Abstract

Revealing hidden patterns in time-evolving data. Data collected over time is everywhere, from biological measurements  in medical studies, to sensor readings in industrial systems, to user  activity on digital platforms. When researchers track multiple  measurements of subjects or entities over many time points, they end  up with enormous, complex datasets that standard analysis tools  struggle to handle. This thesis develops new mathematical methods  designed specifically for that challenge. 

The goal of the project is not to predict outcomes, but rather to  describe and understand the patterns that are present in the data as  well as how they evolve over time and how they differ across  individuals. 

How is the research carried out? The methods belong to a family of mathematical techniques called  matrix and tensor factorizations. Think of a dataset as a three dimensional table, with the axes being e.g. entities, measurements, and time points, and the goal is decomposing that table into a small  number of meaningful building blocks, called factors, that together  explain the observed patterns. 

Existing tools largely ignore the fact that time points are ordered  and connected. Consider tracking how a disease progresses over time:  measurements taken days apart should look more similar than  measurements taken months apart. Ignoring this is like treating each  visit as if it happened in isolation. The methods proposed here take  that structure into account, by encouraging patterns to evolve  smoothly over time or by modelling dynamics using principles from  physics and engineering. 

Real-world datasets often suffer from missing measurements, and  recovered patterns can be hard to interpret without additional  guidance. Imposing meaningful constraints on the factors, for example  requiring them to change smoothly over time or to remain non-negative, improves both interpretability and robustness to noise. New algorithms  introduced in this thesis allow the methods to incorporate such  constraints even when data are incomplete.

What are the key findings? The new time-aware methods recover underlying patterns more accurately  than existing approaches, especially when data is noisy or patterns  are subtle and slow-moving. The thesis also shows how existing methods  can be used to track each individual's evolution over time, revealing  differences between subjects that a group-level analysis would  overlook. 

A further contribution is a principled way to assess whether recovered  patterns are consistent across different runs of the analysis — an  important quality check that is often overlooked. Together, these  contributions can provide scientists with more powerful and  trustworthy tools for understanding how complex systems change over  time.

Trial lecture

Prior to the defence, at 16:00, Christos will present his trial lecture in the same location.

Title: State-Space Models and Sequential Latent-Variable Methods for Analyzing Dynamical Systems

Adjudication committee

• First opponent: Professor Vagelis Papalexakis, University of California Riverside, USA.
• Second opponent: Professor Selin Aviyente, Michigan State University, USA

Chair of the committee

• Professor Jianhua Zhang, OsloMet

Supervisors

• Main supervisor: Chief Research Scientist Evrim Acar Ataman, Simula Metropolitan Center for Digital Engineering
• Co-supervisor: Professor Max Pfeffer, University of Potsdam, Fraunhofer Institute for Cell Therapy and Immunology
• Co-supervisor: Professor Pedro Lind, Kristiania University of Applied Sciences

Chair of defence

TBA

Read more about the research on the announcement at OsloMet's webpage. Information about streaming will become available.