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Extracting from trajectory data meaningful information to understand complex systems might be non-trivial. High-dimensional analyses are typically assumed to be desirable, if not required, to prevent losing important information. However, to what extent such high-dimensionality is really needed/beneficial often remains not clear. Here we challenge such a fundamental general problem. As first representative cases of a system with internal dynamical complexity, we study atomistic molecular dynamics trajectories of liquid water and ice coexisting in dynamical equilibrium in correspondence of the solid/liquid transition temperature. To attain an intrinsically high-dimensional analysis, we use the Smooth Overlap of Atomic Positions (SOAP) descriptor, obtaining a large dataset containing 2.56e6 576-dimensional SOAP vectors that we analyze in various ways. Surprisingly, our results demonstrate how the time-series data contained in one single SOAP dimension accounting only for <0.001% of the total variance (thus considered negligible and discarded in typical variance-based dimensionality reduction approaches) is as much, and even more descriptive than the entire high-dimensional dataset. Adding more dimensions to the analysis is found detrimental due to "frustrated information" phenomena that are proven general, and are observed also in the analysis of, e.g., experimental trajectories of collective convolutions of active microparticles (used as a second case study). This work explicitly demonstrates how high-dimensional analyses are not necessarily better than low-dimensional ones. These results also demonstrate the importance of considering the quality (relevance) over the quantity of information, especially when dealing with noisy high-dimensional datasets, where the noise of one dimension may have higher statistical weight than the relevant information contained into another.

Reconstructing the physical complexity of many-body dynamical systems can be challenging. Starting from the trajectories of their constitutive units (raw data), typical approaches require selecting appropriate descriptors to convert them into time-series, which are then analyzed to extract interpretable information. However, identifying the most effective descriptor is often non-trivial. Here, we report a data-driven approach to compare the efficiency of various descriptors in extracting information from noisy trajectories and translating it into physically relevant insights. As a prototypical system with non-trivial internal complexity, we analyze molecular dynamics trajectories of an atomistic system where ice and water coexist in equilibrium near the solid/liquid transition temperature. We compare general and specific descriptors often used in aqueous systems: number of neighbors, molecular velocities, Smooth Overlap of Atomic Positions (SOAP), Local Environments and Neighbors Shuffling (LENS), Orientational Tetrahedral Order, and distance from the fifth neighbor ($d_5$). Using Onion Clustering -- an efficient unsupervised method for single-point time-series analysis -- we assess the maximum extractable information for each descriptor and rank them via a high-dimensional metric. Our results show that advanced descriptors like SOAP and LENS outperform classical ones due to higher signal-to-noise ratios. Nonetheless, even simple descriptors can rival or exceed advanced ones after local signal denoising. For example, $d_5$, initially among the weakest, becomes the most effective at resolving the system's non-local dynamical complexity after denoising. This work highlights the critical role of noise in information extraction from molecular trajectories and offers a data-driven approach to identify optimal descriptors for systems with characteristic internal complexity., Comment: 19 pages, 5 figures + 3 in supporting information (at the bottom of the manuscript)