The alternating least-squares algorithm for CDPCA

Clustering and Disjoint Principal Component Analysis (CDP CA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology.

A recursive construction of the regular exceptional graphs with least eigenvalue -2

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

Macroinvertebrate communities and habitat structure in least-impacted hill streams of central Portugal

We surveyed macroinvertebrate communities in 31 hill streams in the Vouga River and Mondego River catchments in central Portugal. Despite applying a "least-impacted" criterion, channel and bank management was common, with 38% of streams demonstrating channel modification (damming) and 80% with evidence of bank modification. Principal component analysis (PCA) at the family and species level related the macroinvertebrates to habitat variables derived at three spatial scales -- site (20 m), reach (200 m), and catchment. Variation in community structure between sites was similar at the species and family level and was statistically related to pH, conductivity, temperature, flow, shade, and substrate size at the site scale; channel and bank habitat and riparian vegetation and land-use at the reach scale; and altitude and slope at the catchment scale. While the effects of river management were apparent in various ecologically important habitat features at the site and reach scale, a direct relationship with macroinvertebrate assemblages was only apparent between the extent of walled banks and the secondary PCA axis described by species data. The strong relationship between catchment scale variables and descriptors of physical structure at the reach and site scale suggests that catchment-scale parameters are valuable predicators of macroinvertebrate community structure in these streams despite the anthropogenic modifications of the natural habitat.