Abstract
The last decade has witnessed an increase of interest in the spatial analysis of structured point patterns over networks whose analysis is challenging because of geometrical complexities and unique methodological problems. In this context, it is essential to incorporate the network specificity into the analysis as the locations of events are restricted to areas covered by line segments. Relying on concepts originating from graph theory, we extend the notions of first-order network intensity functions to second-order and local network intensity functions. We consider two types of local indicators of network association functions which can be understood as adaptations of the primary ideas of local analysis on the plane. We develop the nodewise and cross-hierarchical type of local functions. A real data set on urban disturbances is also presented.
Highlights
The statistical analysis of spatial point patterns and processes is a highly attractive field of applied research across many disciplines studying the spatial arrangement of coordinates of events in planar spaces, in the sphere or over networks
Relying on concepts originating from graph theory, we extend the notions of first-order network intensity functions to secondorder and local network intensity functions
In other words, treating the line segments as edges and the planar locations as nodes of an arbitrarily shaped graph, this implies that the positions of events are governed by a geometric structure such that the point pattern can only be observed upon the edges contained in the network
Summary
The statistical analysis of spatial point patterns and processes is a highly attractive field of applied research across many disciplines studying the spatial arrangement of coordinates of events in planar spaces, in the sphere or over networks. A huge range of methodological and applied papers covering global characteristics of spatial point patterns over networks exist Among these papers, various extensions of kernel density smoothers and second-order moment measures and functions have been proposed, including the work of Borruso (2005, 2008), Okabe and Satoh (2009), Okabe and Sugihara (2012), Yu et al (2015), Ni et al (2016), McSwiggan et al (2017) and Moradi et al (2018). Eckardt and Mateu (2017) defined a class of network intensity functions and various intensity-based statistics for differently shaped graphs and various levels of aggregation covering undirected, directed and partially directed networks This approach provides additional information for point patterns over spatial networks, second-order or local characteristics of network intensity functions have not been presented so far.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
