Maximum and minimum likelihood Hebbian learning for exploratory projection pursuit

In this paper, we review an extension of the learning rules in a Principal Component Analysis network which has been derived to be optimal for a specific probability density function. We note that this probability density function is one of a family of pdfs and investigate the learning rules formed in order to be optimal for several members of this family. We show that, whereas we have previously (Lai et al., 2000; Fyfe and MacDonald, 2002) viewed the single member of the family as an extension of PCA, it is more appropriate to view the whole family of learning rules as methods of performing Exploratory Projection Pursuit. We illustrate this on both artificial and real data sets.