Local Sparse Principal Component Analysis for Exploring the Spatial Distribution of Social Infrastructure

The primary purpose of this study is to develop a method that can assist in exploring infrastructure-related multidimensional data. The spatial distribution of social infrastructure, including housing and service facilities, is usually uneven across a nation. The underlying reasons behind the spatial configuration of infrastructure vary, and its comprehensive examination is crucial to understanding the true implications of their skewed distribution. However, simultaneous examination of all social infrastructure is not always straightforward due to the volume of data. The presence of strong correlations between the facilities may further impede the finding of meaningful patterns. To this end, we present an extension of PCA that constructs sparse principal components for local subsets of the data. To demonstrate its strengths and limitations, we apply it to a dataset on housing and service facilities in Korea. The results exhibit clear geographic patterns and offer valuable insights into the spatial patterns of social infrastructure, which the standard PCA only partly addressed. It provides empirical evidence that the proposed method can be an effective alternative to the traditional dimension reduction techniques for exploring spatial heterogeneity in massive multidimensional data.