Analysing time-evolving data is an important and challenging task in many fields, such as neuroimaging analysis, network analysis and signal processing. If the data contains measurements of multiple samples with multiple features that change over time, it forms a multi-way dataset. Such complex data is often generated by signals from several different sub-processes. Tensor factorisation methods, which decompose a multi-way dataset into low-rank components, can be used to extract interpretable temporal patterns from multivariate dynamic data that give insight into these latent subprocesses.
In addition to capturing temporal patterns, capturing dynamic components that evolve over time and tracing their evolution can give deeper insights into the dynamics of complex data. However, there is a lack of methods that can capture such dynamic components. Therefore, we investigate the PARAFAC2 model, which allows the patterns of one mode (e.g. features, voxels or time) to evolve across another (e.g. time or samples). This property makes it a compelling approach for capturing time-evolving patterns. Nevertheless, PARAFAC2's suitability for extracting dynamic components is largely unexplored, and no algorithmic framework currently supports imposing flexible constraints on all modes of the PARAFAC2 model.
In this work, we use both simulated and real-world datasets to demonstrate the PARAFAC2 model’s ability to uncover both temporal patterns and time-evolving components and introduce a new algorithm for fitting constrained PARAFAC2 models. We evaluate the new algorithm on applications from neuroscience and chemometrics, which show that imposing domain-inspired constraints improves the interpretability of the extracted patterns. Moreover, to facilitate findable, accessible, interoperable and reusable (FAIR) research software, we create two open-source software packages, one for fitting PARAFAC2 models with the proposed algorithm and one for visualising and analysing tensor decomposition models. Finally, we uncover multiscale temporal patterns of mobile network speed variation by applying the CANDECOMP/PARAFAC (CP) model to a network speed dataset with missing data.
First opponent: Morten Mørup, Professor/PhD, Cognitive systems, DTU (Technical University of Denmark).
Second opponent: Katrijn Van Deun, Associate Professor/PhD, Department of Methodology and Statistics. Tilburg School of Social and Behavioral Sciences. Tilburg University, the Netherlands.
Leader of the evaluation committee/Chair of the committee: Pedro Lind, Professor, Faculty of Technology, Art and Design, Dept. of Computer Science OsloMet.
Leader of the public defense
Boning Feng, Head of Group, Department of Computer Science, Faculty of Technology, Art and Design, OsloMet.
Main supervisor: Evrim Acar Ataman, Head of Department, Chief Research Scientist, Research Professor, SimulaMet.