Persistent homology for random fields and complexes
By Robert J. Adler, Omer Bobrowski, M. S. Borman, Eliran Subag, Shmuel Weinberger. 2010
126 citations recorded by the source corpus.
We discuss and review recent developments in the area of applied algebraic topology, such as persistent homology and barcodes. In particular, we discuss how these are related to understanding more about manifold learning from random point cloud data, the algebraic structure of simplicial complexes determined by random vertices and, in most detail, the algebraic topology of the excursion sets of random elds.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ff0c3e082d680d072868684ba95cf7671c5f1dd3
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In Computational Theory and Mathematics
- Jonathan E. Taylor
- Omer Bobrowski
- Sayan Mukherjee
- Sivaraman Balakrishnan
- Frédéric Chazal
- Bertrand Michel
In Mathematical Physics
Citations in the corpus
- Finding and Leveraging Structure in Learning Problems (2012, background): “[Adler et al., 2010] study the homology induced by the level sets of certain Gaussian random fields.”
- The topology of probability distributions on manifolds (2013, background): “In topological data analysis there has been work on understanding properties of random abstract simplicial complexes generated from stochastic processes [1, 2, 5, 13, 28, 29, 30, 32, 46, 47] and non-asymptotic bounds on the convergence or consistency of topological summaries as the number of points ”
- Topological Consistency via Kernel Estimation (2014, background): “Asymptotic and non-asymptotic analysis of consistency and convergence of topological summaries as the number of observations increase has been examined for a variety of geometric objects using a variety of statistical and probabilistic tools [1, 2, 3, 4, 5, 8, 9, 12, 16, 30, 31, 36, 37].”