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

2007/01/01 by Singh, Gurjeet, Facundo Mémoli, Gunnar Carlsson · 556 citations
Computer Science · #Topological and Geometric Data Analysis #Image Retrieval and Classification Techniques #Data Management and Algorithms #Cluster analysis #Computer science #Simple (philosophy) #Topological data analysis #Data mining #Set (abstract data type) #Clustering high-dimensional data #Object (grammar) #Data set #Pattern recognition (psychology) #Data structure #Data point #Algorithm #Artificial intelligence

paper · doi:10.2312/spbg/spbg07/091-100

published in Eurographics

openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

Citations

• Topological estimation using witness complexes
• The Sorcerer II Global Ocean Sampling Expedition: Expanding the Universe of Protein Families
• A Global Geometric Framework for Nonlinear Dimensionality Reduction
• Nonlinear Dimensionality Reduction by Locally Linear Embedding
• The Sorcerer II Global Ocean Sampling Expedition: Northwest Atlantic through Eastern Tropical Pacific

Cited by

• A fast algorithm for constructing topological structure in large data
• Topological data analysis [wikipedia]