Probabilistic Derivation and Multiple Canonical Correlation Analysis

摘要

We review a new method of performing Canonical Correlation Analysis (CCA) with Artificial Neural Networks. We have previously 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 stere-ogram 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 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.