论文标题
混合数字和分类数据的拓扑机学习
Topological Machine Learning for Mixed Numeric and Categorical Data
论文作者
论文摘要
拓扑数据分析是机器学习的一个相对较新的分支，它在研究高维数据方面表现出色，从理论上讲是可靠的噪声。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。但是，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学习方法。在提出的方法中，我们使用拓扑数据分析的理论，例如持续的同源性，持久图和Wasserstein距离来研究混合数据。实验在现实世界中心脏病数据集上的实验证明了所提出的方法的性能。实验结果表明，我们的拓扑方法在心脏病的预测中优于几种最先进的算法。
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.
