5 papers
Expected Length of the Euclidean Minimum Spanning Tree and 1-norms of Chromatic Persistence Diagrams in the Plane
OndÅej Draganov, Herbert Edelsbrunner, Sophie Rosenmeier +1
Let be the constant such that the expected length of the Euclidean minimum spanning tree of random points in the unit square is in the limit, when goes to…
Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack
OndÅej Draganov, Sophie Rosenmeier, Nicolò Zava
Chromatic metric pairs consist of a metric space and a coloring function partitioning a subset thereof into various colors. It is a natural extension of the notion of chromatic poi…
The Shape of Word Embeddings: Quantifying Non-Isometry With Topological Data Analysis
OndÅej Draganov, Steven Skiena
Word embeddings represent language vocabularies as clouds of -dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of rep…
The Euclidean MST-ratio for Bi-colored Lattices
Sebastiano Cultrera di Montesano, OndÅej Draganov, Herbert Edelsbrunner +1
Given a finite set, , and a subset, , the \emph{MST-ratio} is the combined length of the minimum spanning trees of and …
Chromatic Alpha Complexes
Sebastiano Cultrera di Montesano, OndÅej Draganov, Herbert Edelsbrunner +1
Motivated by applications in the medical sciences, we study finite chromatic sets in Euclidean space from a topological perspective. Based on the persistent homology for images, ke…