Fusion of Disparate Information Through Joint

Most pattern recognition tasks can be abstracted to a problem of uti-lizing comparisons between objects to perform the given inference task. Often these comparisons are in the form of a distance measure or dis-similarity. The design of appropriate comparison functions for particular inference tasks is an area of extensive research, and often rests on ex-pert knowledge of the problem domain. If the data of interest come from two different sensors, or consist of very different types of data, a single dissimilarity may be inappropriate; instead, one might utilize several dis-similarities, each designed for a specific sensor or data stream. In this work we consider the problem of fusing information obtained from very different sensors or sources, encoded through the use of dissimilarity func-tions. Given n observations from source j, we have an n × n dissimilarity measure Dj, and we wish to utilize all this information in our inference. We describe several methods of utilizing these dissimilarity matrices that are based on embedding the observations into a single space. These meth-ods optimize either the fidelity (whether the distances in the embedded space match the original dissimilarities) or the commensurability (whether matched objects from different sensors are close in the embedded space) or both. We discuss the properties of these embeddings, apply the idea to a problem in network modeling, and point out some interesting areas of further research.