Extracting insights from the shape of complex data using topology
P. Y. Lum, G. Singh,A. Lehman,T. Ishkanov,M. Vejdemo-Johansson,M. Alagappan,J. Carlsson & G. Carlsson
Scientific Reports 3, Article number: 1236 doi:10.1038/srep01236
Received 13 September 2012 Accepted 06 December 2012 Published 07 February 2013
This paper applies topological methods to study complex high dimensional data sets by extracting shapes (patterns) and obtaining insights about them. Our method combines the best features of existing standard methodologies such as principal component and cluster analyses to provide a geometric representation of complex data sets. Through this hybrid method, we often find subgroups in data sets that traditional methodologies fail to find. Our method also permits the analysis of individual data sets as well as the analysis of relationships between related data sets. We illustrate the use of our method by applying it to three very different kinds of data, namely gene expression from breast tumors, voting data from the United States House of Representatives and player performance data from the NBA, in each case finding stratifications of the data which are more refined than those produced by standard methods.
Subject terms: Applied mathematics Computational science Scientific data Software
Published in Nature.com- 07 February 2013
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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.