|Dept.||Kentucky State University|
Algebraic topological tools can be used in understanding the shape of the data and its meaning. The concept of functoriality is applied to data analysis by introducing parametrized maps from the data space into algebraic objects and parametrized morphisms. Data can be viewed as a finite metric space in most scientific practices. Persistent homology which allows multiscale summary of data by persisting homology classes is a well known example in TDA. Hierarchical clustering may be viewed as the zero dimensional persistent homology. A brief review of TDA tools and basic topological background will be presented.