Application of Topological Data Analysis in Complex Network Structure Identification

Abstract

As a new mathematical tool, Topological Data Analysis (TDA) shows great potential in complex network structure identification. This paper systematically discusses the application method and potential value of TDA in identifying complex network structures. Complex networks, such as social networks, biological networks and traffic networks, are highly nonlinear and dynamic, which challenges the traditional data analysis methods. TDA reveals hidden laws and patterns by digging deep into the internal topological structure of data, which provides a new perspective for network science research. This paper first introduces the basic knowledge of complex network and TDA, and then constructs a comprehensive identification framework, including data preprocessing, topological feature extraction, dimensionality reduction and structure identification. Using persistent homology and other TDA methods, we extract key topological features from the networks and reduce the dimensionality of the feature space using techniques such as Principal Component Analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE). Finally, classifiers like Support Vector Machines (SVM) are used to identify and classify network structures. Case analysis indicates that the TDA framework can effectively recognize different types of network structures with high classification accuracy.