Principal Components Analysis: from Global to Local

Principal Components Analysis (PCA) is a widely used technique in the social and physical sciences. Originally developed by Pearson (1901) , the details of extracting components for a data matrix were presented in an extensive two part pa per by Hotelling (1933). In this paper we examine some problems concerning the extraction and interpretation of geographically weighted principal components (Fotheringham et al. 2002: p196-202). We initially consider the basics of principal components, the development of locally weighted principal components (LWPCA) in the exploration of local subsets in attribute space, and finally geographically weighted principal components (GWPCA). As an illustration of the use and interpretation of GWPCA we demonstrate some interpretive methods in a study of social structure in Greater Dublin. A recent application of GWPCA is provided by Lloyd’s (2010) study of population ch aracteristics in Northern Ireland and we extend some of the methodology in this paper