Advanced AI for Topological Data Analysis: Decoding Complex High-Dimensional Structures

Abstract

Abstract: This chapter explores the integration of advanced AI techniques with topological data analysis (TDA) to decode complex high-dimensional data structures. It examines how AI-driven TDA can identify and analyze the geometric and topological features of datasets, offering deeper insights into patterns, clusters, and anomalies that traditional methods might overlook. By leveraging machine learning algorithms such as neural networks, graph neural networks, and autoencoders, AI enhances the ability to process and interpret high-dimensional data from various fields, including biology, finance, and network analysis. The chapter also discusses the application of persistent homology and multi-scale analysis in AI-driven TDA, emphasizing the future potential of these technologies in fields such as genomics, neuroscience, and sensor networks. Challenges related to computational complexity, scalability, and interpretability are addressed, as well as emerging trends in the field. Keywords: advanced AI, topological data analysis, TDA, high-dimensional data, machine learning, neural networks, graph neural networks, autoencoders, persistent homology, multi-scale analysis, data patterns, data clusters, anomaly detection, genomics, neuroscience, sensor networks, computational complexity.