Group average representations in Euclidean distance cones

The set of Euclidean distance matrices has a well-known representation as a convex cone. The problems of representing the group averages of K distance matrices are discussed, but not fully resolved, in the context of SMACOF, Generalized Orthogonal Procrustes Analysis and Individual Differences Scaling. The polar (or dual) cone representation, corresponding to inner-products around a centroid, is also discussed. Some new characterisations of distance cones in terms of circumhyperspheres are presented

Multivariate Prediction with Nonlinear Principal Components Analysis: Theory

biplot, large scale data analysis, nonlinear principal components analysis, prediction,

Probabilistic D-Clustering

Clustering, Probabilistic clustering, Mahalanobis distance, Harmonic mean, Joint distance function, Weiszfeld method, Similarity matrix,

Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units

classification, three-way data, simultaneous modes reduction,

Simultaneous classification and multidimensional scaling with external information

MDS, dissimilarity, classification, multivariate multiple regression, external variables,

The optimality of the centroid method

principal component analysis,