##### AM-08 - Kernels and Density Estimation

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.

## AM-07 - Point Pattern Analysis

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.