Incremental Construction of Low-Dimensional Data Representations

  • Alexander Kuleshov
  • Alexander Bernstein
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9896)


Various Dimensionality Reduction algorithms transform initial high-dimensional data into their lower-dimensional representations preserving chosen properties of the initial data. Typically, such algorithms use the solution of large-dimensional optimization problems, and the incremental versions are designed for many popular algorithms to reduce their computational complexity. Under manifold assumption about high-dimensional data, advanced manifold learning algorithms should preserve the Data manifold and its differential properties such as tangent spaces, Riemannian tensor, etc. Incremental version of the Grassmann&Stiefel Eigenmaps manifold learning algorithm, which has asymptotically minimal reconstruction error, is proposed in this paper and has significantly smaller computational complexity in contrast to the initial algorithm.


Machine learning Dimensionality reduction Manifold learning Tangent bundle manifold learning Incremental learning 



This work is partially supported by the Russian Foundation for Basic Research, research project 16-29-09649 ofi-m.


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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Skolkovo Institute of Science and TechnologyMoscowRussia
  2. 2.Kharkevich Institute for Information Transmission Problems RASMoscowRussia

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