Persistent Homology Analysis of Brain Artery Trees.
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New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.
Published Version (Please cite this version)10.1214/15-AOAS886
Publication InfoBendich, P; Marron, JS; Miller, E; Pieloch, A; & Skwerer, S (n.d.). Persistent Homology Analysis of Brain Artery Trees. Ann Appl Stat, 10(1). pp. 198-218. 10.1214/15-AOAS886. Retrieved from https://hdl.handle.net/10161/11157.
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Associate Research Professor of Mathematics
I am a mathematician whose main research focus lies in adapting theory from ostensibly pure areas of mathematics, such as topology, geometry, and abstract algebra, into tools that can be broadly used in many data-centeredapplications.My initial training was in a recently-emerging field called topological data analysis (TDA). I have beenresponsible for several essential and widely-used elements of its theoretical toolkit, with a particularfocus on building TDA methodology
Professor of Mathematics
Professor Miller's research centers around problems in geometry, algebra, topology, combinatorics, statistics, probability, and computation originating in mathematics and the sciences, including biology, chemistry, computer science, and imaging. The techniques range, for example, from abstract algebraic geometry or commutative algebra of ideals and varieties to concrete metric or discrete geometry of polyhedral spaces; from deep topological constructions such as equivariant K-theor
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