Parallelized Kendall's Tau Coefficient Computation via SIMD Vectorized Sorting On Many-Integrated-Core Processors

TL;DR

This paper presents a SIMD-accelerated parallel algorithm for computing Kendall's tau coefficient on many-core processors, achieving significant speedups over traditional CPU implementations.

Contribution

The paper introduces a novel SIMD vectorized sorting approach and a generic framework for symmetric all-pairs computation on many-core processors, enabling efficient Kendall's tau calculations.

Findings

Achieves two orders-of-magnitude speedup over MATLAB

Achieves three orders-of-magnitude speedup over R

Demonstrates good scalability on multiple Phis

Abstract

Pairwise association measure is an important operation in data analytics. Kendall's tau coefficient is one widely used correlation coefficient identifying non-linear relationships between ordinal variables. In this paper, we investigated a parallel algorithm accelerating all-pairs Kendall's tau coefficient computation via single instruction multiple data (SIMD) vectorized sorting on Intel Xeon Phis by taking advantage of many processing cores and 512-bit SIMD vector instructions. To facilitate workload balancing and overcome on-chip memory limitation, we proposed a generic framework for symmetric all-pairs computation by building provable bijective functions between job identifier and coordinate space. Performance evaluation demonstrated that our algorithm on one 5110P Phi achieves two orders-of-magnitude speedups over 16-threaded MATLAB and three orders-of-magnitude speedups over sequential R, both running on high-end CPUs. Besides, our algorithm exhibited rather good distributed computing scalability with respect to number of Phis. Source code and datasets are publicly available at http://lightpcc.sourceforge.net.