Estimation of smooth vector fields on manifolds by optimization on stiefel group

E. N. Abramov, Yu A. Yanovich

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Real data are usually characterized by high dimensionality. However, real data obtained from real sources, due to the presence of various dependencies between data points and limitations on their possible values, form, as a rule, form a small part of the high-dimensional space of observations. The most common model is based on the hypothesis that data lie on or near a manifold of a smaller dimension. This assumption is called the manifold hypothesis, and inference and calculations under it are called manifold learning. Grassmann & Stiefel eigenmaps is a manifold learning algorithm. One of its subproblems has been considered in the paper: estimation of smooth vector fields by optimization on the Stiefel group. A two-step algorithm has been introduced to solve the problem. Numerical experiments with artificial data have been performed.

Original languageEnglish
Pages (from-to)220-228
Number of pages9
JournalUchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
Issue number2
Publication statusPublished - 2018


  • Dimensionality reduction
  • Manifold learning
  • Optimization on Stiefel manifold
  • Vector field estimation


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