Relevant, Hidden, and Frustrated Information in High-Dimensional Analyses of Complex Dynamical Systems with Internal Noise

576-dimensional SOAP spectra that we analyze in various ways. Our results demonstrate how the time-series data contained in one single SOAP dimension accounting only <0.001% of the total dataset's variance (neglected and discarded in typical variance-based dimensionality reduction approaches) allows resolving a remarkable amount of information, classifying/discriminating the bulk of water and ice phases, as well as two solid-interface and liquid-interface layers as four statistically distinct dynamical molecular environments. Adding more dimensions to this one is found not only ineffective but even detrimental to the analysis due to recurrent negligible-information/non-negligible-noise additions and "frustrated information" phenomena leading to information loss. Such effects are proven general and are observed also in completely different systems and descriptors' combinations. This shows how high-dimensional analyses are not necessarily better than low-dimensional ones to elucidate the internal complexity of physical/chemical systems, especially when these are characterized by non-negligible internal noise.