Adaptive Functional Principal Component Analysis

We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique that is fast and scalable, and then integrate this technique into a probabilistic FPCA framework to adaptively smooth functional principal components. Our simulation results show that our approach is better able to model functional data with sharp changes in smoothness compared to standard approaches. We are motivated by the need to identify coordinated patterns of brain activity across multiple neurons during reaching movements prompted by an auditory cue, which enables understanding of the dynamics in the brain during dexterous movement. Our proposed method captures the underlying biological mechanisms that arise in data obtained from a mouse experiment focused on voluntary reaching movements, offering more interpretable activation patterns that reflect sharp changes in neural activity following the cue. We develop accompanying publicly available software for our proposed methodology, along with implementations to reproduce our results.