  The goal of this paper is to develop novel tools for understanding the local
structure of systems of functions, e.g. time-series data points, such as the
total correlation function, the Cohen class of the data set, the data operator
and the average lack of concentration. The Cohen class of the data operator
gives a time-frequency representation of the data set. Furthermore, we show
that the von Neumann entropy of the data operator captures local features of
the data set and that it is related to the notion of the effective
dimensionality. The accumulated Cohen class of the data operator gives us a
low-dimensional representation of the data set and we quantify this in terms of
the average lack of concentration and the von Neumann entropy of the data
operator by an application of a Berezin-Lieb inequality. The framework for our
approach is provided by quantum harmonic analysis.
