title: Extracting insights from the shape of complex data using topology.
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.
authors: Ayasdi Inc., Palo Alto, CA, USA.
authors: P Y
authors: PY
authors: Lum
authors: G
authors: G
authors: Singh
authors: A
authors: A
authors: Lehman
authors: T
authors: T
authors: Ishkanov
authors: M
authors: M
authors: Vejdemo-Johansson
authors: M
authors: M
authors: Alagappan
authors: J
authors: J
authors: Carlsson
authors: G
authors: G
authors: Carlsson
mesh_terms: D056352:Athletes; D001490:Basketball; D001943:Breast Neoplasms / Q000235:genetics; D016000:Cluster Analysis; D005260:Female; D015972:Gene Expression Regulation, Neoplastic; D006801:Humans; D008433:Mathematics; D010363:Pattern Recognition, Automated / Q000379:methods*; D011057:Politics; D025341:Principal Component Analysis; D014481:United States
references: Mod Pathol. 2005 Jan;18(1):26-35
references: 15332092
references: Mol Cancer Ther. 2006 Nov;5(11):2914-8
references: 17121939
references: Nature. 2002 Jan 31;415(6871):530-6
references: 11823860
references: Nature. 2000 Aug 17;406(6797):747-52
references: 10963602
references: Proc Natl Acad Sci U S A. 2011 Apr 26;108(17):7265-70
references: 21482760
references: Proc Natl Acad Sci U S A. 2001 Sep 11;98(19):10869-74
references: 11553815
references: Science. 2011 Dec 16;334(6062):1518-24
references: 22174245
references: Lancet. 2005 Feb 19-25;365(9460):671-9
references: 15721472
references: Breast Cancer Res. 2003;5(1):57-8
references: 12559048
references: Genome Biol. 2007;8(8):R157
references: 17683518
references: PLoS Comput Biol. 2011 Oct;7(10):e1002240
references: 22028643
references: J Chem Phys. 2009 Apr 14;130(14):144115
references: 19368437
references: N Engl J Med. 2002 Dec 19;347(25):1999-2009
references: 12490681