Quantum Distance Approximation for Persistence Diagrams

arXiv:2402.17295v1 Announce Type: cross
Abstract: Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially complex and high dimensional data sets. The space of persistence diagrams can be endowed with various metrics such as the Wasserstein distance which admit a statistical structure and allow to use these summaries for machine learning algorithms. However, computing the distance between …

abstract analysis approximation arxiv classification clustering cs.lg data data analysis data sets diagrams fields information persistence quant-ph quantum space tasks type