Speaker
Description
Topological Data Analysis (TDA) introduces innovative approaches for interpreting high-dimensional data by leveraging underlying structures and relationships. TDA uncovers qualitative similarities and differences, offering a unique perspective in various applications. In particular, the concept of persistence diagram vectorization enhances Machine Learning (ML) algorithms by providing an intermediary layer that improves performance and yields alternative insights into medical datasets. The assessment of surface topography and roughness is crucial for applications such as friction analysis, contact deformation studies, and coating adhesion investigations. While traditional roughness parameters—such as Ra, Rq, and Rz—offer quantitative measures of surface irregularities, they often struggle to differentiate between surface samples subjected to different treatment stages. These conventional methods primarily rely on statistical descriptors of height variations, which may overlook critical geometric and structural patterns inherent in complex surfaces.
To address this limitation, we explore computational topology techniques, particularly persistent homology, to capture essential geometric and topological features of surfaces. By comparing traditional roughness metrics with topological descriptors, we highlight how persistent homology-based invariants offer a richer characterization of surface morphology. Unlike standard roughness measures that focus on local height variations, topological methods track the evolution of connected components and voids across multiple scales, enabling a more robust differentiation between surface treatments. Furthermore, techniques from scalar field topology are used in the exploratory phase to give insights into different local phenomena.
This study extends earlier effort in [1] to construct novel roughness parameters derived from persistent homology to enhance the classification of surface samples. We will discuss key design choices in integrating TDA into existing ML pipelines by comparing traditional roughness quantification techniques with TDA-driven methodologies, we demonstrate the advantages of incorporating computational topology for improved surface characterization, with the goal to enhance the accuracy and interpretability of ML models in material science applications.
[1] Senge, J.F., Astaraee, A.H., Dlotko, P., Bagherifard, S., Bosbach, W.A., Extending conventional surface roughness ISO parameters using topological data analysis for shot peened surfaces, Scientific Reports, 12, 5538 (2022).
