Topological data analysis is a relatively new branch of machine learning that excels in studying high-dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical attributes are ubiquitous in real-world applications. However, topological methods are usually applied to point cloud data, and to the best of our knowledge there is no available framework for the classification of mixed data using topological methods. In this paper, we propose a novel topological machine learning method for mixed data classification. In the proposed method, we use theory from topological data analysis such as persistent homology, persistence diagrams and Wasserstein distance to study mixed data. The performance of the proposed method is demonstrated by experiments on a real-world heart disease dataset. Experimental results show that our topological method outperforms several state-of-the-art algorithms in the prediction of heart disease.

中文翻译：

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混合数值和分类数据的拓扑机器学习

拓扑数据分析是机器学习的一个相对较新的分支，擅长研究高维数据，理论上已知对噪声具有鲁棒性。同时，具有混合数字和分类属性的数据对象在实际应用中无处不在。然而，拓扑方法通常应用于点云数据，据我们所知，没有可用的框架用于使用拓扑方法对混合数据进行分类。在本文中，我们提出了一种用于混合数据分类的新型拓扑机器学习方法。在所提出的方法中，我们使用来自拓扑数据分析的理论，例如持久同源性、持久性图和 Wasserstein 距离来研究混合数据。通过对真实世界心脏病数据集的实验证明了所提出方法的性能。实验结果表明，我们的拓扑方法在预测心脏病方面优于几种最先进的算法。