Review of Data Structures for Computationally Efficient Nearest-Neighbour Entropy Estimators for Large Systems with Periodic Boundary Conditions

TL;DR

This paper reviews and compares methods for efficiently estimating entropy in large, continuous systems with periodic boundaries, highlighting the advantages of Vantage Point trees over traditional solutions.

Contribution

It introduces Vantage Point trees as a versatile alternative for entropy estimation in systems with both large size and periodic boundary conditions.

Findings

Vantage Point trees effectively handle large system sizes.

They address issues with periodic boundary conditions.

Compared to existing methods, they improve performance and correctness.

Abstract

Information theoretic quantities are extremely useful in discovering relationships between two or more data sets. One popular method---particularly for continuous systems---for estimating these quantities is the nearest neighbour estimators. When system sizes are very large or the systems have periodic boundary conditions issues with performance and correctness surface, however solutions are known for each problem. Here we show that these solutions are inappropriate in systems that simultaneously contain both features and discuss a lesser known alternative solution involving Vantage Point trees that is capable of addressing both issues.