Principal Component Analysis and Qualitative Spatial Reasoning

In this big data modern age, enormous size of data is a challenge for the computer algorithms as well as hardware because important information is hidden in the data. Principal Component Analysis (PCA) is used to transform the data so that meaningful information becomes explicit. The huge dimensional data can be approximated with a few dimensions. Qualitative Spatial Reasoning (QSR), spatial or network, uses pairwise intersection to determine relations between objects. The 9-Intersection model is commonly used to classify the relations. The performance of QSR can be improved by reducing the number of intersections. PCA has been successfully applied to several domains including image processing and data mining but its connection to QSR is non-existent. Herein we show how (1) PCA can be applied to intersection dimension reduction for QSR spatial data, and (2) the 9-Intersection can be reduced to 4-Intersection for all spatial as well as non-spatial objects.