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

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.