Application of the Gaussian mixture model in pulsar astronomy - pulsar classification and candidates ranking for the Fermi 2FGL catalogue

Machine learning, algorithms designed to extract empirical knowledge from data, can be used to classify data, which is one of the most common tasks in observational astronomy. In this paper, we focus on Bayesian data classification algorithms using the Gaussian mixture model and show two applications in pulsar astronomy. After reviewing the Gaussian mixture model and the related expectation-maximization algorithm, we present a data classification method using the Neyman-Pearson test. To demonstrate the method, we apply the algorithm to two classification problems. First, it is applied to the well-known period-period derivative diagram, where we find that the pulsar distribution can be modelled with six Gaussian clusters, with two clusters for millisecond pulsars (recycled pulsars) and the rest for normal pulsars. From this distribution, we derive an empirical definition for millisecond pulsars as 10 -17 3.