Multi-manifold modeling in non-Euclidean spaces

Xu Wang, Konstantinos Slavakis, Gilad Lerman

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


This paper advocates a novel framework for segmenting a dataset on a Riemannian manifold M into clusters lying around low-dimensional submanifolds of M. Important examples of M, for which the proposed algorithm is computationally efficient, include the sphere, the set of positive definite matrices, and the Grassmannian. The proposed algorithm constructs a data-affinity matrix by thoroughly exploiting the intrinsic geometry and then applies spectral clustering. Local geometry is encoded by sparse coding and directional information of local tangent spaces and geodesics, which is important in resolving intersecting clusters and establishing the theoretical guarantees for a simplified variant of the algorithm. To avoid complication, these guarantees assume that the underlying submanifolds are geodesic. Extensive validation on synthetic and real data demonstrates the resiliency of the proposed method against deviations from the theoretical (geodesic) model as well as its superior performance over state-of-the-art techniques.

Original languageEnglish (US)
Pages (from-to)1023-1032
Number of pages10
JournalJournal of Machine Learning Research
StatePublished - 2015
Event18th International Conference on Artificial Intelligence and Statistics, AISTATS 2015 - San Diego, United States
Duration: May 9 2015May 12 2015

Bibliographical note

Publisher Copyright:
Copyright 2015 by the authors.


Dive into the research topics of 'Multi-manifold modeling in non-Euclidean spaces'. Together they form a unique fingerprint.

Cite this