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Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Topological_data_analysis> ?p ?o }

• Topological_data_analysis abstract "In applied mathematics, Topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is in general challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric and provides dimension reduction and robustness to noise. Beyond, it inherits functorality, one of the keys to the modern mathematics, from its topological nature, which makes it adaptive to new tools from mathematics.The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to give mathematically strict and quantitative study of \"shape\". The main tool is persistent homology, a modified concept of homology group. Nowadays, this area has been proven to be successful in practice. It has been applied to many types of data input, and different data resource and numerous fields. Moreover, its mathematical foundation is also of theoretical importance to mathematics itself. Its unique features make it a promising bridge between topology and geometry.".
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• Topological_data_analysis wikiPageWikiLink Algebraic_geometry.
• Topological_data_analysis wikiPageWikiLink Algebraic_topology.
• Topological_data_analysis wikiPageWikiLink Annals_of_Mathematics.
• Topological_data_analysis wikiPageWikiLink Applied_mathematics.
• Topological_data_analysis wikiPageWikiLink Betti_number.
• Topological_data_analysis wikiPageWikiLink Category:Applied_mathematics.
• Topological_data_analysis wikiPageWikiLink Category:Computational_topology.
• Topological_data_analysis wikiPageWikiLink Category:Data_analysis.
• Topological_data_analysis wikiPageWikiLink Category:Homology_theory.
• Topological_data_analysis wikiPageWikiLink Category_theory.
• Topological_data_analysis wikiPageWikiLink Complex_network.
• Topological_data_analysis wikiPageWikiLink Computational_complexity_theory.
• Topological_data_analysis wikiPageWikiLink Computational_topology.
• Topological_data_analysis wikiPageWikiLink Computer_vision.
• Topological_data_analysis wikiPageWikiLink Confidence_interval.
• Topological_data_analysis wikiPageWikiLink Data_mining.
• Topological_data_analysis wikiPageWikiLink Dimensionality_reduction.
• Topological_data_analysis wikiPageWikiLink Discrete_Morse_theory.
• Topological_data_analysis wikiPageWikiLink Extended_real_number_line.
• Topological_data_analysis wikiPageWikiLink Fiber_(mathematics).
• Topological_data_analysis wikiPageWikiLink Field_(mathematics).
• Topological_data_analysis wikiPageWikiLink Functor.
• Topological_data_analysis wikiPageWikiLink Gunnar_Carlsson.
• Topological_data_analysis wikiPageWikiLink Herbert_Edelsbrunner.
• Topological_data_analysis wikiPageWikiLink Homology_(mathematics).
• Topological_data_analysis wikiPageWikiLink Initial_and_terminal_objects.
• Topological_data_analysis wikiPageWikiLink Lotka–Volterra_equations.
• Topological_data_analysis wikiPageWikiLink Machine_learning.
• Topological_data_analysis wikiPageWikiLink Matrix_multiplication.
• Topological_data_analysis wikiPageWikiLink Morse_theory.
• Topological_data_analysis wikiPageWikiLink Multidimensional_scaling.
• Topological_data_analysis wikiPageWikiLink Nerve_of_a_covering.
• Topological_data_analysis wikiPageWikiLink Persistent_homology.
• Topological_data_analysis wikiPageWikiLink Point_cloud.
• Topological_data_analysis wikiPageWikiLink Preorder.
• Topological_data_analysis wikiPageWikiLink Principal_component_analysis.
• Topological_data_analysis wikiPageWikiLink Principal_ideal_domain.
• Topological_data_analysis wikiPageWikiLink Probability_theory.
• Topological_data_analysis wikiPageWikiLink Reeb_graph.
• Topological_data_analysis wikiPageWikiLink Set_(abstract_data_type).
• Topological_data_analysis wikiPageWikiLink Shape_analysis_(digital_geometry).
• Topological_data_analysis wikiPageWikiLink Sheaf_(mathematics).
• Topological_data_analysis wikiPageWikiLink Simplicial_complex.
• Topological_data_analysis wikiPageWikiLink Single-linkage_clustering.
• Topological_data_analysis wikiPageWikiLink Size_theory.
• Topological_data_analysis wikiPageWikiLink Spectral_sequence.
• Topological_data_analysis wikiPageWikiLink Statistical_inference.
• Topological_data_analysis wikiPageWikiLink Topology.
• Topological_data_analysis wikiPageWikiLink Vietoris–Rips_complex.
• Topological_data_analysis wikiPageWikiLink Wasserstein_metric.
• Topological_data_analysis wikiPageWikiLink Čech_cohomology.
• Topological_data_analysis wikiPageWikiLink File:Illustration_of_Typical_Workflow_in_TDA.jpeg.
• Topological_data_analysis wikiPageWikiLinkText "Topological Analysis".
• Topological_data_analysis wikiPageWikiLinkText "Topological data analysis".
• Topological_data_analysis wikiPageWikiLinkText "topological analyses".
• Topological_data_analysis wikiPageWikiLinkText "topological data analysis".
• Topological_data_analysis text "one being the study of homological invariants of data one individual data sets, and the other is the use of homological invariants in the study of databases where the data points themselves have geometric structure.".
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• Topological_data_analysis subject Category:Applied_mathematics.
• Topological_data_analysis subject Category:Computational_topology.
• Topological_data_analysis subject Category:Data_analysis.
• Topological_data_analysis subject Category:Homology_theory.
• Topological_data_analysis hypernym Approach.
• Topological_data_analysis type ProgrammingLanguage.

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