One of the main difficulties in using principal component analysis (PCA) is the selection of the number of principal components (PCs). There exist a plethora of methods to calculate the number of PCs, but most of them use monotonically increasing or decreasing indices. Therefore, the decision to choose the number of principal components is very subjective. In this paper, we present a method based on the variance of the reconstruction error to select the number of PCs. This method demonstrates a minimum over the number of PCs. Conditions are given under which this minimum corresponds to the true number of PCs. Ten other methods available in the signal processing and chemometrics literature are overviewed and compared with the proposed method. Three data sets are used to test the different methods for selecting the number of PCs:  two of them are real process data and the other one is a batch reactor simulation.

SUMMARYWesterhuis et al. (J. Chemometrics 1998; 12: 301-321) show that the scores of consensus PCA and multiblock PLS (Westerhuis and Coenegracht, J. Chemometrics 1997; 11: 379-392) can be calculated directly from the regular PCA and PLS scores respectively. In this paper we show that both the loadings and scores of consensus PCA can be calculated directly from those of regular PCA, and the multiblock PLS loadings, weights and scores can be calculated directly from those of regular PLS. The orthogonal properties of four multiblock PCA and PLS algorithms are explored. The use of multiblock PCA and PLS for decentralized monitoring and diagnosis is derived in terms of regular PCA and PLS scores and residuals. While the multiblock analysis algorithms are basically equivalent to regular PCA and PLS, blocking of process variables in a large-scale plant based on process knowledge helps to localize the root cause of the fault in a decentralized manner. New definitions of block and variable contributions to SPE and T 2 are proposed for decentralized monitoring. This decentralized monitoring method based on proper variable blocking is successfully applied to an industrial polyester film process.

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Two modal particles in Basque display separate syntactic statuses in eastern dialects, namely the evidential omen and the epistemic ote. Despite works on their syntax, no attempt to explain the relation (and development) between the two statuses has been put forward. After concluding that analyses on German and Italian MPs (Grosz, 2005;Coniglio, 2007;Cardinaletti, 2011) are not appropriate for omen/ote, I demonstrate that the recent proposal of Lakarra ( 2019), who postulates that MPs derive from verbs, accounts not only for the canonical behaviour of those particles, but also for their behaviour close to weak adverbs.

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