2023/06/04 by Álvaro Torras-Casas, Torras-Casas, Álvaro, Eduardo Paluzo-Hidalgo +3 · 1 citation
Computer Science · #Algebraic Topology (math.AT) #Artificial Intelligence (cs.AI) #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2306.02411
openalex publication_date 2023/06/04 · openalex created_date 2023/06/07 · openalex updated_date 2026/07/28
Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques. Specifically, we define the persistence matching diagram, a topological invariant derived from combining embeddings with persistent homology. We provide an algorithm to compute it using minimum spanning trees. Also, the invariant allows us to understand whether the subset ``represents well" the clusters from the larger dataset or not, and we also use it to estimate bounds for the Hausdorff distance between the subset and the complete dataset. In particular, this approach enables us to explain why the chosen subset is likely to result in poor performance of a supervised learning model.