  Unsupervised two-view learning, or detection of dependencies between two
paired data sets, is typically done by some variant of canonical correlation
analysis (CCA). CCA searches for a linear projection for each view, such that
the correlations between the projections are maximized. The solution is
invariant to any linear transformation of either or both of the views; for
tasks with small sample size such flexibility implies overfitting, which is
even worse for more flexible nonparametric or kernel-based dependency discovery
methods. We develop variants which reduce the degrees of freedom by assuming
constraints on similarity of the projections in the two views. A particular
example is provided by a cancer gene discovery application where chromosomal
distance affects the dependencies between gene copy number and activity levels.
Similarity constraints are shown to improve detection performance of known
cancer genes.
