|Dept.||Kentucky State University|
This tutorial will give a bref review of papers by G Carlson on topological data analysis (TDA ). Topology can contribute to the analysis of large scale complex data. Metric functions to study spaces are applicable to problems of estimating dissimilarity between objects in data. Topological tools, less sensitive to the choice of specific metric and more flexible to apply on various types of data, can be used to explore large high dimensional (very noisy) data sets. Topological (homotopy) invariants such as homology groups can be assigned to large data sets. Functorial properties are used to study objects and relations between objects simultaneously, and the concept of persistence summarizes the multi-scale properties over the whole domain of parameters.