Clustering is a common task in machine learning, but clusters of unlabelled
data can be hard to quantify. The application of clustering algorithms in
chemistry is often dependant on material representation. Ascertaining the
effects of different representations, clustering algorithms, or data
transformations on the resulting clusters is difficult due to the
dimensionality of these data. We present a thorough analysis of measures for
isotropy of a cluster, including a novel implantation based on an existing
derivation. Using fractional anisotropy, a common method used in medical
imaging for comparison, we then expand these measures to examine the average
isotropy of a set of clusters. A use case for such measures is demonstrated by
quantifying the effects of kernel approximation functions on different
representations of the Inorganic Crystal Structure Database. Broader
applicability of these methods is demonstrated in analysing learnt embedding of
the MNIST dataset. Random clusters are explored to examine the differences
between isotropy measures presented, and to see how each method scales with the
dimensionality. Python implementations of these measures are provided for use
by the community.

本研究提出了一种基于现有推导的新型方法，通过对反应物的不同表征和聚类算法进行全面分析，可以量化簇的各向同性度量以及各向同性的平均度量，并在 Inorganic Crystal Structure Database 和 MNIST 数据集上进行了应用。