Abstract / truncated to 115 words (read the full abstract)

The aim of this thesis is to introduce a variety of signal processing methodologies specifically designed to model, interpret, and learn from data structured within topological spaces. These spaces are loosely characterized as a collection of points together with a neighborhood notion among points. The methodologies and tools discussed herein hold particular relevance and utility when applied to signals defined over combinatorial topological spaces, such as cell complexes, or within metric spaces that exhibit non-trivial properties, such as Riemann manifolds with non-flat metrics. One of the primary motivations behind this research is to address and surmount the constraints encountered with traditional graph-based representations when they are employed to depict intricate systems. This thesis emphasizes the ... toggle 7 keywords

topological signal processing – topological deep learning – manifold learning – sparse representation – latent topology inference – attention neural networks – algebraic topology

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