PhD Defense: 'Bayesian nonparametric dynamical clustering of time series'

Many systems reveal themselves through repetition: a heart beating, a wave arriving at a coast, a machine cycling through its operating modes. The fundamental question is not just what shapes recur, but how many there are, how they evolve, and how they relate in sequence. This thesis introduces the hierarchical Dirichlet Process - Gaussian process clustering (HDP-GPC), a Bayesian nonparametric model that infers an unbounded number of evolving cluster prototypes from sequential data, with calibrated uncertainty and explicit temporal alignment. Validation on ECG arrhythmia analysis, clinical differentiation of Takotsubo syndrome from myocardial infarction, and ocean wave spectra clustering demonstrates that parsimonious, interpretable clustering can itself become a tool for discovering the underlying phenomena.

Supervisor: Paulo Félix Lamas