A study of data fusion in Cayley graphs G(sn,pn)

In this paper, we examine a method for the fusion of ranked data in the context of a Cayley graph. We investigate this Cayley graph model for optimization of fusion by rank combination. We outline a method of data fusion by combination of weighted rankings. Information systems are represented as nodes in a Cayley graph. Our goal is to determine a metric of diversity and performance in this graph in order to build a model for optimizing fusion by rank combination. We use the Kendall distance between nodes in the Cayley graph of the symmetric group S_n as a measure of performance. In doing so we demonstrate that in S₆ there is a quadratic relationship between the weights of the fusion of two information systems and the performance of the fusion in our abstract space. From such a relationship we propose a set of functions for extrapolating optimal fusion weights in the symmetric group S_n.