The triangular inequality is a defining property of a metric space, while the stronger ultrametric inequality is a defining property of an ultrametric space. Ultrametric distance is defined from p-adic valuation. It is known that ultrametricity is a natural property of spaces that are sparse. Here we look at the quantification of ultrametricity. We also look at data compression based on a new ultrametric wavelet transform. We conclude with computational implications of prevalent and perhaps ubiquitous ultrametricity.
|Title of host publication||Classification, Clustering, and Data Mining Applications|
|Place of Publication||Berlin|
|Publication status||Published - 2004|
|Name||Studies in Classification, Data Analysis & Knowledge Organization|