PARAFAC and missing values

Giorgio Tomasi

doi:10.1016/j.chemolab.2004.07.003

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PARAFAC and missing values

2005-02-01

208

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Giorgio Tomasi

Rasmus Bro

DOI：10.1016/j.chemolab.2004.07.003

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Abstract

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Missing values are a common occurrence in chemometrics data, and different approaches have been proposed to deal with them. In this work, two different concepts based on two algorithms are compared in their efficiency in dealing with incomplete data when fitting the PARAFAC model: single imputation (SI) combined with a standard PARAFAC-altemating least squares (ALS) algorithm, and fitting the model only to the existing elements using a computationally more expensive method (Levenberg-Marquadt) appropriately modified and optimised. The performance of these two algorithms and the effect of the incompleteness of the data on the final model have been evaluated on the basis of a Monte Carlo study and real data sets with different amounts and patterns of missing values (randomly missing values, randomly missing spectra/vectors, and systematically missing spectra/vectors). The evaluation is based on the quality of the solution as well as on computational aspects (time requirement and number of iterations). The results show that a PARAFAC model can be correctly determined even when a large fraction of the data is missing (up to 70%), and that the pattern matters more than the fraction of missing values. Computationally, the Levenberg-Marquadt-based approach appeared superior for the pattern of missing values typical of fluorescence measurements when the fraction of missing elements exceeded 30%. (C) 2004 Elsevier B.V All rights reserved.

Keywords:

PARAFAC

missing values

INDAFAC

fluorescence

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