The distributed, partial, and conditional Karhunen-Loeve transforms

The Karhunen-Loeve transform (KLT) is a key element of many signal processing tasks, including approximation, compression, and classification. Many recent applications involve distributed signal processing where it is not generally possible to apply the KLT to the signal; the KLT must be approximated in a distributed fashion. Investigations were carried out on the distributed approximations to the KLT. First, explicit solutions to special cases were presented including a partial KLT, a conditional KLT, and the combination of these two special cases. These results were used to derive an algorithm that finds the best distributed approximation to the KLT. Applications of the results from sensor networks and distributed databases were discussed.