Fréchet Sufficient Dimension Reduction for Metric Space-Valued Data via Distance Covariance
提出一种基于核距离协方差的弗雷歇充分降维方法，处理计数数据、概率密度等度量空间值响应，比现有方法更快且效果更好。
We propose a novel Fréchet sufficient dimension reduction (SDR) method based on kernel distance covariance, tailored for metric-space-valued responses such as count data, probability densities, and other complex structures. The method leverages a kernel-based transformation to map metric-space-valued responses into a feature space, enabling efficient dimension reduction. By incorporating kernel distance covariance, the proposed approach offers enhanced flexibility and adaptability for datasets with diverse and non-Euclidean characteristics. The effectiveness of the method is demonstrated through synthetic simulations and several real-world applications. In all cases, the proposed method runs faster and consistently outperforms the existing Fréchet SDR approaches, demonstrating its broad applicability and robustness in addressing complex data challenges.