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      Fast, Linear Time Hierarchical Clustering using the Baire Metric

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          Abstract

          The Baire metric induces an ultrametric on a dataset and is of linear computational complexity, contrasted with the standard quadratic time agglomerative hierarchical clustering algorithm. In this work we evaluate empirically this new approach to hierarchical clustering. We compare hierarchical clustering based on the Baire metric with (i) agglomerative hierarchical clustering, in terms of algorithm properties; (ii) generalized ultrametrics, in terms of definition; and (iii) fast clustering through k-means partititioning, in terms of quality of results. For the latter, we carry out an in depth astronomical study. We apply the Baire distance to spectrometric and photometric redshifts from the Sloan Digital Sky Survey using, in this work, about half a million astronomical objects. We want to know how well the (more costly to determine) spectrometric redshifts can predict the (more easily obtained) photometric redshifts, i.e. we seek to regress the spectrometric on the photometric redshifts, and we use clusterwise regression for this.

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          Hierarchical clustering schemes.

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            On Ultrametricity, Data Coding, and Computation

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              Generalized Distance Functions in the Theory of Computation

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                Author and article information

                Journal
                11 June 2011
                Article
                10.1007/s00357-012-9106-3
                1106.2229
                85564f77-35f3-4490-a560-2095fd13d45c

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                11Z05
                Journal of Classification, July 2012, Volume 29, Issue 2, pp 118-143
                27 pages, 6 tables, 10 figures
                stat.ML cs.IR stat.AP

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