Topological data analysis is a family of recent mathematical techniques seeking to understand the ‘shape’ of data, and has been used to understand the structure of the descriptor space produced from a standard chemical informatics software from the point of view of solubility. We have used the mapper algorithm, a TDA method that creates low-dimensional representations of data, to create a network visualization of the solubility space. While descriptors with clear chemical implications are prominent features in this space, reflecting their importance to the chemical properties, an unexpected and interesting correlation between chlorine content and rings and their implication for solubility prediction is revealed. A parallel representation of the chemical space was generated using persistent homology applied to molecular graphs. Links between this chemical space and the descriptor space were shown to be in agreement with chemical heuristics. The use of persistent homology on molecular graphs, extended by the use of norms on the associated persistence landscapes allow the conversion of discrete shape descriptors to continuous ones, and a perspective of the application of these descriptors to quantitative structure property relations is presented.

中文翻译：

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通过拓扑数据分析提高了对水溶性建模的理解。

拓扑数据分析是一系列旨在了解数据“形状”的最新数学技术，并已从溶解度的角度用于理解由标准化学信息学软件生成的描述符空间的结构。我们使用了映射器算法（一种可创建数据的低维表示形式的TDA方法）来创建溶解度空间的网络可视化。尽管具有明确化学含义的描述符是该空间中的突出特征，反映了它们对化学性质的重要性，但揭示了氯含量和环之间的意外和有趣的相关性，以及它们对溶解度预测的含义。使用应用于分子图的持久同源性生成化学空间的平行表示。该化学空间和描述符空间之间的链接被证明与化学启发法一致。通过在分子图上使用持久性同源性，再通过在相关的持久性景观上使用范数，可以将离散的形状描述符转换为连续的形状描述符，并提供了将这些描述符应用于定量结构性质关系的观点。