# Principal component analysis balancing prediction and approximation accuracy for spatial data

arXiv: https://arxiv.org/abs/2408.01662 · HTML: https://mlsanity.com/paper/2408.01662/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 3 Aug 2024.

## Builds on (most cited first, 3 of 3)

- [Prediction models for network-linked data](https://mlsanity.com/paper/1602.01192/) (2016)
- [Random Spatial Forests](https://mlsanity.com/paper/2006.00150/) (2020)
- [A novel principal component analysis for spatially-misaligned multivariate air pollution data](https://mlsanity.com/paper/1509.01171/) (2015)

## Abstract (arXiv)

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not take the downstream modeling task into consideration when finding the lower-dimensional representation. We formalize the closeness of approximation to the original data and the utility of lower-dimensional scores for downstream modeling as two complementary, sometimes conflicting, metrics for dimension reduction. We illustrate how existing methodologies fall into this framework and propose a flexible dimension reduction algorithm that achieves the optimal trade-off. We derive a computationally simple form for our algorithm and illustrate its performance through simulation studies, as well as two applications in air pollution modeling and spatial transcriptomics.