The Future of Search and Discovery in Big Data Analytics Ultrametric Information Spaces : Ultrametric Information Spaces. / Murtagh, Fionn; Contreras, Pedro.

In: NA, 15.02.2012.

Research output: Contribution to journalArticle

In preparation

Abstract

Consider observation data, comprised of n observation vectors with values on a set of attributes. This gives us n points in attribute space. Having data structured as a tree, implied by having our observations embedded in an ultrametric topology, offers great advantage for proximity searching. If we have preprocessed data through such an embedding, then an observation's nearest neighbor is found in constant computational time, i.e. O(1) time. A further powerful approach is discussed in this work: the inducing of a hierarchy, and hence a tree, in linear computational time, i.e. O(n) time for n observations. It is with such a basis for proximity search and best match that we can address the burgeoning problems of processing very large, and possibly also very high dimensional, data sets.
Original languageEnglish
JournalNA
StateIn preparation - 15 Feb 2012
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 4491713