Supervised Kernel PCA For Longitudinal Data

TL;DR

This paper introduces sklPCA, a supervised dimension reduction method tailored for longitudinal data, which improves model accuracy by accounting for within- and between-cluster dependencies.

Contribution

The paper develops a novel supervised kernel PCA method for longitudinal data that decomposes dependence measures to enhance dimension reduction accuracy.

Findings

sklPCA outperforms existing methods in model accuracy

Decomposition of Hilbert-Schmidt Independence Criterion improves relevance

Effective dimension reduction for complex longitudinal datasets

Abstract

In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduction techniques assume data are $i.i.d.$, which is not appropriate for longitudinal data comprising multiple subjects with repeated measurements over time. In this paper, we derive a decomposition of the Hilbert-Schmidt Independence Criterion as a supervised loss function for longitudinal data, enabling dimension reduction between and within clusters separately, and propose a dimensionality-reduction technique, $sklPCA$, that performs this decomposed dimension reduction. We also show that this technique yields superior model accuracy compared to the model it extends.