2013/02/07 by Pek Yee Lum, Satwinder Singh, Amy Lehman +5 · 549 citations
Computer Science · Mathematics · Biochemistry, Genetics and Molecular Biology · #Topological and Geometric Data Analysis #Morphological variations and asymmetry #Cell Image Analysis Techniques #Computer science #Data mining #Topological data analysis #Representation (politics) #Principal component analysis #Voting #External Data Representation #Topology (electrical circuits) #Pattern recognition (psychology) #Artificial intelligence #Algorithm #Mathematics
paper · pdf · doi:10.1038/srep01236
published in Scientific Reports 3(1), 1236 (Nature Portfolio)
openalex publication_date 2013/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
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.