Statistics and Visualization of Point-Patterns

Many data sets come as point patterns of the form (longitude, latitude, time, magnitude). The examples of data sets in this format includes tornado events, origins/destination of internet flows, earthquakes, terrorist attacks and etc. It is difficult to visualize the data with simple plotting. This research project studies and implements non-parametric kernel smoothing in Python as a way of visualizing the intensity of point patterns in space and time. A two-dimensional grid M with size mx, my is used to store the calculation result for the kernel smoothing of each grid points. The heat-map in Python then uses the grid to plot the resulting images on a map where the resolution is determined by mx and my. The resulting images also depend on a spatial and a temporal smoothing parameters, which control the resolution (smoothness) of the figure. The Python code is applied to visualize over 56,000 tornado landings in the continental U.S. from the period 1950 - 2014. The magnitudes of the tornado are based on Fujita scale.