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Hierarchical Matching and Regression with Application to Photometric Redshift Estimation

Published online by Cambridge University Press:  30 May 2017

Fionn Murtagh Open the ORCID record for Fionn Murtagh [Opens in a new window]
Fionn Murtagh*
Affiliation:
Big Data Lab, Department of Electronics, Computing and Mathematics, University of Derby, Derby DE22 1GB, UK Department of Computing, Goldsmiths University of London, London SE14 6NW, UK email: [email protected]
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Abstract

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This work emphasizes that heterogeneity, diversity, discontinuity, and discreteness in data is to be exploited in classification and regression problems. A global a priori model may not be desirable. For data analytics in cosmology, this is motivated by the variety of cosmological objects such as elliptical, spiral, active, and merging galaxies at a wide range of redshifts. Our aim is matching and similarity-based analytics that takes account of discrete relationships in the data. The information structure of the data is represented by a hierarchy or tree where the branch structure, rather than just the proximity, is important. The representation is related to p-adic number theory. The clustering or binning of the data values, related to the precision of the measurements, has a central role in this methodology. If used for regression, our approach is a method of cluster-wise regression, generalizing nearest neighbour regression. Both to exemplify this analytics approach, and to demonstrate computational benefits, we address the well-known photometric redshift or ‘photo-z’ problem, seeking to match Sloan Digital Sky Survey (SDSS) spectroscopic and photometric redshifts.

Keywords

Cluster-wise regressionp-adic and m-adic number representationinherent hierarchical properties of data
Type
Contributed Papers
Information
Proceedings of the International Astronomical Union , Volume 12 , Symposium S325: Astroinformatics , October 2016 , pp. 145 - 155
Copyright
Copyright © International Astronomical Union 2017 

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