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Pacific-Asia Conference on Knowledge Discovery and Data Mining

PAKDD 2016: Advances in Knowledge Discovery and Data Mining pp 309–321Cite as

A Greedy Algorithm to Construct L1 Graph with Ranked Dictionary

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9652))

Abstract

\(\mathcal {L}_1\) graph is an effective way to represent data samples in many graph-oriented machine learning applications. Its original construction algorithm is nonparametric, and the graphs it generates may have high sparsity. Meanwhile, the construction algorithm also requires many iterative convex optimization calculations and is very time-consuming. Such characteristics would severely limit the application scope of \(\mathcal {L}_1\) graph in many real-world tasks. In this paper, we design a greedy algorithm to speed up the construction of \(\mathcal {L}_1\) graph. Moreover, we introduce the concept of “Ranked Dictionary” for \(\mathcal {L}_1\) minimization. This ranked dictionary not only preserves the locality but also removes the randomness of neighborhood selection during the process of graph construction. To demonstrate the effectiveness of our proposed algorithm, we present our experimental results on several commonly-used datasets using two different ranking strategies: one is based on Euclidean metric, and another is based on diffusion metric.

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Acknowledgments

This research is supported in part by NSF (IIS-0949467, IIS-1047715, and IIS-1049448), and NSFC (61532002, 61190120, 61190125, 61190124). We thank the anonymous reviewers for their constructive critiques.

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Authors and Affiliations

  1. Stony Brook University (SUNY), Stony Brook, USA

    Shuchu Han & Hong Qin

Authors
  1. Shuchu Han
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  2. Hong Qin
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Corresponding author

Correspondence to Shuchu Han .

Editor information

Editors and Affiliations

  1. The University of Melbourne, Melbourne, Victoria, Australia

    James Bailey

  2. The University of Texas at Dallas, Richardson, Texas, USA

    Latifur Khan

  3. Osaka University, Osaka, Japan

    Takashi Washio

  4. University of Auckland, Auckland, New Zealand

    Gill Dobbie

  5. Shenzhen University, Shenzhen, China

    Joshua Zhexue Huang

  6. Massey University, Auckland, New Zealand

    Ruili Wang

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© 2016 Springer International Publishing Switzerland

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Han, S., Qin, H. (2016). A Greedy Algorithm to Construct L1 Graph with Ranked Dictionary. In: Bailey, J., Khan, L., Washio, T., Dobbie, G., Huang, J., Wang, R. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2016. Lecture Notes in Computer Science(), vol 9652. Springer, Cham. https://doi.org/10.1007/978-3-319-31750-2_25

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  • DOI: https://doi.org/10.1007/978-3-319-31750-2_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31749-6

  • Online ISBN: 978-3-319-31750-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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