Geometric and topological inference deals with the retrieval of
information about a geometric object using only a finite set of
possibly noisy sample points. It has connections to manifold
learning and provides the mathematical and algorithmic foundations
of the rapidly evolving field of topological data analysis.
Building on a rigorous treatment of simplicial complexes and
distance functions, this self-contained book covers key aspects of
the field, from data representation and combinatorial questions to
manifold reconstruction and persistent homology. It can serve as a
textbook for graduate students or researchers in mathematics,
computer science and engineering interested in a geometric approach
to data science.
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