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.

该论文提出了一种利用 BIC 准则对数据集进行聚类的算法，将高斯聚类的最优数量组合成从统计上可分离的超聚类，该算法包括三个阶段：将数据集表示为高斯分布的混合聚类，使用马氏距离估计聚类间的距离和聚类大小，利用 DBSCAN 方法将聚类组合成超聚类，该算法自动检测最佳数量和形状的超聚类，具有较好的结果和能预测新数据的软聚类能力，但速度较慢，最终聚类结果具有随机性。

通过寻找具有统计显著性的可分离的最佳高斯簇，进行超聚类

Superclustering by finding statistically significant separable groups of  optimal gaussian clusters

In many applications we have both observational and (randomized)
interventional data. We propose a Gaussian likelihood framework for joint
modeling of such different data-types, based on global parameters consisting of
a directed acyclic graph (DAG) and correponding edge weights and error
variances. Thanks to the global nature of the parameters, maximum likelihood
estimation is reasonable with only one or few data points per intervention. We
prove consistency of the BIC criterion for estimating the interventional Markov
equivalence class of DAGs which is smaller than the observational analogue due
to increased partial identifiability from interventional data. Such an
improvement in identifiability has immediate implications for tighter bounds
for inferring causal effects. Besides methodology and theoretical derivations,
we present empirical results from real and simulated data.

该研究提出了一种基于高斯似然框架的有向无环图模型，用于联合建模观察数据和干预数据，以及通过 BIC 准则对干预马尔可夫等价类进行一致性估计，从而改善了干预数据的部分可鉴别性，提供更紧密的因果效应推断。