TopoDimRed: a novel dimension reduction technique for topological data analysis

Abstract

Topological data analysis (TDA) has emerged as a powerful approach for analyzing complex datasets, capturing the underlying shape and structure inherent in the data. However, TDA often encounters challenges when dealing with high-dimensional data due to the curse of dimensionality. To address this issue, we propose a novel dimension reduction technique called TopoDimRed that integrates topological analysis with advanced dimension reduction algorithms. TopoDimRed aims to reduce the dimensionality of topological data while preserving important topological features, enabling efficient visualization and analysis. In this paper, we present the methodology of TopoDimRed, highlighting its ability to capture and preserve relevant topological structures during the dimension reduction process. We conduct extensive experimental evaluations on diverse datasets from different domains, comparing TopoDimRed with traditional dimension reduction techniques. The results demonstrate that TopoDimRed outperforms or achieves comparable performance in terms of preserving topological features, visualization quality, and computational efficiency. Furthermore, we showcase the application of TopoDimRed in various domains, including biological networks, social networks, materials science, and neuroscience, illustrating its utility in gaining insights from high-dimensional topological data. We discuss the strengths and limitations of TopoDimRed and propose potential future directions for its development and application. Overall, TopoDimRed offers a valuable tool for researchers and practitioners to explore, visualize, and analyze high-dimensional topological data, facilitating the discovery of hidden structures and meaningful insights in complex datasets.