Knowledge and Information Systems

, Volume 47, Issue 1, pp 99–129 | Cite as

Efficient discovery of contrast subspaces for object explanation and characterization

  • Lei DuanEmail author
  • Guanting Tang
  • Jian Pei
  • James Bailey
  • Guozhu Dong
  • Vinh Nguyen
  • Akiko Campbell
  • Changjie Tang
Regular Paper


We tackle the novel problem of mining contrast subspaces. Given a set of multidimensional objects in two classes \(C_+\) and \(C_-\) and a query object \(o\), we want to find the top-\(k\) subspaces that maximize the ratio of likelihood of \(o\) in \(C_+\) against that in \(C_-\). Such subspaces are very useful for characterizing an object and explaining how it differs between two classes. We demonstrate that this problem has important applications, and, at the same time, is very challenging, being MAX SNP-hard. We present CSMiner, a mining method that uses kernel density estimation in conjunction with various pruning techniques. We experimentally investigate the performance of CSMiner on a range of data sets, evaluating its efficiency, effectiveness, and stability and demonstrating it is substantially faster than a baseline method.


Contrast subspace Kernel density estimation Likelihood contrast 



The authors are grateful to the editor and the anonymous reviewers for their constructive comments, which help to improve this paper. Lei Duan’s research was supported in part by National Natural Science Foundation of China (Grant No. 61103042), China Postdoctoral Science Foundation (Grant No. 2014M552371), and SRFDP 20100181120029. Jian Pei’s and Guanting Tang’s research was supported in part by an NSERC Discovery grant, a BCIC NRAS Team Project. James Bailey’s work was supported by an ARC Future Fellowship (FT110100112). Work by Lei Duan and Guozhu Dong at Simon Fraser University was supported in part by an Ebco/Eppich visiting professorship. All opinions, findings, conclusions, and recommendations in this paper are those of the authors and do not necessarily reflect the views of the funding agencies.


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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Lei Duan
    • 1
    Email author
  • Guanting Tang
    • 2
  • Jian Pei
    • 2
  • James Bailey
    • 3
  • Guozhu Dong
    • 4
  • Vinh Nguyen
    • 3
  • Akiko Campbell
    • 5
  • Changjie Tang
    • 1
  1. 1.School of Computer ScienceSichuan UniversityChengduChina
  2. 2.School of Computing ScienceSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Computing and Information SystemsThe University of MelbourneMelbourneAustralia
  4. 4.Department of Computer Science and EngineeringWright State UniversityDaytonUSA
  5. 5.Pacific Blue CrossBurnabyCanada

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