A Price We Pay for Inexact Dimensionality Reduction

  • Sarunas Raudys
  • Vytautas Valaitis
  • Zidrina Pabarskaite
  • Gene Biziuleviciene
Conference paper

DOI: 10.1007/978-3-319-16480-9_29

Volume 9044 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Raudys S., Valaitis V., Pabarskaite Z., Biziuleviciene G. (2015) A Price We Pay for Inexact Dimensionality Reduction. In: Ortuño F., Rojas I. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2015. Lecture Notes in Computer Science, vol 9044. Springer, Cham

Abstract

In biometrical and biomedical pattern classification tasks one faces high dimensional data. Feature selection or feature extraction is necessary. Accuracy of both procedures depends on the data size. An increase in classification error caused by employment of sample based K-class linear discriminant analysis for dimensionality reduction was considered both analytically and by simulations. We derived analytical expression for expected classification error by applying statistical analysis. It was shown theoretically that with an increase in the sample size, classification error of (K-1)-dimensional data decreases at first, however, later it starts increasing. The maximum is reached when the size of K class training sets, n, approaches dimensionality, p. When p, classification error decreases permanently. The peaking effect for real world biomedical and biometric data sets is demonstrated. We show that regularisation of the within-class scattering can reduce or even extinguish the peaking effect.

Keywords

dimensionality reduction complexity sample size biometrics linear discriminant analysis 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sarunas Raudys
    • 1
  • Vytautas Valaitis
    • 1
  • Zidrina Pabarskaite
    • 1
  • Gene Biziuleviciene
    • 1
    • 2
  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityLithuania
  2. 2.State Research Institute, Centre for Innovative MedicineVilniusLithuania