Multiple Component Analysis and Its Application in Classification of Environments

Abstract

Multiple component analysis has been developed as a quantitative method for classifying samples drawn from multivariate populations where the underlying populations are unknown and are to be determined. The method is most effective in environmental studies where the variables of interest have separate, but systematic patterns of variation across the total environment. A multiple component is defined as a subset of variables having maximum intercorrelation. The number of such components is determined by cluster analysis. Distinct sample groups are identified by the bimodal character of the distribution of scores calculated for each sample for each component. With this approach, the number of samples that can be classified is unlimited. This method, applied practically to Bahama Bank samples, has been compared with a regular Q-mode-type analysis in a study of recent carbonate sediments which involved 216 samples and 12 variables. In the original study, five facies were recognized: (1) coralgal, (2) oolite, (3) grapestone, (4) mud, and (5) pellet mud. If it is assumed that the mud and pellet-mud facies are indistinguishable, the two methods are found to be in 90 percent agreement in their classification of the 216 samples. If all five groups are considered, an 83 percent agreement is found. In either case, the resulting facies patterns are very similar. With the same data, two other methods also have been compared: (1) principal components and (2) hierarchical grouping. Of the four methods, multiple components yields the classification with the smallest partition variance resulting in the most homogeneous subgrouping of the samples. This is true whether four or five facies groups are assumed present.