paper: Hierarchical Factor Analysis and Topographic Maps

[Zoubin Ghahramani]

The following paper is now available at:

    ftp://ftp.cs.toronto.edu/pub/zoubin/nips97.ps.gz
    http://www.cs.toronto.edu/~zoubin

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     Hierarchical Non-linear Factor Analysis and Topographic Maps

	       Zoubin Ghahramani and Geoffrey E. Hinton
		    Department of Computer Science
			University of Toronto

We first describe a hierarchical, generative model that can be viewed
as a non-linear generalisation of factor analysis and can be
implemented in a neural network.  The model performs perceptual
inference in a probabilistically consistent manner by using top-down,
bottom-up and lateral connections. These connections can be learned
using simple rules that require only locally available information.
We then show how to incorporate lateral connections into the
generative model.  The model extracts a sparse, distributed,
hierarchical representation of depth from simplified random-dot
stereograms and the localised disparity detectors in the first hidden
layer form a topographic map. When presented with image patches from
natural scenes, the model develops topographically organised local
feature detectors.

 
  To appear in Jordan, M.I, Kearns, M.J., and Solla, S.A. Advances in
  Neural Information Processing Systems 10. MIT Press: Cambridge, MA,
  1998.