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.