Point pattern analysis (PPA) focuses on the analysis, modeling, visualization, and interpretation of point data. With the increasing availability of big geo-data, such as mobile phone records and social media check-ins, more and more individual-level point data are generated daily. PPA provides an effective approach to analyzing the distribution of such data. This entry provides an overview of commonly used methods in PPA, as well as demonstrates the utility of these methods for scientific investigation based on a classic case study: the 1854 cholera outbreaks in London.

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.
 

Kernel density estimation is an important nonparametric technique to estimate density from point-based or line-based data. It has been widely used for various purposes, such as point or line data smoothing, risk mapping, and hot spot detection. It applies a kernel function on each observation (point or line) and spreads the observation over the kernel window. The kernel density estimate at a location will be the sum of the fractions of all observations at that location. In a GIS environment, kernel density estimation usually results in a density surface where each cell is rendered based on the kernel density estimated at the cell center. The result of kernel density estimation could vary substantially depending on the choice of kernel function or kernel bandwidth, with the latter having a greater impact. When applying a fixed kernel bandwidth over all of the observations, undersmoothing of density may occur in areas with only sparse observation while oversmoothing may be found in other areas. To solve this issue, adaptive or variable bandwidth approaches have been suggested.

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.