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Efficient discovery of contrast subspaces for object explanation and characterization

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Abstract

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.

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Notes

  1. While [8] presented a contrast-pattern length based algorithm to detection global outliers, their problem setting is different from ours.

  2. Generally, given a set of observations \(Q\), the plausibility of two models \(M_1\) and \(M_2\) can be assessed by the Bayes factor \(K=\frac{Pr(Q\mid M_1)}{Pr(Q \mid M_2)}\).

  3. If it is not unimodal, then there could be multiple peaks at different distances from the query, which is counter to intuition. Similarly, we have no basis for preferring any direction over another, so symmetry is natural.

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Acknowledgments

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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Authors and Affiliations

  1. School of Computer Science, Sichuan University, Chengdu, Sichuan, China

    Lei Duan & Changjie Tang

  2. School of Computing Science, Simon Fraser University, Burnaby, BC, Canada

    Guanting Tang & Jian Pei

  3. Department of Computing and Information Systems, The University of Melbourne, Melbourne, VIC, Australia

    James Bailey & Vinh Nguyen

  4. Department of Computer Science and Engineering, Wright State University, Dayton, OH, USA

    Guozhu Dong

  5. Pacific Blue Cross, Burnaby, BC, Canada

    Akiko Campbell

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  1. Lei Duan
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  2. Guanting Tang
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  3. Jian Pei
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  4. James Bailey
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  5. Guozhu Dong
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  6. Vinh Nguyen
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  7. Akiko Campbell
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  8. Changjie Tang
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Correspondence to Lei Duan.

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Duan, L., Tang, G., Pei, J. et al. Efficient discovery of contrast subspaces for object explanation and characterization. Knowl Inf Syst 47, 99–129 (2016). https://doi.org/10.1007/s10115-015-0835-6

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