Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition
Gurjeet Singh1 , Facundo Mémoli2 and Gunnar Carlsson†2
1Institute for Computational and Mathematical Engineering, Stanford University, California, USA.
2Department of Mathematics, Stanford University, California, USA.
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.
Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling.
In Eurographics Symposium on Point-Based Graphics (2007) M. Botsch, R. Pajarola (Editors)
DOWNLOAD PAPER (Link to .PDF).
Note of the Editor: The core algorithm, called “Mapper”, developed at Stanford in the Computational Topology group by Gunnar Carlsson and Gurjeet Singh has been turned into a product by a company called Ayasdi.