Covariance matrix computations with federated databases

We present an approach to computing the covariance matrix with federated databases. This is a useful tool in principal components analysis and other pattern recognition methodologies. The databases are implicitly joined by a set of arbitrary shared attributes. We compute the covariance matrix exactly rather than an approximation. We show the correctness of the approach with minimal data exchanged. Each node shares the composition of the global result. We assume that the values for shared attributes are allowed to be shared. Each node is allowed to ask for information and it will be truthfully given the summary it requests. We provide no proof of theorems or lemmas due to lack of space.