Nearest Embedded and Embedding Self-Nested Trees

TL;DR

This paper introduces a new, more efficient algorithm for computing self-nested tree approximations, improving plant self-similarity measurement by providing closer and more computationally feasible models.

Contribution

A novel algorithm for nearest embedding and embedded self-nested trees with reduced complexity and improved approximation accuracy.

Findings

The new algorithm is faster than previous methods.

Nearest embedded self-nested trees are generally closer to original data.

Better approximation enhances plant self-similarity assessment.

Abstract

Self-nested trees present a systematic form of redundancy in their subtrees and thus achieve optimal compression rates by DAG compression. A method for quantifying the degree of self-similarity of plants through self-nested trees has been introduced by Godin and Ferraro in 2010. The procedure consists in computing a self-nested approximation, called the nearest embedding self-nested tree, that both embeds the plant and is the closest to it. In this paper, we propose a new algorithm that computes the nearest embedding self-nested tree with a smaller overall complexity, but also the nearest embedded self-nested tree. We show from simulations that the latter is mostly the closest to the initial data, which suggests that this better approximation should be used as a privileged measure of the degree of self-similarity of plants.