Ball Impurity: Measuring Heterogeneity in General Metric Spaces
提出一种名为球不纯度的新异质性度量，适用于非欧几里得数据，可用于特征选择和树模型，在合成数据和英国生物银行真实数据上验证了有效性。
Data in various domains, such as neuroimaging and network data analysis, often come in complex forms without possessing a Hilbert structure. The complexity necessitates innovative approaches for effective analysis. We propose a novel measure of heterogeneity, ball impurity, which is designed to work with complex non-Euclidean objects. Our approach extends the notion of impurity to general metric spaces, providing a versatile tool for feature selection and tree models. The ball impurity measure exhibits desirable properties, such as the triangular inequality, and is computationally tractable, enhancing its practicality and usefulness. Extensive experiments on synthetic data and real data from the UK Biobank validate the efficacy of our approach in capturing data heterogeneity. Remarkably, our results compare favorably with state-of-the-art methods in metric spaces, highlighting the potential of ball impurity as a valuable tool for addressing complex data analysis tasks.