Stratified space learning: Reconstructing embedded graphs

Reconstructing linearly embedded graphs: A first step to stratified space learning

Foundations of Data Science ◽

10.3934/fods.2021026 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Yossi Bokor ◽

Katharine Turner ◽

Christopher Williams

Keyword(s):

Data Analysis ◽

Computational Geometry ◽

Algebraic Topology ◽

Point Cloud ◽

Topological Data Analysis ◽

Stratified Spaces ◽

Embedded Graphs ◽

Embedded Graph ◽

Stratified Space ◽

Abstract Structure

<p style='text-indent:20px;'>In this paper, we consider the simplest class of stratified spaces – linearly embedded graphs. We present an algorithm that learns the abstract structure of an embedded graph and models the specific embedding from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding. The algorithm is implemented in the Julia package Skyler, which we used for the numerical simulations in this paper.</p>

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The cycle’s structure of embedded graphs in surfaces

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-015-0530-0 ◽

2015 ◽

Vol 31 (4) ◽

pp. 1073-1082

Author(s):

Zhao-xiang Li ◽

Han Ren

Keyword(s):

Embedded Graphs

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Structural Classifier Ensembles for Vector Space Embedded Graphs

2007 International Joint Conference on Neural Networks ◽

10.1109/ijcnn.2007.4371180 ◽

2007 ◽

Author(s):

Kaspar Riesen ◽

Horst Bunke

Keyword(s):

Vector Space ◽

Classifier Ensembles ◽

Embedded Graphs

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A Near-Linear Approximation Scheme for Multicuts of Embedded Graphs with a Fixed Number of Terminals

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms ◽

10.1137/1.9781611975031.95 ◽

2018 ◽

pp. 1439-1458

Author(s):

Vincent Cohen-Addad ◽

Éric Colin de Verdière ◽

Arnaud de Mesmay

Keyword(s):

Linear Approximation ◽

Approximation Scheme ◽

Fixed Number ◽

Embedded Graphs

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The Enumeration of Maps on the Torus and the Projective Plane

Canadian Mathematical Bulletin ◽

10.4153/cmb-1988-039-4 ◽

1988 ◽

Vol 31 (3) ◽

pp. 257-271 ◽

Cited By ~ 33

Author(s):

E. A. Bender ◽

E. R. Canfield ◽

R. W. Robinson

Keyword(s):

Projective Plane ◽

Generating Functions ◽

Recurrence Relations ◽

Embedded Graphs ◽

Asymptotic Expressions ◽

Explicit Expressions

AbstractThe enumeration of rooted maps (embedded graphs), by number of edges, on the torus and projective plane, is studied. Explicit expressions for the generating functions are obtained. From these are derived asymptotic expressions and recurrence relations. Numerical tables for the numbers with up to 20 edges are presented.

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