Abstract not found

1 Canonical community ordination comprises a collection of methods that relate species assemblages to their environment, in both observational studies and designed experiments. Canonical ordination differs from ordination sensu stricto in that species and environment data are analyzed simultaneously. Part I reviews the theory in a non-mathematical way with emphasis on new insights for the interpretation of ordination diagrams. The interpretation depends on the ordination method used to create the diagram. After the basic theory, Part I is focused on the ordination diagrams in linear methods of canonical community ordination, in particular principal components analysis, redundancy analysis and canonical correlation analysis. Special attention is devoted to the display of qualitative environmental variables. Key words: principal components analysis, redundancy analysis, canonical correlation analysis, biplot, ordination diagram, species-environment relations. 2

Constrained multidimensional scaling was put on a firm theoretical basis by Jan De Leeuw and Willem Heiser in the 1980's. There is a simple method of fitting, based on distance via innerproducts, and a numerically more complicated one that is truly based on least-squares on distances. The unconstrained forms are known as principal coordinate analysis and nonmetric multidimensional scaling, respectively. Constraining the solution by external variables brings the power of classical regression analysis back into multidimensional data analysis. This idea is developed and illustrated, with emphasis on constrained principal coordinate analysis.

We analyze data from a gamut-mapping experiment using several statistical procedures for ranked data. In this experiment six gamut-mapping algorithms were applied to six different images and the results were ranked by 31 judges according to how well the images matched an original. We fitted two distance-based statistical models to the data: both analyses showed that aggregate preference among the six algorithms depended on the image viewed. Based on the first model we classified the images into four classes or clusters. We applied unidimensional unfolding, a technique from mathematical psychology, to extract latent reference frames upon which judges plausibly ordered the algorithms. Four color experts gave interpretations of the derived reference frames. We used the second model to generate confidence sets for the consensus rankings, and another cluster analysis. 2001 SPIE and IS&T.