"Local Structure and effective Dimensionality of Time Series Data Sets"
Dörfler, MonikaIn this talk, we discuss the development of novel tools for understanding the local structure of systems of functions, e.g. time-series data points. Some of the envisaged tools are 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. 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. This is joint work with Franz Luef and Eirik Skrettingland.