Superclustering by finding statistically significant separable groups of optimal gaussian clusters

The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability, superclusters. The algorithm consists of three stages: representation of the dataset as a mixture of Gaussian distributions - clusters, which number is determined based on the minimum of the BIC criterion; using the Mahalanobis distance, to estimate the distances between the clusters and cluster sizes; combining the resulting clusters into superclusters using the DBSCAN method by finding its hyperparameter (maximum distance) providing maximum value of introduced matrix quality criterion at maximum number of superclusters. The matrix quality criterion corresponds to the proportion of statistically significant separated superclusters among all found superclusters. The algorithm has only one hyperparameter - statistical significance level, and automatically detects optimal number and shape of superclusters based of statistical hypothesis testing approach. The algorithm demonstrates a good results on test datasets in noise and noiseless situations. An essential advantage of the algorithm is its ability to predict correct supercluster for new data based on already trained clusterer and perform soft (fuzzy) clustering. The disadvantages of the algorithm are: its low speed and stochastic nature of the final clustering. It requires a sufficiently large dataset for clustering, which is typical for many statistical methods.