Cited by 514Topological and Geometric Data Analysis3D Shape Modeling and AnalysisComputer Graphics and Visualization Techniques

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Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

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Singh, Gurjeet, Memoli, Facundo, Carlsson, Gunnar·2007·The Eurographics Association

DOI 10.2312/spbg/spbg07/091-100

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Abstract

We present a computational method for extracting simple descriptions of high dimensional data sets in the form of simplicial complexes. Our method, called Mapper, is based on the idea of partial clustering of the data guided by a set of functions defined on the data. The proposed method is not dependent on any particular clustering algorithm, i.e. any clustering algorithm may be used with Mapper. We implement this method and present a few sample applications in which simple descriptions of the data present important information about its structure.

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Authors: Singh, G., Memoli, F., & Carlsson, G.
ORCID: Carlsson, Gunnar
Venue: The Eurographics Association
Publisher: The Eurographics Association
Published: 2007
DOI: 10.2312/spbg/spbg07/091-100
OpenAlex: W1607787316
Cited by: 514
References: 18
Citations by year: 2026: 9 · 2025: 33 · 2024: 33 · 2023: 37 · 2022: 39 · 2021: 54 · 2020: 73 · 2019: 74 · 2018: 44 · 2017: 29 · 2016: 26 · 2015: 16 · 2014: 18 · 2013: 5 · 2012: 6
FWCI: 5.06
Type: journal article
Language: en
Open access: green
doi.org
Locations: Eurographics
Topics: Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › 3D Shape Modeling and Analysis
Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
Keywords: Mapper algorithm, simplicial complexes, topological data analysis, high-dimensional data, 3D object recognition

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Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition

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