  Understanding the loss of information in spectral analytics is a crucial
first step towards finding root causes for failures and uncertainties using
spectral data in artificial intelligence models built from modern complex data
science applications. Here, we show from an elementary Shannon entropy model
analysis with quantum statistics of Gaussian distributed spectral data, that
the relative loss of information from dimensionality reduction due to the
projection of an initial five-dimensional dataset onto two-dimensional diagrams
is less than one percent in the parameter range of small data sets with sample
sizes on the order of few hundred data samples. From our analysis, we also
conclude that the density and expectation value of the entropy probability
distribution increases with the sample number and sample size using artificial
data models derived from random sampling Monte Carlo simulation methods.
