# On metric choice in dimension reduction for Fr'echet regression

arXiv: https://arxiv.org/abs/2410.01783 · HTML: https://mlsanity.com/paper/2410.01783/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 4 of 4)

- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [Exploring the reproducibility of functional connectivity alterations in Parkinson's Disease](https://mlsanity.com/paper/1611.04794/) (2016)
- [Dimension Reduction for Fr'echet Regression](https://mlsanity.com/paper/2110.00467/) (2021)
- [Modeling and Measuring Graph Similarity: The Case for Centrality Distance](https://mlsanity.com/paper/1406.5481/) (2014)

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

- [Fr'echet Cumulative Covariance Net for Deep Nonlinear Sufficient Dimension Reduction with Random Objects](https://mlsanity.com/paper/2502.15374/) (2025)

## Abstract (arXiv)

Fr'echet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such as continuous monitoring and imaging data. Fr'echet regression utilizes the pairwise distances between the random objects, which makes the choice of metric crucial in the estimation. In this paper, existing dimension reduction methods for Fr'echet regression are reviewed, and the effect of metric choice on the estimation of the dimension reduction subspace is explored for the regression between random responses and Euclidean predictors. Extensive numerical studies illustrate how different metrics affect the central and central mean space estimators. Two real applications involving analysis of brain connectivity networks of subjects with and without Parkinson's disease and an analysis of the distributions of glycaemia based on continuous glucose monitoring data are provided, to demonstrate how metric choice can influence findings in real applications.