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Abstract:
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The persistent homology quantifies the salient topological features of data. In this talk, I will present how the confidence band can be computed for determining the significance of the topological features in the persistent homology, based on the bootstrap procedure. First, I will present how the confidence band can be computed for the persistent homology of KDEs (kernel density estimators) computed on a grid. In practice, however, computing the persistent homology on a grid can be computationally inefficient when the dimension of the ambient space is high or topological features are in different scales. Hence, I will consider the persistent homology of KDEs on Rips complexes, and describe how to construct a valid confidence band for the persistent homology based on the bootstrap procedure.
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