Grouping Time-varying Data for Interactive Exploration

TL;DR

This paper introduces algorithms and data structures for interactively analyzing the dynamic grouping patterns in multi-dimensional time-varying data, enabling efficient exploration across various parameters.

Contribution

It provides bounds and efficient computation methods for maximal groups in time-varying data, extending to higher dimensions and supporting interactive analysis.

Findings

Established bounds on the number of maximal groups.

Developed efficient algorithms for computing maximal groups.

Designed data structures for output-sensitive reporting of group changes.

Abstract

We present algorithms and data structures that support the interactive analysis of the grouping structure of one-, two-, or higher-dimensional time-varying data while varying all defining parameters. Grouping structures characterise important patterns in the temporal evaluation of sets of time-varying data. We follow Buchin et al. [JoCG 2015] who define groups using three parameters: group-size, group-duration, and inter-entity distance. We give upper and lower bounds on the number of maximal groups over all parameter values, and show how to compute them efficiently. Furthermore, we describe data structures that can report changes in the set of maximal groups in an output-sensitive manner. Our results hold in $\mathbb{R}^d$ for fixed $d$.