Applications of Zigzag Persistence to Topological Data Analysis

The theory of zigzag persistence is a substantial extension of persistent homology, and its development has enabled the investigation of several unexplored avenues in the area of topological data analysis. In this paper, we discuss three applications of zigzag persistence: topological bootstrapping, parameter thresholding, and the comparison of witness complexes. The newly emerging area of topological data analysis attempts to use techniques from algebraic topology to study qualitative properties of datasets. Its applicability has been demonstrated in areas as diverse as object recognition, sensor networks, and bioinformatics (Car09). The need for a topological approach to data analysis tasks is justied