Time Series Analysis using a Kernel based Multi-Modal Uncertainty Decomposition Framework

This paper proposes a kernel based information theoretic framework that provides a sensitive multi-modal quantification of time series uncertainty by leveraging a quantum physical description of the projected feature space of data in a Reproducing Kernel Hilbert Space (RKHS). We specifically modify the kernel mean embedding, which yields an intuitive physical interpretation of the signal structure, to produce a data based “dynamic potential field”. This results in a new energy based formulation that exploits the mathematics of quantum theory and facilitates a multi-modal physics based uncertainty representation of the signal at each data sample. We demonstrate in this paper that such uncertainty features provide a better ability for online detection of statistical change points in time series data when compared to existing non-parametric and unsupervised methods. We also demonstrate a better ability of the framework in clustering time series sequences when compared to discrete wavelet transform features on a subset of VidTIMIT speaker recognition corpus.