# Functional Principal Component Analysis for Extrapolating Multi-stream Longitudinal Data

arXiv: https://arxiv.org/abs/1903.03871 · HTML: https://mlsanity.com/paper/1903.03871/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2019.

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

- [Real-time Adaptation for Condition Monitoring Signal Prediction using Label-aware Neural Processes](https://mlsanity.com/paper/2403.16377/) (2024)

## Abstract (arXiv)

The advance of modern sensor technologies enables collection of multi-stream longitudinal data where multiple signals from different units are collected in real-time. In this article, we present a non-parametric approach to predict the evolution of multi-stream longitudinal data for an in-service unit through borrowing strength from other historical units. Our approach first decomposes each stream into a linear combination of eigenfunctions and their corresponding functional principal component (FPC) scores. A Gaussian process prior for the FPC scores is then established based on a functional semi-metric that measures similarities between streams of historical units and the in-service unit. Finally, an empirical Bayesian updating strategy is derived to update the established prior using real-time stream data obtained from the in-service unit. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the-art approaches and can effectively account for heterogeneity as well as achieve high predictive accuracy.