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Spectral Methods

  • René Vidal
  • Yi Ma
  • S. Shankar Sastry
Chapter
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 40)

Abstract

The preceding two chapters studied the subspace clustering problem using algebraic-geometric and statistical techniques, respectively. Under the assumption that the data are not corrupted, we saw in Chapter 5 that algebraic-geometric methods are able to solve the subspace clustering problem in full generality, allowing for an arbitrary union of different subspaces of any dimensions and in any orientations, as long as sufficiently many data points in general configuration are drawn from the union of subspaces. However, while algebraic-geometric methods are able to deal with moderate amounts of noise, they are unable to deal with outliers. Moreover, even in the noise-free setting, the computational complexity of linear-algebraic methods for fitting polynomials grows exponentially with the number of subspaces and their dimensions. As a consequence, algebraic-geometric methods are most effective for low-dimensional problems with moderate amounts of noise.

Keywords

Face Image Spectral Cluster Subspace Cluster Affinity Matrix Spectral Cluster Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York 2016

Authors and Affiliations

  • René Vidal
    • 1
  • Yi Ma
    • 2
  • S. Shankar Sastry
    • 3
  1. 1.Center for Imaging Science Department of Biomedical EngineeringJohns Hopkins UniversityBaltimoreUSA
  2. 2.School of Information Science and Technology ShanghaiTech UniversityShanghaiChina
  3. 3.Department of Electrical Engineering and Computer ScienceUniversity of California BerkeleyBerkeleyUSA

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