Hierarchical Nonlinear Factor Analysis and Topographic Maps
Zoubin Ghahramani and Geoffrey Hinton
Department of Computer Science
University of Toronto
Canada
Abstract
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.
Download [Postscript] [pdf]
in Jordan, M.I, Kearns, M.J., and Solla, S.A. Advances in Neural
Information Processing Systems 10. MIT Press: Cambridge, MA.
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