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math.MG2025
Geometry and Dress groups with non-symmetric cost functions
Lukas Silvester Barth, Parvaneh Joharinad, Jürgen Jost +1
A metric relation by definition is symmetric. Since many data sets are non-symmetric, in this paper we develop a systematic theory of non-symmetric cost functions. Betweenness rela…
math.MG2022
Geometry of Data
Parvaneh Joharinad, Jürgen Jost
Topological data analysis asks when balls in a metric space intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this princip…
math.MG2019★ 17 cited
Topology and curvature of metric spaces
Parvaneh Joharinad, Jürgen Jost
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Bues…