Comparing Stochastic Young Stellar Object Light Curves Using Dimension Reduction and Clustering Algorithms

Terrestrial planet formation occurs within the inner regions of circumstellar discs. Areas that remain beyond the reach of direct imaging due to current resolution limitations. However, insights into the physical processes shaping these regions can be gained by analysing the photometric variability of Young Stellar Objects. This variability arises from a range of mechanisms, including accretion dynamics, variable extinction, and stellar surface inhomogeneities, each contributing valuable information about the structure and evolution of the planet-forming environment. Wepresent a quantitative framework for comparing light curves based on variability fingerprints. These are two-dimensional histograms encoding the probability of observing a given increase or decrease in brightness over all timescales. Applied to a refined subset of 240 highly variable young stellar objects from our dataset, these fingerprints span variability from ±0.05 to ±2.0mag over timescales of 1 day to 8.6 years, with > 90% achieving S/N > 3. Dimensionality reduction via principal component analysis was found to yield a topologically stable variability landscape, in contrast to the sample-sensitive output of non-linear dimension reduction. The projections were minimally affected by the addition or removal of individual sources, enabling robust comparison between observed and model-generated light curves. Simple sinusoidal models with the cadence of an observed dataset and random phase occupied a restricted region of principal component analysis space, indicating that cadence, observing baseline, and photometric noise do not dominate the global structure. Although principal component analysis provided a stable low-dimensional representation, neither it nor t-stochastic neighbour embedding in conjunction with clustering algorithms revealed distinct clusters. Instead, the data formed a continuum, reflecting the overlapping physical processes driving variability of young stellar objects. Indicating that a continuous, rather than categorical, framework is more appropriate. Analysis of the loadings matrices for the two dominant principal components revealed that the primary axis of variance corresponds to the onset timescale of significant (∆mag > 0.3) variability, with 1–3 month trends being most influential. The second component primarily encodes long-term (> 1.5 yr) variability of either increasing or decreasing brightness. By manually inspecting the light curves of objects that lie near one another in the principal component analysis projection, we confirmed that these neighbours display genuinely similar variability patterns. This shows that the principal component coordinates successfully group together stars with comparable light-curve morphology. These results demonstrate that principle component analysis of variability fingerprints provides a statistically robust and interpretable landscape for comparing observed young stellar object light curves and constraining synthetic variability models rooted in planet formation scenarios.