Extracting insights from the shape of complex data using topology

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 repre...

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Bibliographic Details
Published in:Scientific reports 2013-02, Vol.3 (1), p.1236-1236, Article 1236
Main Authors: Lum, P. Y., Singh, G., Lehman, A., Ishkanov, T., Vejdemo-Johansson, M., Alagappan, M., Carlsson, J., Carlsson, G.
Format: Article
Language:English
Subjects:
639/705/1041
639/705/1042
639/705/1046
639/705/794
Athletes
Basketball
Breast Neoplasms - genetics
BREAST-CANCER
CARCINOMAS
Cluster Analysis
Data processing
Datasets
Female
Gene expression
Gene Expression Regulation, Neoplastic
Humanities and Social Sciences
Humans
Mathematics
multidisciplinary
Pattern Recognition, Automated - methods
Politics
PREDICT
Principal Component Analysis
Science
SURVIVAL
Topology
Tumors
United States
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/srep01236