Maximum and minimum likelihood Hebbian rules for exploratory projection pursuit

We develop an algorithm which identifies a low dimensional basis of high dimensional data in such a way that the interesting structure in the high dimensional data is optimally preserved. We do this by extending a principal component analysis network so that instead of minimising mean squared error, the network minimises other functions of the error between the projections of the data and the original data set. We do this by considering the residuals from the network in a probabilistic perspective and show that the original PCA network is optimal for Gaussian data. We relate the new rules to the statistical method of exploratory projection pursuit and show it working on both real and artificial data.