  Fusion and inference from multiple and massive disparate data sources - the
requirement for our most challenging data analysis problems and the goal of our
most ambitious statistical pattern recognition methodologies - -has many and
varied aspects which are currently the target of intense research and
development. One aspect of the overall challenge is manifold matching -
identifying embeddings of multiple disparate data spaces into the same
low-dimensional space where joint inference can be pursued. We investigate this
manifold matching task from the perspective of jointly optimizing the fidelity
of the embeddings and their commensurability with one another, with a specific
statistical inference exploitation task in mind. Our results demonstrate when
and why our joint optimization methodology is superior to either version of
separate optimization. The methodology is illustrated with simulations and an
application in document matching.
