We develop a framework for analyzing communitity structures in dynamic networks based on the established community tree representation. With the information revealed by community trees and the corresponding persistence diagrams, our proposed approach can efficiently detect clique communities and keep track of the major structural changes during their evolution given a stability threshold.
We present a new method, referred as Sparse-TDA method, that combines persistence image-based TDA method with QR pivoting-based sparse sampling algorithm to transform topological features into image pixels and identify discriminative pixel samples in the presence of noisy and redundant information.
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a …
We apply TDA for the first time (to the best of our knowledge) on manufacturing process data to extract the key process variables that have the most significant impact on the outputs. The results are summarized in the form of a topological network to facilitate a better understanding of the casual relationships between process variables and outputs through direct visualization.
In this paper, we extend the application of topological data analysis (TDA) to the field of manufacturing for the first time to the best of our knowledge. We apply a particular TDA method, known as the Mapper algorithm, on a benchmark chemical …