A Comparison of Empirical Tree Entropies

TL;DR

This paper systematically compares various empirical entropy measures for trees, including theoretical analysis and experimental validation on real XML data, to understand their differences and applications.

Contribution

It provides a comprehensive comparison of different tree entropy notions, combining theoretical insights with empirical evaluation on real-world XML datasets.

Findings

Different entropy measures capture distinct structural properties of trees.

Empirical results highlight the practical differences between entropy notions.

The study guides the choice of entropy measures for tree data analysis.

Abstract

Whereas for strings, higher-order empirical entropy is the standard entropy measure, several different notions of empirical entropy for trees have been proposed in the past, notably label entropy, degree entropy, conditional versions of the latter two, and empirical entropy of trees (here, called label-shape entropy). In this paper, we carry out a systematic comparison of these entropy measures. We underpin our theoretical investigations by experimental results with real XML data.