Quick Shift and Kernel Methods for Mode Seeking

  • Andrea Vedaldi
  • Stefano Soatto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5305)

Abstract

We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under- and over-fragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Andrea Vedaldi
    • 1
  • Stefano Soatto
    • 1
  1. 1.Computer Science DepartmentUniversity of CaliforniaLos Angeles 

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