Distance-based variable generation with applications to the FACT experiment. (English) Zbl 07281549

Summary: We introduce a new way to construct variables for classification in a setting of astronomy. The newly constructed variables complement the currently used Hillas parameters and are specifically designed to improve the classification. They are based on fitting elliptic or skewed bivariate distributions to images gathered by imaging atmospheric Cherenkov telescopes and evaluating the distance between the observed and the fitted distribution. As distance measures we use the Chi-square distance, the Kullback-Leibler divergence and the Hellinger distance. The new variables lead to an improved classification in terms of misclassification errors.


62-XX Statistics


Full Text: DOI


[1] S.M. Ali and S.D Silvey, A general class of coefficients of divergence of one distribution from another, J. R. Stat. Soc. B 28 (1966), pp. 131-142. · Zbl 0203.19902
[2] H. Anderhub, M. Backes, A. Biland, V. Boccone, I. Braun, T. Bretz, J. Buß, F. Cadoux, V. Commichau, L. Djambazov, D. Dorner, S. Einecke, D. Eisenacher, A. Gendotti, O. Grimm, H. von Gunten, C. Haller, D. Hildebrand, U. Horisberger, B. Huber, K.-S. Kim, M.L. Knoetig, J.-H. Köhne, T. Krähenbühl, B. Krumm, M. Lee, E. Lorenz, W. Lustermann, E. Lyard, K. Mannheim, M. Meharga, K. Meier, T. Montaruli, D. Neise, F. Nessi-Tedaldi, A.-K. Overkemping, A. Paravac, F. Pauss, D. Renker, W. Rhode, M. Ribordy, U. Röser, J.-P. Stucki, J. Schneider, T. Steinbring, F. Temme, J. Thaele, S. Tobler, G. Viertel, P. Vogler, R. Walter, K. Warda, Q. Weitzel, and M. Zänglein Design and operation of FACT - the first G-APD Cherenkov telescope, J. Instrum. 8 (2013), p. P06008.
[3] A. Azzalini, The R ‘sn’ Package: The Skew-normal and Skew-t Distributions ##img## ##img####img##\((\) Version 1.0-0##img## ##img####img##\(), 2014\). Available at http://azzalini.stat.unipd.it/SN.
[4] A. Azzalini and A Capitanio, Statistical applications of the multivariate skew-normal distribution, J. R. Stat. Soc. Ser. B 61 (1999), pp. 579-602. · Zbl 0924.62050
[5] A. Azzalini and A Dalla Valle, The multivariate skew-normal distribution, Biometrika 83 (4) (1996), pp. 715-726. · Zbl 0885.62062
[6] Y. Becherini, A. Djannati-Atai, V. Marandon, M. Punch, and S Pita, A new analysis strategy for detection of faint \(γ\)-ray sources with imaging atmospheric Cherenkov telescopes, Astropart. Phys. 34 (2011), pp. 858-870. doi:10.1016/j.astropartphys.2011.03.005,1104.5359.
[7] R.K. Bock, A. Chilingarian, M. Gaug, F. Hakl, T. Hengstebeck, M. Jirina, J. Klaschka, E. Kotrc, P. Savicky, S.  Towers, A. Vaiciulis, and W. Wittek, Methods for multidimensional event classification: A case study using images from a Cherenkov gamma-ray telescope, Nucl. Instrum. Methods Phys. Res. A 516 (2004), pp. 511-528. doi:10.1016/j.nima.2003.08.157.
[8] P. Boinee, F. Barbarino, A. de Angelis, A. Saggion, and M. Zacchello, Neural networks for Gamma-Hadron separation in MAGIC, in Frontiers of Fundamental and Computational Physics, B. G. Sidharth, F. Honsell, and A. de Angeles, eds., 2006, p. 297. Available at arXiv:astro-ph/0503539.
[9] L Breiman, Random forests, Mach. Learn. 45 (2001), pp. 5-32. · Zbl 1007.68152
[10] I.V Cadez, G.J. McLachlan, and C.E. McLaren, Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data, Machine Learning, 47 (2002), pp. 7-34. · Zbl 1012.68057
