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On Ultrametric Algorithmic Information
Fionn Murtagh
How best to quantify the information of an object, whether natural or artifact, is a problem of wide interest. A related problem is the computability of an object. We present pract…
The Haar Wavelet Transform of a Dendrogram: Additional Notes
Fionn Murtagh
We consider the wavelet transform of a finite, rooted, node-ranked, -way tree, focusing on the case of binary () trees. We study a Haar wavelet transform on this tree. Wa…
Hilbert Space Becomes Ultrametric in the High Dimensional Limit: Application to Very High Frequency Data Analysis
Fionn Murtagh
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a natural hierarchical embeddin…
A Note on Local Ultrametricity in Text
Fionn Murtagh
High dimensional, sparsely populated data spaces have been characterized in terms of ultrametric topology. This implies that there are natural, not necessarily unique, tree or hier…
Ontology from Local Hierarchical Structure in Text
F. Murtagh, J. Mothe, K. Englmeier
We study the notion of hierarchy in the context of visualizing textual data and navigating text collections. A formal framework for ``hierarchy'' is given by an ultrametric topolog…