Statistical Multi-dimensional Scaling with a Geographical Penalty

Understanding the structure of cities and facilities in terms of similarity and proximity when considering wide-area or national land planning is crucial. For this purpose, this chapter proposed a novel method to visualize the similarities or various distances of regions, referred to as Bayesian geographical multi-dimensional scaling. Multi-dimensional scaling (MDS) is the fundamental method that is generally used for this purpose; however, its projections are often substantially different from the geographical locations to facilitate appropriate comparison or understanding. Thus, to overcome this weakness, we introduced a geographical penalty for MDS, and its weight was determined using a statistical criterion. This penalty was introduced because dissimilarities or distances should be small if the two regions are geographically close in many cases. Furthermore, this method was applied to visualize the accessibility of public transit in Japan. The obtained results can be easily compared with geographical locations and facilitate an understanding of the transitions that improve accessibility in each prefecture.