Faster Parallel Exact Density Peaks Clustering

TL;DR

This paper introduces fast, parallel algorithms for exact Density Peaks Clustering, significantly improving scalability and speed over previous methods, enabling large-scale data analysis in various fields.

Contribution

It presents novel parallel algorithms for exact DPC with optimal work and low span, outperforming existing methods in speed and scalability.

Findings

Achieves $O( ext{log} n ext{log} ext{log} n)$ span with priority search kd-trees.

Realizes up to 13169x speedup over previous parallel algorithms.

Maintains work-efficiency matching the best sequential algorithms.

Abstract

Clustering multidimensional points is a fundamental data mining task, with applications in many fields, such as astronomy, neuroscience, bioinformatics, and computer vision. The goal of clustering algorithms is to group similar objects together. Density-based clustering is a clustering approach that defines clusters as dense regions of points. It has the advantage of being able to detect clusters of arbitrary shapes, rendering it useful in many applications. In this paper, we propose fast parallel algorithms for Density Peaks Clustering (DPC), a popular version of density-based clustering. Existing exact DPC algorithms suffer from low parallelism both in theory and in practice, which limits their application to large-scale data sets. Our most performant algorithm, which is based on priority search kd-trees, achieves $O(\log n\log\log n)$ span (parallel time complexity) for a data set of $n$ points. Our algorithm is also work-efficient, achieving a work complexity matching the best existing sequential exact DPC algorithm. In addition, we present another DPC algorithm based on a Fenwick tree that makes fewer assumptions for its average-case complexity to hold. We provide optimized implementations of our algorithms and evaluate their performance via extensive experiments. On a 30-core machine with two-way hyperthreading, we find that our best algorithm achieves a 10.8--13169x speedup over the previous best parallel exact DPC algorithm. Compared to the state-of-the-art parallel approximate DPC algorithm, our best algorithm achieves a 1.5--4206x speedup, while being exact.