Kernels for Periodic Time Series Arising in Astronomy

Authors:
Gabriel Wachman;Roni Khardon;Pavlos Protopapas;Charles R. Alcock
Affiliations:
Tufts University, Medford, USA;Tufts University, Medford, USA;Harvard-Smithsonian Center for Astrophysics, Cambridge, USA and Harvard Initiative in Innovative Computing, Cambridge, USA;Harvard-Smithsonian Center for Astrophysics, Cambridge, USA
Venue:
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Year:
2009

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Abstract

We present a method for applying machine learning algorithms to the automatic classification of astronomy star surveys using time series of star brightness. Currently such classification requires a large amount of domain expert time. We show that a combination of phase invariant similarity and explicit features extracted from the time series provide domain expert level classification. To facilitate this application, we investigate the cross-correlation as a general phase invariant similarity function for time series. We establish several theoretical properties of cross-correlation showing that it is intuitively appealing and algorithmically tractable, but not positive semidefinite, and therefore not generally applicable with kernel methods. As a solution we introduce a positive semidefinite similarity function with the same intuitive appeal as cross-correlation. An experimental evaluation in the astronomy domain as well as several other data sets demonstrates the performance of the kernel and related similarity functions.