Extraction of Spatial Features Using Factor Methods, Illustrated on Stream Sediment Data

Abstract

Descriptive analysis of multivariate spatial data is considerably aided by preliminary extraction of underlying factors or components, followed by analysis of the derived factor or componentscores. Much work has been done in this area, and a recent study proposed two contrasting types ofsuch factors which differ in their spatial features. One type comprises orthogonal factors that exhibit lack of spatial cross-correlation across the study region, while the other focusses on extracting maximum spatial structure but results in cross-correlated factors. Many applications would benefit from a combination of these types, so the present paper shows how they can be synthesized in order to produce factors that are approximately orthogonal and also maximise spatial structure. An alternating least squares process is described for doing the computations and its efficacy is evaluated by Monte Carlo simulation. The proposed method is illustrated on a study of trace elements across Vancouver Island, where it is shown that the extracted factors are orthogonal, have approximately zero spatial cross-correlations, and when their scores are plotted on maps of the study region then there is a definite indication of spatial structure. The main features of the two separate previous types of factors have thus been combined successfully into a single set.