Ponencia
Separating Topological Noise from Features Using Persistent Entropy
Autor/es | Atienza Martínez, María Nieves
González Díaz, Rocío Rucco, Matteo |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2016 |
Fecha de depósito | 2019-07-01 |
Publicado en |
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ISBN/ISSN | 978-3-319-50229-8 0302-9743 |
Resumen | Topology is the branch of mathematics that studies shapes
and maps among them. From the algebraic definition of topology a new
set of algorithms have been derived. These algorithms are identified
with “computational ... Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology a new set of algorithms have been derived. These algorithms are identified with “computational topology” or often pointed out as Topological Data Analysis (TDA) and are used for investigating high-dimensional data in a quantitative manner. Persistent homology appears as a fundamental tool in Topological Data Analysis. It studies the evolution of k−dimensional holes along a sequence of simplicial complexes (i.e. a filtration). The set of intervals representing birth and death times of k−dimensional holes along such sequence is called the persistence barcode. k−dimensional holes with short lifetimes are informally considered to be topological noise, and those with a long lifetime are considered to be topological feature associated to the given data (i.e. the filtration). In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy. |
Identificador del proyecto | MTM2015-67072-P |
Cita | Atienza Martínez, M.N., González Díaz, R. y Rucco, M. (2016). Separating Topological Noise from Features Using Persistent Entropy. En STAF 2016: Collocated Workshops: DataMod, GCM, HOFM, MELO, SEMS, VeryComp (3-12), Vienna Austria: Springer. |
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Separating Topological Noise.pdf | 652.1Kb | [PDF] | Ver/ | |