Scalable implementation of measuring distances in a Riemannian manifold based on the Fisher Information metric

This paper focuses on the scalability of the Fisher Information manifold by applying techniques of distributed computing. The main objective is to investigate methodologies to improve two bottlenecks associated with the measurement of distances in a Riemannian manifold formed by the Fisher Information metric. The first bottleneck is the quadratic increase in the number of pairwise distances. The second is the computation of global distances, approximated through a fully connected network of the observed pairwise distances, where the challenge is the computation of the all sources shortest path (ASSP). The scalable implementation for the pairwise distances is performed in Spark. The scalable global distance computations are addressed by applying the Dijkstra algorithm (SSSP) sequentially on two proposed networks based on prototypes that approximate the manifold. The proposed solutions are compared with a single-machine implementation in Matlab with experiments showing the first bottleneck solution is faster in Spark, but the distributed solutions for the second bottleneck is slower. Therefore, our conclusion is that the most appropriate method is a hybrid approach, where in terms of runtime and scalability a hybrid approach performs best; running the distributed method and the single-machine approach to solve bottleneck one then two, respectively.