Extending Spatial Hot Spot Detection Techniques to Temporal Dimensions

This paper presents how hot spot detection methods can be extended to allow for temporal dimensions. Major concerns are how temporal dimension is incorporated into the framework of point pattern analysis, while maintaining the capability of multi-scale analysis. The study elaborates on expanding the scope of (space) K function in order to count time in the analysis. With the explicit treatment of time as well as space, K function falls into three category depending on the way space and time are controlled; (1) space K function, (2) time K function, (3) space-time K function. Space K function is equivalent to the original K function, the method for detecting spatial hot spots where time is controlled. Time K function is the method for detecting temporal hot spots where space is controlled. Space-time K function is broken down to three distinct types: The first type examines spatial pattern of observations disaggregated into temporal category. The second type examines temporal pattern of observations disaggregated into spatial category. The third type detects spatio-temporal pattern, or any interaction between space and time. A set of K function is tested on traffic crash data. The case study illustrates how each category of K function can be used to answer different queries, such as whether there is significant spatial/temporal hot spots, in which scale, and where if any. In addition, temporal variation of spatial hot spots can be explored using the first type of space-time K function. This study demonstrates the explicit treatment of temporal dimensions can enhance the process of knowledge discovery. Newly formulated K functions can provide the methodological framework for exploring spatial, temporal, and spatio-temporal patterns of point events across varying scales.