Optimized data-driven order selection method for Gaussian mixtures on clustering problems

Perhaps the most fundamental consideration when modeling data as a mixture of Gaussians is the number of components in the mixture. To this end, numerous approaches have been proposed, ranging from the classic use of statistical hypothesis testing methods to make decisions, to the determination of balance between the model Goodness-of-Fit (GoF) and complexity. In this paper, we explore an existing simple yet powerful order selection method developed in the field of information theory, the Jump method. This method infers the model order by estimating, transforming, and analyzing a description of the distortion-rate function, R(D) of the input data. The description of the R(D) curve is efficiently estimated through the popular K-means clustering algorithm using proper seeding techniques. The proposed adaptations to the Jump method allow for higher sensitivity and improved performance at low dimensionality. These adaptations are experimentally tested in a clustering setting with synthetic and natural data. The results suggest better performance than with the original version.