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Robust PARAFAC for incomplete data
Author(s) -
Hubert Mia,
Van Kerckhoven Johan,
Verdonck Tim
Publication year - 2012
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2452
Subject(s) - outlier , computer science , missing data , least squares function approximation , focus (optics) , data mining , algorithm , artificial intelligence , mathematics , statistics , machine learning , physics , estimator , optics
Different methods exist to explore multiway data. In this article, we focus on the widely used PARAFAC (parallel factor analysis) model, which expresses multiway data in a more compact way without ignoring the underlying complex structure. An alternating least squares procedure is typically used to fit the PARAFAC model. It is, however, well known that least squares techniques are very sensitive to outliers, and hence, the PARAFAC model as a whole is a nonrobust method. Therefore a robust alternative, which can deal with fully observed data possibly contaminated by outlying samples, has already been proposed in literature. In this paper, we present an approach to perform PARAFAC on data that contain both outlying cases and missing elements. A simulation study shows the good performance of our methodology. In particular, we can apply our method on a dataset in which scattering is detected and replaced with missing values. This is illustrated on a real data example. Copyright © 2012 John Wiley & Sons, Ltd.