Reductive enhanced multivariance product representation for multi-way arrays

Ozay E. K., Demiralp M.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.52, sa.10, ss.2546-2558, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 10
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1007/s10910-014-0396-z
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2546-2558
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as amulti-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR's efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.