Skip to main content

Mean Squared Error vs. Frame Potential for Unsupervised Variable Selection

  • Conference paper
  • First Online:

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 762))

Abstract

Forward Selection Component Analysis (FSCA) provides a pragmatic solution to the NP-hard unsupervised variable selection problem, but is not guaranteed to be optimal due to the multi-modal nature of the mean squared error (MSE) selection metric used. Frame potential (FP) is a metric that has recently been shown to yield near-optimal greedy sensor selection performance for linear inverse problems. This paper explores if FP offers similar benefits in the unsupervised variable selection context. In addition, the backward elimination counterpart of FSCA is introduced for the first time (BECA) and compared with forward and backward FP based variable selection on a number of simulated and real world datasets. It is concluded that FP does not improve on FSCA and that while BECA yields comparable results to FSCA it is not a competitive alternative due to its much higher computational complexity.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

References

  1. Prakash, P., et al.: Optimal wafer site selection using forward selection component analysis. In: 2012 23rd Annual SEMI Advanced Semiconductor Manufacturing Conference (ASMC), pp. 91–96. IEEE (2012)

    Google Scholar 

  2. McCabe, G.P.: Principal variables. Technometrics 26(2), 137–144 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  3. Puggini, L., McLoone, S.: Forward selection component analysis: algorithms and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence (2017). doi:10.1109/TPAMI.2017.2648792

  4. Jolliffe, I.T., et al.: A modified principal component technique based on the lasso. J. Comput. Graph. Stat. 12(3), 531–547 (2003)

    Article  MathSciNet  Google Scholar 

  5. d’Aspremont, A., et al.: A direct formulation for sparse PCA using semidefinite programming. SIAM Rev. 49(3), 434–448 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zou, H., et al.: Sparse principal component analysis. J. Comput. Graph. Stat. 15(2), 265–286 (2006)

    Article  MathSciNet  Google Scholar 

  7. Masaeli, M., et al.: Convex principal feature selection. In: SDM. SIAM, pp. 619–628 (2010)

    Google Scholar 

  8. Ranieri, J., et al.: Near-optimal sensor placement for linear inverse problems. IEEE Trans. Sig. Process. 62(5), 1135–1146 (2014)

    Article  MathSciNet  Google Scholar 

  9. Das, A., Kempe, D.: Algorithms for subset selection in linear regression. In: Proceedings of ACM Symposium on Theory of Computing (STOC) (2009)

    Google Scholar 

  10. Das, A., Kempe, D.: Submodular meets spectral: greedy algorithms for subset selection, sparse approximation and dictionary selection. In: Proceedings of International Conference on Machine Learning (ICML) (2011)

    Google Scholar 

  11. Nemhauser, G., et al.: An analysis of approximations for maximizing submodular set functions-I. Math. Prog. 14, 265–294 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  12. Waldron, S.: Generalised welch bound equality sequences are tight frames. Department of Mathematics, University of Auckland, Auckland, New Zealand, Technical report (2003)

    Google Scholar 

  13. Vergara, A., et al.: Chemical gas sensor drift compensation using classifier ensembles. Sens. Actuators B: Chem. 166, 320–329 (2012)

    Article  Google Scholar 

  14. Rodriguez-Lujan, I., et al.: On the calibration of sensor arrays for pattern recognition using the minimal number of experiments. Chemometr. Intell. Lab. Syst. 130, 123–134 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

The first author gratefully acknowledges Irish Manufacturing Research (IMR) for its financial support of his PhD.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Seán McLoone .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this paper

Cite this paper

Zocco, F., McLoone, S. (2017). Mean Squared Error vs. Frame Potential for Unsupervised Variable Selection. In: Yue, D., Peng, C., Du, D., Zhang, T., Zheng, M., Han, Q. (eds) Intelligent Computing, Networked Control, and Their Engineering Applications. ICSEE LSMS 2017 2017. Communications in Computer and Information Science, vol 762. Springer, Singapore. https://doi.org/10.1007/978-981-10-6373-2_36

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6373-2_36

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6372-5

  • Online ISBN: 978-981-10-6373-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics