Fast redshift clustering with the Baire (ultra) metric

TL;DR

This paper introduces a fast clustering method using the Baire ultrametric, applied to astronomical redshift data, enabling efficient regression of spectrometric redshifts from photometric data with linear complexity.

Contribution

It presents a novel application of the Baire ultrametric for rapid clustering and regression in large astronomical datasets, improving computational efficiency over traditional methods.

Findings

Achieved linear time complexity clustering on half a million objects.

Demonstrated effective regression of spectrometric redshifts from photometric data.

Provided insights into redshift prediction accuracy using ultrametric clustering.

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. 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 cos\ tly 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 develop a clusterwise nearest neighbor regression procedure for this.