The rapid development of high-speed trains has brought a significant demand to increase the reliability and optimize the maintenance of train wheels. As the state-of-the-art practice in high-speed trains, the maximal radial run-out and equivalent conicity are two leading health indicators (HIs) to assess the health status of the wheels. However, these two HIs cannot effectively assess the degree of wheel polygonal wear, which has been associated with the service failure of structural components. In the article, we propose a data-driven supervised learning framework for extracting a multi-dimensional HI to assess the condition of the wheels using group-profile data. To the authors ' knowledge, it is the first proposed multi-dimensional HI for the high-speed train wheels. The proposed framework is based on the proper integration of feature extraction and regression techniques, e.g., Hilbert-Huang transform, Functional Principal Component Analysis, and Logistic Regression. A set of real-world high-speed train wheel profile data are collected to validate the proposed framework. The statistical results show that the HI generated from the proposed framework outperforms the traditional HIs in abnormal wheels detection, i.e., classification. Additionally, the conditional probability based on the wheel profile data is proposed in this paper to achieve condition-based maintenance.