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Cluster identification via persistent homology and other clustering techniques, with application to liver transplant data. (English) Zbl 1405.62086

Chambers, Erin Wolf (ed.) et al., Research in computational topology. Based on the first workshop for women in computational topology, Minneapolis, MN, USA, August 2016. Cham: Springer; Minneapolis, MN: Institute for Mathematics and its Applications (IMA) (ISBN 978-3-319-89592-5/hbk; 978-3-319-89593-2/ebook). Association for Women in Mathematics Series 13, 145-177 (2018).
Summary: Clustering, an unsupervised learning method, can be very useful in detecting hidden patterns in complex and/or high-dimensional data. Persistent homology, a recently developed branch of computational topology, studies the evolution of topological features under a varying filtration parameter. At a fixed filtration parameter value, one can find different topological features in a dataset, such as connected components (zero-dimensional topological features), loops (one-dimensional topological features), and more generally, \(k\)-dimensional holes (\(k\)-dimensional topological features). In the classical sense, clusters correspond to zero-dimensional topological features. We explore whether higher dimensional homology can contribute to detecting hidden patterns in data. We observe that some loops formed in survival data seem to be able to detect outliers that other clustering techniques do not detect. We analyze patterns of patients in terms of their covariates and survival time, and determine the most important predictor variables in predicting survival times of liver transplant patients by applying a random survival forest.
For the entire collection see [Zbl 1401.55001].

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
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