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Hierarchical Non-linear Factor Analysis and Topographic Maps

 Zoubin Ghahramani and Geoffrey E. Hinton
  
 

Abstract:
We first describe a hierarchical, generative model that can be viewed as a non-linear generalization 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 non-adaptive lateral connections into the generative model. The model extracts a sparse, distributed, hierarchical representation of depth from simplified random-dot stereograms and the localized disparity detectors in the first hidden layer form a topographic map.

 
 


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