GRAPH FOURIER TRANSFORM: A STUDY OF TIME-DEPENDENT GRAPH SIGNALS

Many real-world systems can be modeled as networks, where elements are connected and influence one another. Traditional analytical tools often fall short when analyzing such systems, as they lack the ability to exploit the explicit relationships between nodes. This problem is further complicated when trying to account for changes over time. This thesis explores the Graph Fourier Transform (GFT), a central tool in the Graph Signal Processing (GSP) field, to analyze time-evolving signals on fixed-structure networks. Two distinct real-world cases are studied: human gait analysis, where the human body is modeled as a biomechanical graph of joints, and public transport analysis, where the evolution of delays at train stations is studied to understand congestion periods. In both cases, GFT is used to decompose signals into normal variational modes, enabling dimensionality reduction and interpretability. The study guides the reader on how GFT can effectively simplify the complexity of time-varying graph signals and suggest its use for feature extraction in Machine Learning tasks. These findings aim to promote the practical adoption of GSP in applied data science and offer a reference framework for other instances of evolving graph signals.