Clustering is a data analysis method for extracting knowledge by discovering
groups of data called clusters. Among these methods, state-of-the-art
density-based clustering methods have proven to be effective for
arbitrary-shaped clusters. Despite their encouraging results, they suffer to
find low-density clusters, near clusters with similar densities, and
high-dimensional data. Our proposals are a new characterization of clusters and
a new clustering algorithm based on spatial density and probabilistic approach.
First of all, sub-clusters are built using spatial density represented as
probability density function ($p.d.f$) of pairwise distances between points. A
method is then proposed to agglomerate similar sub-clusters by using both their
density ($p.d.f$) and their spatial distance. The key idea we propose is to use
the Wasserstein metric, a powerful tool to measure the distance between $p.d.f$
of sub-clusters. We show that our approach outperforms other state-of-the-art
density-based clustering methods on a wide variety of datasets.

通过提出新的聚类特征和一种基于空间密度和概率方法的聚类算法，本研究在广泛的数据集上展示出较其他先进的基于密度的聚类方法更好的性能。

DECWA：基于 Wasserstein 距离的密度聚类

DECWA : Density-Based Clustering using Wasserstein Distance

This study aims to alleviate the trade-off between utility and privacy in the
task of differentially private clustering. Existing works focus on simple
clustering methods, which show poor clustering performance for non-convex
clusters. By utilizing Morse theory, we hierarchically connect the Gaussian
sub-clusters to fit complex cluster distributions. Because differentially
private sub-clusters are obtained through the existing methods, the proposed
method causes little or no additional privacy loss. We provide a theoretical
background that implies that the proposed method is inductive and can achieve
any desired number of clusters. Experiments on various datasets show that our
framework achieves better clustering performance at the same privacy level,
compared to the existing methods.

通过使用 Morse 理论，构建子高斯簇将复杂簇分布与不同隐私保护保持一定的性能平衡，由于差分隐私子簇是通过现有方法进行获得的，所以所提出的方法几乎不存在额外的隐私损失。实验结果表明，在相同的隐私级别下，我们的方法能够实现更好的聚类性能。