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Elenco seminari del ciclo di seminari
“TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS”
The aim of this cycle of seminars is twofold. On one side, we want to focus on the applied side of topology. We would like to discuss how deep, abstract mathematical frameworks can be applied to creative contexts, in particular to music, which will be the leitmotif of the three seminars. We aim at showing how topological persistence allows to compute novel, unexpected features, even when applied to a complex and subjective field, as music can be. On the other side, we would like to discuss a simple analysis of musical lyrics, involving both deep learning and topology. We will shoe how the latter can be used to better understand the results coming form a deep learning model. Hopefully, this last purpose will bring to discuss how artificial intelligence and mathematics can be integrated, in order to achieve a better understanding of deep learning.
2017
16 gennaio
Mattia G. Bergomi
nel ciclo di seminari: TOPOLOGY, DEEP LEARNING, AND APPLICATIONS TO CREATIVE CONTEXTS
Seminario interdisciplinare
Can music be represented as a meaningful geometric and topological object? We propose a strategy to describe some music features as a polyhedral surface obtained by a simplicial interpretation of the Tonnetz. The Tonnetz is a graph largely used in computational musicology to describe the harmonic relationships of notes in equal tuning. In particular, we use persistent homology to describe the persistent properties of music encoded in the aforementioned model. Both the relevance and the characteristics of this approach are discussed by analysing some paradigmatic compositional styles. Eventually, the task of automatic music style classification is addressed by computing the hierarchical clustering of the topological fingerprints associated with some collections of compositions.
Keywords: Tonnetz, persistent homology, clustering
75 minutes talk, 45 minutes discussion.