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Poor scaling of dynamics simulations with number of dimensions is currently a major limiting factor in the simulation of photochemical processes. In this work, we investigate ways to reduce the dimensionality of many-atom systems with a view toward enhancing computational efficiency while maintaining accuracy. Using mixed quantum-classical Trajectory Surface Hopping (TSH) simulations of three photoreactive molecules-trans-azomethane (tAZM), butyrolactone (Bulac), and furanone (Fur)-we explore two different dimensionality reduction techniques: Principal Component Analysis (PCA) and Normal Mode Variance (NMV). Dynamics simulations are run in full dimensionality and reduced dimensionality, employing either PCA or NMV, and the impact of the dimensionality reduction on selected electronic and geometric properties of the dynamics is evaluated. For all three molecules, both PCA and NMV can be used to select lower-dimensional spaces in which the full-dimensionality dynamics results are reproduced. PCA reduction outperforms NMV in all systems, allowing for a more significant dimensionality reduction without loss of accuracy. The improved accuracy of PCA is, for tAZM, mostly seen in the electronic properties while for both Fur and Bulac the advantage is clear in the ring-opening reaction itself as well. The present approach opens routes to simulation of larger photochemically relevant systems, through the use of automated dimensionality reduction, avoiding human bias.