Fusion and inference from multiple and massive disparate data sources - therequirement for our most challenging data analysis problems and the goal of ourmost ambitious statistical pattern recognition methodologies - -has many andvaried aspects which are currently the target of intense research anddevelopment. One aspect of the overall challenge is manifold matching -identifying embeddings of multiple disparate data spaces into the samelow-dimensional space where joint inference can be pursued. We investigate thismanifold matching task from the perspective of jointly optimizing the fidelityof the embeddings and their commensurability with one another, with a specificstatistical inference exploitation task in mind. Our results demonstrate whenand why our joint optimization methodology is superior to either version ofseparate optimization. The methodology is illustrated with simulations and anapplication in document matching.
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