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Sparse Gradient Pursuit for Robust Visual Analysis

  • Jiangxin Dong
  • Risheng LiuEmail author
  • Kewei Tang
  • Yiyang Wang
  • Xindong Zhang
  • Zhixun Su
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10111)

Abstract

Many high-dimensional data analysis problems, such as clustering and classification, usually involve the minimization of a Laplacian regularization, which is equivalent to minimize square errors of the gradient on a graph, i.e., the disparity among the adjacent nodes in a data graph. However, the Laplacian criterion usually preserves the locally homogeneous data structure but suppresses the discrimination among samples across clusters, which accordingly leads to undesirable confusion among similar observations belonging to different clusters. In this paper, we propose a novel criterion, named Sparse Gradient Pursuit (SGP), to simultaneously preserve the within-class homogeneity and the between-class discrimination for unsupervised data clustering. In addition, we show that the proposed SGP criterion is generic and can be extended to handle semi-supervised learning problems by incorporating the label information into the data graph. Though this unified semi-supervised learning model leads to a nonconvex optimization problem, we develop a new numerical scheme for the SGP related nonconvex optimization problem and analyze the convergence property of the proposed algorithm under mild conditions. Extensive experiments demonstrate that the proposed algorithm performs favorably against the state-of-the-art unsupervised and semi-supervised methods.

Notes

Acknowledgement

Risheng Liu is supported by National Natural Science Foundation of China (NSFC) (Nos. 61300086, 61432003, 61672125), Fundamental Research Funds for the Central Universities (No. DUT15QY15), and the Hong Kong Scholar Program (No. XJ2015008). Zhixun Su is supported by NSFC (No. 61572099) and National Science and Technology Major Project (Nos. ZX20140419, 2014ZX04001011).

Supplementary material

416257_1_En_24_MOESM1_ESM.pdf (2.4 mb)
Supplementary material 1 (pdf 2488 KB)

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Jiangxin Dong
    • 1
  • Risheng Liu
    • 1
    Email author
  • Kewei Tang
    • 2
  • Yiyang Wang
    • 1
  • Xindong Zhang
    • 1
  • Zhixun Su
    • 1
  1. 1.Dalian University of TechnologyDalianChina
  2. 2.Liaoning Normal UniversityDalianChina

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