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In this chapter, we will introduce persistent homology, which is the mathematical tool we are going to use to apply the process of Topological Data Analysis to musical analysis. We will begin with a brief reminder of simplicial homology, and then move on to the definitions of filtration, persistence and barcodes. Notice that all computations will be done in \(\mathbb {F}_2\) , the ground field with two elements.

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Mathematical Background

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  • 发表日期：

    2025年

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  • Victoria Callet-Feltz

摘要

In this chapter, we will introduce persistent homology, which is the mathematical tool we are going to use to apply the process of Topological Data Analysis to musical analysis. We will begin with a brief reminder of simplicial homology, and then move on to the definitions of filtration, persistence and barcodes. Notice that all computations will be done in \(\mathbb {F}_2\) , the ground field with two elements.