Probabilistic derivation and Multiple Canonical Correlation Analysis

We review a new method of performing Canonical Correlation Analysis (CCA) with Artificial Neural Networks. We have previously [5, 4] compared its capabilities with standard statistical methods on simple data sets where the maximum correlations are given by linear filters. In this paper, we extend the method by implementing a very precise set of constraints which allow multiple correlations to be found at once. We demonstrate the network’s capabilities on the standard random dot stereogram data set. We also re-derive the learning rules from a probabilistic perspective and then by use of a specific prior on the weights, simplify the algorithm. We demonstrate its capabilities on a standard problem [2]which is an abstraction of the Random Dot Stereogram matching problem and show how a second layer network using Factor Analysis can be used to combine the results of the CCA network to obtain higher order information.