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A method that indicates the numbers of components to use in fitting the three-mode principal components analysis (3MPCA) model is proposed. This method, called DIFFIT, aims to find an optimal balance between the fit of solutions for the 3MPCA model and the numbers of components. The achievement of DIFFIT is compared with that of two other methods, both… (More)

The present study aimed to examine the construct validity of three aspects of attention, namely focused, divided, and supervisory control of attention. Factor-analytic techniques were applied to scores of healthy subjects on a series of neuropsychological tests tapping these aspects of attention. The two components found did not match the hypothesized… (More)

- Patrick J.F. Groenen, Patrizia Giaquinto, Henk A. L. Kiers, Anton Béguin
- 2003

We would like to thank Anton Béguin and Norman Verhelst for their valuable remarks that have helped to improve this paper. Abstract For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal… (More)

Several three-mode principal component models can be considered for the modelling of three-way, three-mode data, including the Candecomp/Parafac, Tucker3, Tucker2, and Tucker1 models. The following question then may be raised: given a specific data set, which of these models should be selected, and at what complexity (i.e. with how many components)? We… (More)

MOTIVATION
Modern functional genomics generates high-dimensional datasets. It is often convenient to have a single simple number characterizing the relationship between pairs of such high-dimensional datasets in a comprehensive way. Matrix correlations are such numbers and are appealing since they can be interpreted in the same way as Pearson's correlations… (More)

Three-way component analysis techniques are designed for descriptive analysis of 3-way data, for example, when data are collected on individuals, in different settings, and on different measures. Such techniques summarize all information in a 3-way data set by summarizing, for each way of the 3-way data set, the associated entities through a few components… (More)

Confidence intervals (CIs) in principal component analysis (PCA) can be based on asymptotic standard errors and on the bootstrap methodology. The present paper offers an overview of possible strategies for bootstrapping in PCA. A motivating example shows that CI estimates for the component loadings using different methods may diverge. We explain that this… (More)

For the last decades, research studies have been developed in which a coalition of Fuzzy Sets Theory and Statistics has been established with different purposes. These namely are: (i) to introduce new data analysis problems in which the objective involves either fuzzy relationships or fuzzy terms; (ii) to establish well-formalized models for elements… (More)