) quadratic
forms (functions). We compared these with complex cells in primary visual
cortex of primates and found that they have many properties in common.
Obtaining the results was fairly straightforward and a matter of weeks,
really. Analyzing the units (quadratic forms) we had gotten and comparing
them with physiological results was the hard part. For the analysis we
have partly used traditional methods known from experiments and partly have
developed new methods, see the project
Analysis of inhomogeneous quadratic forms as receptive fields. The
units we have obtained
- have optimal
stimuli that look like Gabor wavelets,
- are insensitive to
the phase of the wavelets,
- have a similar set of orientation tuning curves as complex cells, see Figure 1,
- show sometimes end- and side-inhibition, see Figure 2, and
- are sometimes direction selective, see Figure 1.
Thus, our units are remarkably similar to complex cells in primary visual
cortex. What we don't get is much of a localization of the receptive
fields. They usually cover the whole image patch we are simulating.
Figure 1: Orientation tuning curves of complex cells (left, black
lines) and SFA units (right, blue lines) in comparison. The response of
the cells/units is plotted in radial direction as a function of the
orientation of a grating shown to the cell/unit. Drifting gratings were
used and responses 180° apart come from the same grating orientation but
different drifting direction. Thus, the cell/unit at the bottom left is
direction selective while the others are not.
Figure 2: As one moves a grating into a receptive field of a
complex cell (left) the response typically increases. There are some cells
where the response starts to decrease again at some point (middle). Such
cells are called end- or side-inhibited, depending on the orientation of
the grating relative to the direction of movement. Some of our SFA units
show exactly that same bahavior (right). The level to which the response
dropes varies greatly within each class of cells/units so that the
differences seen here are not significant.
Interestingly, the results that we get do not depend on the higher-order
statistics of the images. We get virtually identical results if we start
with colored noise images. What matters are the transformations that we
apply to the static images to generate the image sequences. The most
important one is translation.
See also the project page "Slowness as
a computational principle for the visual cortex" by Pietro Berkes, which
includes Matlab code for performing the simulations of this
project. Python source code for SFA and several other learning algorithms
written by Pietro Berkes and Tiziano Zito is available at http://mdp-toolkit.sourceforge.net/.
Relevant Publications:
Black colored reference are the principal
ones. Gray colored references are listed for the
sake of completeness only. They contain little additional
information. .ps-files are optimized for printing; .pdf-files are
optimized for viewing at the computer.
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Wiskott, L., Franzius, M., Berkes, P., and Sprekeler, H. (15. September 2007).
Is slowness a learning principle of the visual system?
Proc. 39th Annual European Brain and Behaviour Society, EBBS,
Triest, Italy, September 15-19, eds. Alessandro Treves et al., special
issue of Neural
Plasticity, Article ID 23250, pp. 14-15 (abstract).
(bibtex, abstract.html)
-
Wiskott, L., Sprekeler, H., and Berkes, P. (29. March 2007).
Towards an analytical derivation of complex cell receptive field properties.
Proc. 7th Meeting of the
German Neuroscience Society - 31st Göttingen Neurobiology Conference,
Göttingen, March 29 - April 1, S12-2 (abstract).
(bibtex, abstract.html)
-
Wiskott, L. (1. February 2006).
Is slowness a learning principle of visual cortex?
Proc. Japan-Germany Symposium on Computational Neuroscience, Wako, Saitama, Japan, February 1-4, publ. RIKEN Brain Science Institute, p. 25, (abstract).
(bibtex, abstract.html)
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Berkes, P. and Wiskott, L. (20. July 2005).
Slow feature analysis yields a rich repertoire of complex cell properties.
Journal of Vision, 5(6):579-602, http://journalofvision.org/5/6/9/, doi:10.1167/5.6.9.
(bibtex, abstract.html, paper, paper.pdf, paper.pdf)
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Berkes, P. and Wiskott, L. (28. May 2004).
Slow feature analysis yields a rich repertoire of complex-cell properties.
Proc. Early Cognitive Vision Workshop, Isle Of Skye, Scotland, May 28-June 1.
(bibtex, abstract.html)
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Wiskott, L. and Berkes, P. (2003).
Is slowness a learning principle of the visual cortex?
Proc. Jahrestagung der Deutschen Zoologischen Gesellschaft 2003, Berlin, June 9-13, special issue of
Zoology, 106(4):373-382.
(bibtex, abstract.html)
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Berkes, P. and Wiskott, L. (12. June 2003).
Slow feature analysis yields a rich repertoire of complex-cell properties.
Proc. 29th Göttingen Neurobiology Conference, Göttingen, June 12-15 (abstract).
(bibtex, abstract.html)
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Berkes, P. and Wiskott, L. (4. March 2003).
Slow feature analysis yields a rich repertoire of complex-cell
properties.
Cognitive Sciences EPrint Archive
(CogPrints) 2804, http://cogprints.org/2804/.
(bibtex, abstract.html, paper, paper.pdf, paper.ps, results.shtml)
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Berkes, P. and Wiskott, L. (27. August 2002).
Applying slow feature analysis to image sequences yields a rich
repertoire of complex cell properties.
Proc. Int'l Conf. on Artificial Neural Networks, ICANN'02, Madrid, August 27-30, ed. José R. Dorronsoro, in series Lecture Notes in Computer Science, publ. Springer-Verlag, pp. 81-86.
(bibtex, abstract.html, paper.pdf, results.shtml)
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Wiskott, L. and Berkes, P. (18. April 2002).
Is slowness a principle for the emergence of complex cells in
primary visual cortex?
Proc. Berlin Neuroscience Forum 2002, Bad Liebenwalde, April 18-20, ed. Helmut Kettenmann, publ. Max-Delbrück-Centrum für Molekulare Medizin (MDC), Berlin, p. 43, (abstract).
(bibtex, abstract.html)
Related Projects:
setup April 24, 2002; updated April 3, 2008
Laurenz Wiskott, http://www.neuroinformatik.ruhr-uni-bochum.de/PEOPLE/wiskott/