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Sparse and Low-Rank Methods

  • René Vidal
  • Yi Ma
  • S. Shankar Sastry
Chapter
  • 7.5k Downloads
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 40)

Abstract

The previous chapter studies a family of subspace clustering methods based on spectral clustering. In particular, we have studied both local and global methods for defining a subspace clustering affinity, and have noticed that we seem to be facing an important dilemma. On the one hand, local methods compute an affinity that depends only on the data points in a local neighborhood of each data point. Local methods can be rather efficient and somewhat robust to outliers, but they cannot deal well with intersecting subspaces. On the other hand, global methods utilize geometric information derived from the entire data set (or a large portion of it) to construct the affinity. Global methods might be immune to local mistakes, but they come with a big price: their computational complexity is often exponential in the dimension and number of subspaces. Moreover, none of the methods comes with a theoretical analysis that guarantees the correctness of clustering. Therefore, a natural question that arises is whether we can construct a subspace clustering affinity that utilizes global geometric relationships among all the data points, is computationally tractable when the dimension and number of subspaces are large, and is guaranteed to provide the correct clustering under certain conditions.

Keywords

Sparse Subspace Clustering (SSC) Alternating Direction Method Of Multipliers (ADMM) Uncorrupted Data Disjoint Subspaces Outer Entrance 
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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