A new efficient method for determining the number of components in PARAFAC models

Journal of Chemometrics - Tập 17 Số 5 - Trang 274-286 - 2003
Rasmus Bro1, Henk A. L. Kiers2
1Chemometrics Group, Department of Food and Dairy Science, Royal Veterinary and Agricultural University, DK-1958 Frederiksberg C, Denmark
2Heymans Institute (DPMG), University of Groningen, Groningen, The Netherlands

Tóm tắt

Abstract

A new diagnostic called the core consistency diagnostic (CORCONDIA) is suggested for determining the proper number of components for multiway models. It applies especially to the parallel factor analysis (PARAFAC) model, but also to other models that can be considered as restricted Tucker3 models. It is based on scrutinizing the ‘appropriateness’ of the structural model based on the data and the estimated parameters of gradually augmented models. A PARAFAC model (employing dimension‐wise combinations of components for all modes) is called appropriate if adding other combinations of the same components does not improve the fit considerably. It is proposed to choose the largest model that is still sufficiently appropriate. Using examples from a range of different types of data, it is shown that the core consistency diagnostic is an effective tool for determining the appropriate number of components in e.g. PARAFAC models. However, it is also shown, using simulated data, that the theoretical understanding of CORCONDIA is not yet complete. Copyright © 2003 John Wiley & Sons, Ltd.

Từ khóa


Tài liệu tham khảo

10.1016/S0169-7439(97)00032-4

Harshman RA, 1970, Foundations of the PARAFAC procedure: models and conditions for an ‘explanatory’ multi‐modal factor analysis, UCLA Working Papers Phonet., 16, 1

10.1090/psapm/028/9883

10.1037/0021-9010.68.4.572

10.1016/0169-7439(93)80011-6

10.1002/(SICI)1099-128X(199609)10:5/6<615::AID-CEM450>3.0.CO;2-S

10.1002/cem.1180090305

10.1021/ac00092a010

BroR.Multi‐way analysis in the food industry. Models algorithms and applications.PhD Thesis University of Amsterdam 1998(http://www.mli.kvl.dk/staff/foodtech/brothesis.pdf).

10.1016/S0169-7439(00)00071-X

10.1016/S0169-7439(01)00140-X

10.1016/S0003-2670(00)01380-5

10.1016/S0039-9140(00)00650-0

Rao CR, 1971, Generalized Inverse of Matrices and Its Applications

10.1111/j.2044-8317.1980.tb00606.x

Harshman RA, 1984, Research Methods for Multimode Data Analysis, 122

10.1002/cem.1180080104

Lundy ME, 1989, Multiway Data Analysis, 123

Harshman RA, 1984, Research Methods for Multimode Data Analysis, 602

10.1002/(SICI)1099-128X(199905/08)13:3/4<295::AID-CEM547>3.0.CO;2-Y

10.1016/S0169-7439(98)00181-6

10.1121/1.381581

Ewing GW, 1985, Instrumental Methods of Chemical Analysis

10.1016/S0003-2670(99)00374-8

Bro R, New rank‐deficient models for multi‐way data, J. Chemometrics

Thông tin
Thông tin xuất bản

Journal of Chemometrics

Tập 17 Số 5

274-286

Thông tin tác giả