Characterising Stochastic Stellar Variability with PCA: Insights from HOYS Light Curves

Stellar variability spans a spectrum from well-understood periodic signals to irregular, stochastic behaviour, particularly in young stellar objects (YSOs). While periodic variability is readily characterised, stochastic light curves remain challenging to quantify and compare across populations. We present a new approach to analysing such variability using Principal Component Analysis (PCA), an unsupervised machine learning method that reduces dimensionality while retaining key features of the light curves.We apply this method to a large sample of high-cadence light curves from YSOs observed by the Hunting Outbursting Young Stars (HOYS) citizen science project. HOYS provides long-term, multi-band monitoring of 25 star-forming regions, with cadences up to twice daily, capturing variability patterns often missed by other large-scale surveys.Our PCA-based technique isolates dominant variability features, enabling robust, quantitative comparisons even when periodicity is absent. We find that the key drivers of variance in YSO light curves are the timescale of the onset of significant (~0.3 mag) variability and long-term (multi-year) trends in brightness. Although demonstrated on YSOs, our method is broadly applicable to other classes of variable stars with stochastic or complex light curves.As upcoming surveys like LSST and future Gaia data releases expand the variability parameter space, scalable tools for analysing irregular light curves are increasingly vital. Our approach provides a flexible framework for characterising complex stellar variability, complementing traditional classification and opening new paths for understanding variability across the Hertzsprung-Russell diagram.