Lecture 2 : Canonical Component Analysis

Our goal is to find linear transforms for xn and yn that we can use to reduce the dimensionality of each data set to the dimension that we think the latent variable is. However, because both data sets are generated from the same latent variable, we want the transforms to be such that the transformed xs and ys are maximally covariant. Furthermore we want the transformed xs to be uncorrelated from themselves (and the same for the transformed ys).