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- Q4460773 subject Q11711429.
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- Q4460773 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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- Q4460773 comment "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.".
- Q4460773 label "Topological data analysis".