Skip to main content
SpringerLink
Log in

A NSGA-II with ADMM Mutation for Solving Multi-objective Robust PCA Problem

  • Conference paper
  • First Online:
Bio-Inspired Computing -- Theories and Applications (BIC-TA 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 562))

Included in the following conference series:

  • 1967 Accesses

Abstract

Robust Principal Component Analysis is generalized to a multi-objective optimization problem, named as Multi-objective Robust Principal Component Analysis (MRPCA) in this paper. We aim to solve MRPCA via Evolutionary Algorithm. To the best knowledge of authors, this is the first attempt to use evolutionary algorithm to solve MRPCA problem, which is a high dimension convex optimization problem. Specifically, one of the popular evolutionary algorithm, NSGA-II, is tested on MRPCA problem. The curse of dimensionality is observed when the dimension of MRPCA problem increases. Since this problem is convex, which is a friendly structure, we propose a modified NSGA-II by introducing a new mutation method: ADMM (Alternating Direction Method of Multipliers) mutation. Numerical experiments show our modified NSGA-II algorithm converges much faster than the standard one.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Real-coded NSGA-II use Simulated Binary Crossover (SBX) [10, 11] operator for crossover and polynomial mutation [10, 12].

  2. 2.

    HV metric is not used for comparing because it has different reference point for different dimensions. Besides, the value of Hypervolume can not be compared for different dimension because of different pareto-optimal solutions set.

References

  1. Hwang, C.L., Masud, A.S.M.: Multiple Objective Decision Making Methods and Applications. Lecture Notes in Economics and Mathematical Systems, vol. 164. Springer, Berlin (1979)

    Book  MATH  Google Scholar 

  2. Li, K., Zhang, Q., Kwong, S., Li, M., Wang, R.: Stable matching based selection in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 6(18), 909–923 (2014)

    Google Scholar 

  3. Li, K., Fialho, Á., Kwong, S., Zhang, Q.: Adaptive operator selection with bandits for multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 1(18), 114–130 (2014)

    Article  Google Scholar 

  4. Li, K., Kwong, S., Zhang, Q., Deb, K.: Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans. Cybern. 45, 2076–2088 (2015)

    Article  Google Scholar 

  5. Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(3), 1–37 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  7. Jiang, S., Zhang, J., Ong, Y., Feng, L.: Consistencies and contradictions of performance metrics in multiobjective optimization. IEEE Trans. Cybern. 44, 2391–2404 (2014)

    Article  Google Scholar 

  8. Parikh, N., Boyd, S.: Proximal algorithms. Found. Trends Optim. 1(3), 123–231 (2014)

    Google Scholar 

  9. Sboyd, S., Boyd, N., Parikh, E., Chu, B., Eckstein, J.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends Optim. 3(1), 1–122 (2011)

    MATH  Google Scholar 

  10. Deb, K., Agarwal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9(2), 115–148 (1995)

    MathSciNet  MATH  Google Scholar 

  11. Beyer, H., Deb, K.: On self-adaptive features in real-parameter evolutionary algorithm. IEEE Trans. Evol. Comput. 3(5), 250–270 (2001)

    Article  Google Scholar 

  12. Raghuwanshi, M.M., Kakde, O.G.: Survey on multiobjective evolutionary and real coded genetic algorithms. In: Proceedings of the 8th Asia Paciffic Symposium on Intelligent and Evolutionary Systems, pp. 150–161 (2004)

    Google Scholar 

  13. Zhang, X., Tian, Y., Cheng, R., Jin, Y.: An efficient approach to non-dominated sorting for evolutionary multi-objective optimization. IEEE Trans. Evol. Comput. 19(2), 201–213 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin, People’s Republic of China

    Weitao Yuan, Hanning Chen, Xiaodan Liang & Maowei He

  2. Beijing Shenzhou Aerospace Software Technology Co. Ltd., Beijing, China

    Na Lin

Authors
  1. Weitao Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Na Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hanning Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaodan Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Maowei He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanning Chen .

Editor information

Editors and Affiliations

  1. Xidian University, Xi'an, China

    Maoguo Gong

  2. Huazhong Univ. of Science and Technology, Wuhan, China

    Pan Linqiang

  3. University of Petroleum, Qingdao, China

    Song Tao

  4. University of Science and Technology of China, Hefei, China

    Ke Tang

  5. Anhui University, Hefei, China

    Xingyi Zhang

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yuan, W., Lin, N., Chen, H., Liang, X., He, M. (2015). A NSGA-II with ADMM Mutation for Solving Multi-objective Robust PCA Problem. In: Gong, M., Linqiang, P., Tao, S., Tang, K., Zhang, X. (eds) Bio-Inspired Computing -- Theories and Applications. BIC-TA 2015. Communications in Computer and Information Science, vol 562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49014-3_52

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-49014-3_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-49013-6

  • Online ISBN: 978-3-662-49014-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation