COMMENTS ON THE NIPALS ALGORITHM

The Non-linear lterative Partial Least Squares(NIPALS)algorithm is used in principal componentanalysis to decompose a data matrix into score vectors and eigenvectors(loading vectors)plus a residualmatrix.N1PALS starts with some guessed starting vector.The principal components obtained by NIPALSdepends on the starting vector;the first principal component could not always be computed.Wold hassuggested a starting vector for NIPALS,but we have found that even if this starting vector is used,thefirst principal component cannot be obtained in all cases.The reason why such a situation occurs isexplained by the power method.A simple modification of the original NIPALS procedure to avoid gettingsmaller eigenvalues is presented.     

ASSIGNING THE ORIGIN OF CATALAN MEDIEVAL STAINED GLASSES BY PATTERN RECOGNITION METHODS OF X-RAY FLUORESCENCE DATA

Thirteen different components of six samples belonging to stained medieval glass windows and twelvesimilar samples found in the archives of Girona Cathedral(Catalonia,Spain)during restoration workwere determined by x-ray fluorescence analysis.The use of display and cluster analysis methods,principal components analysis,non-linear mapping,minimal spanning tree and agglomerativehierarchical clustering applied to these results,together with those of nine samples from the samecathedral previously studied,showed the presence of a quite compact cluster formed by the soda-typesamples,indicating a probably similar origin and confirming the peculiarities of this Mediterranean area.The potash-type glasses were highly scattered with little similarity among them,suggesting a likelydifferent source of these samples.The twelve glasses of strictly unknown origin were found to have a highdegree of resemblance to the samples of known context,thus excluding the possibility of them beingsamples made in a very different age or site.Three of them were classified into the same group as thewell-defined soda-type glasses by the pattern recognition method SIMCA.     

Projective ordination by SIMCA: A dynamic strategy for cost-efficient environmental monitoring around offshore installations

A method for environmental monitoring using benthic species profiles as input is developed in this work. The method, referred to as projective ordination, utilises local principal component modelling (SIMCA) to obtain a cross-validated model which spans the natural variation in a region around offshore oil-producing installations. The borderline between regions with disturbed and non-disturbed species communities is subsequently decided from the residual distribution. This distribution is used to design an approximate F-test for assessing whether a community at a particular sampling location is disturbed or not. If so, the nature of the disturbance is determined by projecting the data on the PC model.Projective ordination utilises information from previous surveys to define the permissible variation in species communities, i.e. the limit of the natural variation. In addition, the method is dynamic, in a sense that the sampling locations may vary from survey to survey.Furthermore, our analysis shows that the customary number of replicate samples per station can be reduced. Modelling with only four randomly chosen replicates out of the complete set of five for each sampling location, does not affect the model significantly. On the other hand, taking only 3 replicates into account leads to significant divergences.A model based on the 1990 and 1993 surveys at the Statfjord field is presented as an example of the technique.