Product Manifold Learning

Sharon Zhang, Amit Moscovich, Amit Singer

Research output: Contribution to journalConference articlepeer-review

4 Scopus citations


We consider dimensionality reduction for data sets with two or more independent degrees of freedom. For example, measurements of deformable shapes with several parts that move independently fall under this characterization. Mathematically, if the space of each continuous independent motion is a manifold, then their combination forms a product manifold. In this paper, we present an algorithm for manifold factorization given a sample of points from the product manifold. Our algorithm is based on spectral graph methods for manifold learning and the separability of the Laplacian operator on product spaces. Recovering the factors of a manifold yields meaningful lower-dimensional representations, allowing one to focus on particular aspects of the data space while ignoring others. We demonstrate the potential use of our method for an important and challenging problem in structural biology: mapping the motions of proteins and other large molecules using cryo-electron microscopy data sets.

Original languageEnglish (US)
Pages (from-to)3241-3249
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: Apr 13 2021Apr 15 2021

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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