Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T20:19:49.576Z Has data issue: false hasContentIssue false
  • English
  • Français

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: fmurtagh@acm.org
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 

References

Adelman-McCarthy, J. K., et al. 2007, ApJ Supplement Series, 172 (2), 634 Google Scholar
Bolton, A. S., Schlegel, D. J., Aubourg, É., Bailey, S., Bhardwaj, V., Brownstein, J. R., Burles, S., Chen, Y.-M., Dawson, K., Eisenstein, D. J., Gunn, J. E., Knapp, G. R., Loomis, C. P., Lupton, R. H., Maraston, G., Muna, D., Myers, A. D., Olmstead, M. D., Padmanabhan, N., Pâris, I., Percival, W. J., Petitjean, P., Rockosi, C. M., Ross, N. P., Schneider, D. P., Shu, Y., Strauss, M. A., Thomas, D., Tremonti, C. A., Wake, D. A., Weaver, B. A., & Wood-Vasey, W. M. 2012, AJ, 144, 144 Google Scholar
Csabai, I., Budavari, T., Connolly, A. J., Szalay, A. S., Gyory, Z., Benitez, N., Annis, J., Brinkmann, J., Eisenstein, D., Fukugita, M., Gunn, J., Kent, S., Lupton, R., Nichol, R. C., & Stoughton, C. 2003, AJ, 125, 580 (http://arxiv.org/abs/astro-ph/0211080, 5 Nov. 2002)CrossRefGoogle Scholar
d’Abrusco, R., Longo, G., Paolillo, M., Brescia, M., De Filippis, E., Staiano, A., & Tagliaferri, R. 2006, “The use of neural networks to probe the structure of the nearby universe”, Proc. ADA-4: Astronomical Data Analysis IV (Sept. 2006, Marseilles), p. 79 (arXiv:astro-ph/0701137v1, 5. Jan. 2007)Google Scholar
d’Abrusco, R., Staiano, A., Longo, G., Brescia, M., Paolillo, M., De Filippis, E., & Tagliaferri, R. 2007, ApJ, 663, 752 (https://arxiv.org/abs/astro-ph/0703108)Google Scholar
Dragovich, B. 2006, “p-Adic and adelic cosmology: p-Adic origin of dark energy and dark matter”, Proc. 2nd International Conference on p-Adic Mathematical Physics. (arXiv:hep-th/0602044v1, 4 Feb. 2006)Google Scholar
Firth, A. E., Lahav, O., & Somerville, R. S. 2003, MNRAS, 339, 1195 Google Scholar
Khrennikov, A., Oleshko, K., & de Jesús Correa López, M. 2016, “Modeling fluid’s dynamics with master equations in ultrametric spaces representing the treelike structure of network of capillaries”, Entropy, 18 (7), 249 CrossRefGoogle Scholar
Murtagh, F. 1988, Computer Physics Communications, 52, 15 Google Scholar
Murtagh, F., Raftery, A. E., & Starck, J. L. 2005, “Bayesian inference for multiband image segmentation via model-based cluster trees”, Image & Vision Computing, 23, 587 CrossRefGoogle Scholar
Murtagh, F. 2016, “Sparse p-adic data coding for computationally efficient and effective big data analytics”, p-Adic Numbers, Ultrametric Analysis and Applications, 8 (3), 236 Google Scholar
Murtagh, F., Spagat, M., & Restrepo, J. A. 2011, “Ultrametric wavelet regression of multivariate time series: application to Colombian conflict analysis”, IEEE Transactions on Systems, Man, and Cybernetics–Part A: Systems and Humans, 41, 254 Google Scholar
Murtagh, F. 2017, Data Science Foundations: Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics, Chapman and Hall, CRC Press (Taylor and Francis), Boca Raton, FL, forthcoming.Google Scholar
Shu, Y., Bolton, A. S., Schlegel, D. J., Dawson, K. S., Wake, D. A., Brownstein, J. R., Brinkmann, J., & Weaver, B. A. 2012, AJ, 134, 90 Google Scholar
Stripe 82 2016, Images Tutorial, http://www.sdss.org/dr12/tutorials/get_stripe82_images/ Google Scholar
Vanzella, E., Cristiani, S., Fontana, A., Nonino, M., Arnouts, S., Giallongo, E., Grazian, A., Fasano, G., Popesso, P., Saracco, P., & Zaggia, S. 2004, A&A, 423, 761 (arXiv:astroph/0312064v1, 2 Dec. 2003)Google Scholar