Discrete Morse Theory in Topological Data Analysis: A Practical Demonstration of Morse-Smale Complex Extraction for Data Analysis
Aldiputera Laksamana, Yudi Soeharyadi

Department of Mathematics,
FMIPA Institut Teknologi Bandung

Abstract

The study explores the application of discrete Morse theory within Topological Data Analysis (TDA), focusing specifically on the extraction and simplification of Morse-Smale complexes. Utilizing discrete Morse functions on simplicial complexes, one can effectively derive Morse-Smale complexes, which offer a multitude of features, including various separatrices and segmentations essential for image segmentation and clustering problems. Our demonstration employs the Topology Toolkit (TTK) in conjunction with the 3D multi-purpose renderer ParaView, enabling us to construct pipelines for processing and visualizing multidimensional data. This practical demonstration will underscore the advantages of this feature-extraction approach, particularly the utility of persistence in enhancing the clarity and interpretability of topological features.

Keywords: Topological data analysis, Morse-Smale complex, persistence

Topic: Others