Hierarchical Non-linear Factor Analysis and Topographic Maps

We first describe a hierarchical, generative model that can be viewed as a nonlinear generalisation of factor analysis and can be implemented in a neural network. The model performs perceptual inferencein 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 intothe 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 organisedlocal feature detectors.