Extracting insights from the shape of complex data using topology

P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Alagappan, J. Carlsson, G. Carlsson*, Mikael Vilhelm Vejdemo Johansson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number1236
Number of pages8
JournalScientific Reports
Volume3
DOIs
Publication statusPublished - 7 Feb 2013

Keywords

  • Breast-cancer
  • Carcinomas
  • Survival
  • Predict

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