Loïc Gasser
Traditionally, spatial analysis of point pattern has been mostly focused on Euclidean space. As many human related phenomena take place on a network, the assumption of a continuous isotropic space fails to describe events which actually occur on a one-dimensional subset of this space. Thus, recently, researchers have begun integrating network structure constraints to study point patterns. The focus of this report is primarily aimed at the integration of the network structure constraints in studying the first order property of point processes with Kernel Density Estimation (KDE). Two different approaches and the computational methods used to calculate network based kernel density estimation (NetKDE) are described, and are then compared to each other as well as to KDE. An original approach which aim is to replace the conventional search area in flat disk through Euclidean space is introduced. In urban context, polygons of various shapes can be generated and used over the network as an approximation of the potential accessible area for a given distance. As a first case-study, network based density values for various types of economic activities are generated for each building in Geneva. The integration of urban structures in the characterization of neighborhood attributes is an innovative approach which possesses many advantages. A classification based on the attributes generated with this method is performed, and a detailed analysis of the results is carried out. In a second case-study in urban environment, time is considered as an additional dimension in kernel density estimates. A three dimensional KDE approach is used in an attempt to monitor the risk associated with the explosions of improvised explosive devices (IED) in Baghdad through space and time. An animation of the simulations is presented as a visualization technique to detect sensitive areas.
2011
