Issues of robustness and high dimensionality in cluster analysis

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena. While normal mixture models are often used to cluster data sets of continuous multivariate data, a more robust clustering can be obtained by considering the t mixture model-based approach. Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data where the number of observations n is very large relative to their dimension p. As the approach using the multivariate normal family of distributions is sensitive to outliers, it is more robust to adopt the multivariate t family for the component error and factor distributions. The computational aspects associated with robustness and high dimensionality in these approaches to cluster analysis are discussed and illustrated.

Spatial distribution of benthic microalgae on coral reefs determined by remote sensing

Understanding the ecological role of benthic microalgae, a highly productive component of coral reef ecosystems, requires information on their spatial distribution. The spatial extent of benthic microalgae on Heron Reef (southern Great Barrier Reef, Australia) was mapped using data from the Landsat 5 Thematic Mapper sensor. integrated with field measurements of sediment chlorophyll concentration and reflectance. Field-measured sediment chlorophyll concentrations. 2 ranging from 23-1.153 mg chl a m(2), were classified into low, medium, and high concentration classes (1-170, 171-290, and > 291 mg chl a m(-2)) using a K-means clustering algorithm. The mapping process assumed that areas in the Thematic Mapper image exhibiting similar reflectance levels in red and blue bands would correspond to areas of similar chlorophyll a levels. Regions of homogenous reflectance values corresponding to low, medium, and high chlorophyll levels were identified over the reef sediment zone by applying a standard image classification algorithm to the Thematic Mapper image. The resulting distribution map revealed large-scale ( > 1 km 2) patterns in chlorophyll a levels throughout the sediment zone of Heron Reef. Reef-wide estimates of chlorophyll a distribution indicate that benthic Microalgae may constitute up to 20% of the total benthic chlorophyll a at Heron Reef. and thus contribute significantly to total primary productivity on the reef.