Topological data analysis
Topological data analysis 5 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia In applied mathematics , topological based 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. [ citation needed ] 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 homol