[11] R. Diaz-Uriarte and S. Alvarez de Andres, Variable selection from random forests: Application to gene expression data, Technical Report, 2005.
[12] E. Di Nardo, A new approach to Sheppard’s corrections, Math. Methods Statist. 9(2) (2010), pp. 151-162. doi:10.3103/S1066530710020043. · Zbl 1282.62138
[13] T. Fawcett, An introduction to ROC analysis, Pattern Recognit. Lett. 27 (2006), pp. 861-874.
[14] P.E. Greenwood and M.S. Nikulin, A Guide to Chi-squared Testing, in Wiley Series in Probability and Statistics, Wiley, New York, 1996.
[15] I. Guyon and A Elisseeff, An introduction to variable and feature selection, J. Mach. Learn. Res. 3 (2003), pp. 1157-1182. · Zbl 1102.68556
[16] D. Hadasch, Study of the MAGIC performance at high Zenith angles and application of the results on a very high energy gamma ray flare of the Blazar PKS 2155-304, Diploma thesis, Technische Universitaet Dortmund, Dortmund, 2008.
[17] A.M. Hillas, Cherenkov light images of EAS produced by primary gamma, Proceedings of the 19th International Cosmic Ray Conference ICRC, San Diego, Vol. 3, 1985, p. 445.
[18] A. Kohnle, F. Aharonian, A. Akhperjanian, S. Bradbury, A. Daum, T. Deckers, J. Fernandez, V. Fonseca, M. Hemberger, G. Hermann, M. Heß, A. Heusler, W. Hofmann, R. Kankanian, C. Köhler, A. Konopelko, E. Lorenz, R. Mirzoyan, N. Müller, M. Panter, D. Petry, A. Plyasheshnikov, G. Rauterberg, M. Samorski, W. Stamm, M. Ulrich, H.J. Völk, C.A. Wiedner, and H. Wirth, Stereoscopic imaging of air showers with the first two HEGRA Cherenkov telescopes, Astropart. Phys. 5 (1996), pp. 119-131.
[19] S. Kullback and R.A Leibler, On information and sufficiency, Ann. Math. Statist. 22 (1951), pp. 79-86. · Zbl 0042.38403
[20] D. Mazin, A study of very high energy gamma-ray emission from AGNs and constraints on the extragalactic background light, PhD thesis, Technische Universitaet Muenchen, 2007.
[21] M. de Naurois and L. Rolland, A high performance likelihood reconstruction of γ-rays for imaging atmospheric Cherenkov telescopes. Astropart. Phys. 56 (1996), pp. 26-34.
[22] M.S. Nikulin (originator), Hellinger distance, Encyclopedia of Mathematics, 2011. Available at http://www.encyclopediaofmath.org/index.php?title=Hellinger_distance&oldid=16453.
[23] S. Ohm, C. van Eldik, and K Egberts, \(γ\)/hadron separation in very-high-energy \(γ\)-ray astronomy using a multivariate analysis method, Astropart. Phys. 31 (2009), pp. 383-391. doi:10.1016/j.astropartphys.2009.04.001.
[24] H. Peng, F. Long, and C. Ding, Feature selection based on mutual information: Criteria of max-dependency, max-relevance, and min-redundancy, IEEE Trans. Pattern Anal. Mach. Intell. 27 (2005), pp. 1226-1238.
[25] F. Temme, FACT - data analysis: Analysis of Crab Nebula data using PARFACT a newly developed analysis software for the first G-APD Cherenkov telescope, Diploma thesis, Technische Universitaet Dortmund, Dortmund, 2012.
[26] The FACT collaboration, The FACT Telescope Web Pages, 2014. Available at http://isdc.unige.ch/fact/.
[27] T. Weekes, Very High Energy Gamma-Ray Astronomy, Institute of Physics Publishing, Bristol/Philadelphia, 2003.
[28] M. Wornowizki and R. Fried, Two-sample homogeneity tests based on divergence measures, 2015, preprint. · Zbl 1342.65070
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.