Abstract—

Adequate formalization of problems is the most important task that has to be solved in order to apply the modern methods of so-called “machine learning” to real problems. The effective application of the metric, logical, regression, and other algorithms of machine learning becomes possible only when feature generation procedures and classes of objects are adequately defined. In this study, the theory of topological analysis of poorly formalized problems and the theory of analysis of labeled graphs were applied to the problem of predicting numerical characteristics of crystalline materials. The methods developed were tested on the problem of predicting the critical temperature of superconducting transition (T_c) of high-temperature cuprate superconductors (1450 structures). As a result, in a tenfold 6 : 1 cross-validation, the best model with a linear recognition operator yielded quite high average value of the correlation coefficient (r = 0.77) between the predicted and experimentally determined values of T_c.

中文翻译：

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材料科学中的拓扑数据分析：高温铜酸盐超导体的情况

摘要-

为了将所谓的“机器学习”的现代方法应用于实际问题，充分解决问题的形式化是必须解决的最重要的任务。只有适当定义了特征生成过程和对象类别，才能有效地应用度量，逻辑，回归和其他机器学习算法。在这项研究中，将形式化不良问题的拓扑分析理论和标记图的分析理论应用于预测晶体材料数值特征的问题。测试了开发的方法，以预测超导转变的临界温度（T _c）的高温铜酸盐超导体（1450结构）。结果，在十倍的6：1交叉验证中，具有线性识别算子的最佳模型在T _c的预测值和实验确定值之间产生了很高的相关系数平均值（r = 0.77）。