The Haar Wavelet Transform of a Dendrogram

TL;DR

This paper introduces a novel wavelet transform tailored for hierarchical data structures like dendrograms, providing a new framework for data analysis with applications in smoothing, condensation, and reproducibility of complex data sets.

Contribution

It presents a new wavelet transform specifically designed for hierarchies, expanding the analytical tools available for tree-structured data.

Findings

Effective data smoothing and filtering using the wavelet transform

Hierarchical tree condensation achieved through the method

Insights into the reproducibility and generation of complex data sets

Abstract

We describe a new wavelet transform, for use on hierarchies or binary rooted trees. The theoretical framework of this approach to data analysis is described. Case studies are used to further exemplify this approach. A first set of application studies deals with data array smoothing, or filtering. A second set of application studies relates to hierarchical tree condensation. Finally, a third study explores the wavelet decomposition, and the reproducibility of data sets such as text, including a new perspective on the generation or computability of such data objects.