Topological data analysis (TDA)


Topic | v3 | updated by janarez |
Description

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 generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools. The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields.


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uses Topology

In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is conce...

a tool for Data science

Data science is an inter-disciplinary field that uses scientific methods, processes, algorithms and s...


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is treated in Topological data analysis

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Basic topological concepts and models and their use in data analysis will be introduced. Course c...

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is treated in Topological Data Analysis

Introductory Topological Data Analysis (TDA) course that includes notes and class videos as well as p...