The comparison of L11 and L22-norm minimization methods


BEKTAŞ S., ŞİŞMAN Y.

International Journal of Physical Sciences, cilt.5, sa.11, ss.1721-1727, 2010 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 5 Sayı: 11
  • Basım Tarihi: 2010
  • Dergi Adı: International Journal of Physical Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1721-1727
  • Anahtar Kelimeler: Gross errors, L1 and L2-norm, Outlier detection, Similarity transformation
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

L2-norm, also known as the least squares method was widely used in the adjustment calculus. The weaknesses of the least squares method were the effect of gross measurements error on the solution and the disturbance and absorbance of gross error on the solution. L1-norm, also known as the least absolute values method, was affected by almost none or very little from gross error. Therefore L1-norm method, used for parameters estimation in some special case, has been successfully used for outlier measurements detection. In this study, the L1 and L2-norm adjustment methods have been taken relatively to each other's advantages and disadvantages and the numerical application of the two-dimensional similarity coordinate transformation were made and the results of both methods are discussed. © 2010 Academic Journals.