Density peaks clustering (DP) has the ability of detecting clusters of
arbitrary shape and clustering non-Euclidean space data, but its quadratic
complexity in both computing and storage makes it difficult to scale for big
data. Various approaches have been proposed in this regard, including MapReduce
based distribution computing, multi-core parallelism, presentation
transformation (e.g., kd-tree, Z-value), granular computing, and so forth.
However, most of these existing methods face two limitations. One is their
target datasets are mostly constrained to be in Euclidian space, the other is
they emphasize only on local neighbors while ignoring global data distribution
due to restriction to cut-off kernel when computing density. To address the two
issues, we present a faithful and parallel DP method that makes use of two
types of vector-like distance matrices and an inverse leading-node-finding
policy. The method is implemented on a message passing interface (MPI) system.
Extensive experiments showed that our method is capable of clustering
non-Euclidean data such as in community detection, while outperforming the
state-of-the-art counterpart methods in accuracy when clustering large
Euclidean data. Our code is publicly available at
this https URL

通过使用两种向量距离矩阵和反向领先节点发现策略，我们提出了一种忠实且并行的密度峰值聚类方法，该方法能够在聚类大规模欧几里得数据时显示出优越的准确性，并且能够聚类非欧几里得数据，例如在社区检测中。

通过 MPI 并行计算系统进行矩阵计算的密度峰聚类算法

Faithful Density-Peaks Clustering via Matrix Computations on MPI  Parallelization System

Many algorithms require discriminative boundaries, such as separating
hyperplanes or hyperballs, or are specifically designed to work on spherical
data. By applying inversive geometry, we show that the two discriminative
boundaries can be used interchangeably, and that general Euclidean data can be
transformed into spherical data, whenever a change in point distances is
acceptable. We provide explicit formulae to embed general Euclidean data into
spherical data and to unembed it back. We further show a duality between
hyperspherical caps, i.e., the volume created by a separating hyperplane on
spherical data, and hyperballs and provide explicit formulae to map between the
two. We further provide equations to translate inner products and Euclidean
distances between the two spaces, to avoid explicit embedding and unembedding.
We also provide a method to enforce projections of the general Euclidean space
onto hemi-hyperspheres and propose an intrinsic dimensionality based method to
obtain "all-purpose" parameters. To show the usefulness of the
cap-ball-duality, we discuss example applications in machine learning and
vector similarity search.

利用逆向几何方法，将欧几里得数据转换为球形数据，实现了可互换使用的区分边界，并提出了嵌入和反嵌入的具体公式。研究表明球形数据中的分割超平面体积与球体之间存在对偶关系，并提供了两者之间的映射公式。此外，还提出了一种投影方法和通过内在维度方法获得 “通用” 参数的途径，并在机器学习和向量相似性搜索领域讨论了实例应用。