翻訳と辞書 Words near each other ・ Topolobampo ・ Topolog ・ Topolog River (Danube) ・ Topolog River (Olt) ・ Topolog Viaduct ・ Topolog, Tulcea ・ Topologel River ・ Topological abelian group ・ Topological algebra ・ Topological Boolean algebra ・ Topological category ・ Topological censorship ・ Topological combinatorics ・ Topological complexity ・ Topological conjugacy ・ Topological data analysis ・ Topological defect ・ Topological degeneracy ・ Topological degree theory ・ Topological derivative ・ Topological divisor of zero ・ Topological drugs ・ Topological dynamics ・ Topological entropy ・ Topological entropy in physics ・ Topological excitations ・ Topological fluid dynamics ・ Topological functioning model ・ Topological game ・ Topological graph Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Topological data analysis ： ウィキペディア英語版 Topological data analysis Topological data analysis (TDA) is a new and vastly growing branch of applied mathematics. Data analysis is of extreme importance in almost all areas of modern applied science. However, to extract information from real data which are usually large, high-dimensional, incomplete and noisy is challenging. TDA provides a general framework to analyze data, being successful in coordinate-freeness, insensitive to particular metric, 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. == Basic theory == Basic concepts and theoretical results in TDA will be introduced. Specially, the focus would be on the standard paradigm, namely the barcode of point clouds. These results are widely used in applications. For the basic concepts of algebraic topology, please refer to section 2 of Carlsson for a short introduction, or to the standard textbooks, such as Hatcher. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Topological data analysis」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.