2018/07/01 by F. Patricia Medina, Linda Ness, Medina, F. Patricia +5 · 2 citations
Computer Science · #57-04 #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1807.00349
openalex publication_date 2018/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold) of lower dimension than the ambient space. This question can be phrased as a (multi-) manifold hypothesis. The identification of such intrinsic multiscale features is a cornerstone of data analysis and representation and has given rise to a large body of work on manifold learning. In this work, we review key results on multi-scale data analysis and intrinsic dimension followed by the introduction of a heuristic, multiscale framework for testing the multi-manifold hypothesis. Our method implements a hypothesis test on a set of spline-interpolated manifolds constructed from variance-based intrinsic dimensions. The workflow is suitable for empirical data analysis as we demonstrate on two use cases.