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Randomly Walking Can Get You Lost: Graph Segmentation with Unknown Edge Weights

  • Hanno Ackermann
  • Björn Scheuermann
  • Tat-Jun Chin
  • Bodo Rosenhahn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)

Abstract

Spectral graph clustering is among the most popular algorithms for unsupervised segmentation. Applications include problems such as speech separation, segmenting motions or objects in video sequences and community detection in social media. It is based on the computation of a few eigenvectors of a matrix defining the connections between the graph nodes.

In many real world applications, not all edge weights can be defined. In video sequences, for instance, not all 3d-points of the observed objects are visible in all the images. Relations between graph nodes representing the 3d-points cannot be defined if these never co-occur in the same images. It is common practice to simply assign an affinity of zero to such edges.

In this article, we present a formal proof that this procedure decreases the separation between two clusters. An upper bound is derived on the second smallest eigenvalue of the Laplacian matrix. Furthermore, an algorithm to infer missing edges is proposed and results on synthetic and real image data are presented.

Keywords

Edge Weight Small Eigenvalue Spectral Cluster Neural Information Processing System Solid Blue Line 
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 International Publishing Switzerland 2015

Authors and Affiliations

  • Hanno Ackermann
    • 1
  • Björn Scheuermann
    • 1
  • Tat-Jun Chin
    • 2
  • Bodo Rosenhahn
    • 1
  1. 1.Institute for Information ProcessingLeibniz University HannoverGermany
  2. 2.The University of AdelaideAustralia

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