The surge in availability of genomic data holds promise for enabling determination of genetic causes of observed individual traits, with applications to problems such as discovery of the genetic roots of phenotypes, be they molecular phenotypes such as gene expression or metabolite concentrations, or complex phenotypes such as diseases. However, the growing sizes of these datasets and the quadratic, cubic or higher scaling characteristics of the relevant algorithms pose a serious computational challenge necessitating use of leadership scale computing. In this paper we describe a new approach to performing vector similarity metrics calculations, suitable for parallel systems equipped with graphics processing units (GPUs) or Intel Xeon Phi processors. Our primary focus is the Proportional Similarity metric applied to Genome Wide Association Studies (GWAS) and Phenome Wide Association Studies (PheWAS). We describe the implementation of the algorithms on accelerated processors, methods used for eliminating redundant calculations due to symmetries, and techniques for efficient mapping of the calculations to many-node parallel systems. Results are presented demonstrating high per-node performance and parallel scalability with rates of more than five quadrillion elementwise comparisons achieved per second on the ORNL Titan system. In a companion paper we describe corresponding techniques applied to calculations of the Custom Correlation Coefficient for comparative genomics applications.