Recently, Odrzywolek and Rafelski have found three distinct categories of exoplanets, when they are classified based on density. We first carry out a similar classification of exoplanets according to their density using the Gaussian Mixture Model, followed by information theoretic criterion (AIC and BIC) to determine the optimum number of components. Such a one-dimensional classification favors two components using AIC and three using BIC, but the statistical significance from both the tests is not significant enough to decisively pick the best model between two and three components. We then extend this GMM-based classification to two dimensions by using both the density and the Earth similarity index, which is a measure of how similar each planet is compared to the Earth. For this two-dimensional classification, both AIC and BIC provide decisive evidence in favor of three components.