Model-Based Clustering with HDBSCAN

We propose an efficient model-based clustering approach for creating Gaussian Mixture Models from finite datasets. Models are extracted from HDBSCAN* hierarchies using the Classification Likelihood and the Expectation Maximization algorithm. Prior knowledge of the number of components of the model, corresponding to the number of clusters, is not necessary and can be determined dynamically. Due to relatively small hierarchies created by HDBSCAN* compared to previous approaches, this can be done efficiently. The lower the number of objects in a dataset, the more difficult it is to accurately estimate the number of parameters of a fully unrestricted Gaussian Mixture Model. Therefore, more parsimonious models can be created by our algorithm, if necessary. The user has a choice of two information criteria for model selection, as well as a likelihood test using unseen data, in order to select the best-fitting model. We compare our approach to two baselines and show its superiority in two settings: recovering the original data-generating distribution and partitioning the data correctly. Furthermore, we show that our approach is robust to its hyperparameter settings. (Data and code are publicly available at: https://github.com/mjstrobl/HCEM)