Product Manifold Learning with Independent Coordinate Selection

Published: 18 Jun 2023, Last Modified: 30 Jun 2023TAGML2023 PosterEveryoneRevisions
Keywords: manifold learning, dimensionality reduction
TL;DR: We identify challenges in learning product manifolds and address them with a new method
Abstract: In many dimensionality reduction tasks, we wish to identify the constituent components that explain our observations. For manifold learning, this can be formalized as factoring a Riemannian product manifold. Recovering this factorization, however, may suffer from certain difficulties in practice, especially when data is sparse or noisy, or when one factor is distorted by the other. To address these limitations, we propose identifying non-redundant coordinates on the product manifold before applying product manifold learning to identify which coordinates correspond to different factor manifolds. We demonstrate our approach on both synthetic and real-world data.
Type Of Submission: Proceedings Track (8 pages)
Submission Number: 27