2019-07-012019-07-012016Atienza 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.978-3-319-50229-80302-9743https://hdl.handle.net/11441/87712Topology 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Persistent homologyPersistence barcodesShannon entropyTopological noiseTopological featureinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess10.1007/978-3-319-50230-4_1