Mercoledì 8 Febbraio 2023, alle 4:00 pm (CET) in aula U5-3014, nel quadro della serie di seminari Insalate di Matematica, Victoria Callet (IRMA, Université de Strasbourg) parlerà di
Title: Persistent Homology and Application to Music Classification"
Abstract: Persistent homology is a computational tool which was created in the end of the 20th century for applied algebraic topology. The main idea is to understand the topological structure of a starting object by progressive approximations: for that we use simplicial theory and more precisely simplicial complexes and homology, which we will begin by remind the basis. In practice, we extract from our starting object a point cloud and we change it into a filtered simplicial complex by using an algorithm called the Vietoris-Rips filtration. Persistent homology then encodes the evolution of homology classes and more precisely their lifespan in the new created filtration. We will represent all these informations on a family of graphs called barcodes, from which we will be able to analyze or even compare several starting objects: this process is called Topological Data Analysis. As an illustration of persistent homology and TDA, we will see how we can apply it to classification of musical style.
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