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. Our second example is to calculate the likelihood of unidentified Fermi point sources being pulsars.