# Fr'echet Sufficient Dimension Reduction for Metric Space-Valued Data via Distance Covariance

arXiv: https://arxiv.org/abs/2412.13122 · HTML: https://mlsanity.com/paper/2412.13122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Unsupervised Feature Selection via Robust Autoencoder and Adaptive Graph Learning](https://mlsanity.com/paper/2512.18720/) (2025)

## Abstract (arXiv)

We propose a novel Fr'echet 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 Fr'echet SDR approaches, demonstrating its broad applicability and robustness in addressing complex data challenges.