Adaptive Modeling and Signal Discovery in Time Series Data

Many natural and engineered processes evolve over time, producing sequences of observations known as time series. This dissertation contains two different perspectives on the analysis of time series data. First, it examines Gaussian processes regarding their application on continuous data streams and their latent structure information. A novel algorithm is introduced for incrementally updating Gaussian process models with incoming data, supported by a model-based online change point detection mechanism that enables real-time inference. Additionally, two novel approaches are presented to extract and compare latent structural information from multiple time series using Gaussian process kernels. The second part of this dissertation contains new methods for tracking signals in high-frequency sensor data by identifying occurrences of similar, related signals. While broadly applicable to various domains involving high-frequency measurements, this thesis focuses on pharmacological recordings of the electrical activity of pancreatic β-cells. Inter-cellular influence can cause the propagation of individual signals, which is a current topic of discussion in diabetes research. This dissertation presents MoTrack, an algorithm to identify the spatio-temporal propagation of an individual signal within large time series data. We further introduce a clustering-based expansion of MoTrack, facilitating the efficient search for all propagating signals within a dataset. Both methods have been used for preliminary experiments and produced promising results, revealing influence patterns and areas of high interconnectivity between β-cells.