pcds-package {pcds}

pcds: A package for Proximity Catch Digraphs and Their Applications

Description

pcds is a package for construction and visualization of proximity catch digraphs (PCDs) and computation of two graph invariants of the PCDs and testing spatial patterns using these invariants.

Details

The PCD families considered are Arc-Slice (AS) PCDs, Proportional-Edge (PE) PCDs and Central Similarity (CS) PCDs.

The graph invariants used in testing spatial point data are the domination number (Ceyhan (2011)) and arc density (Ceyhan et al. (2006); Ceyhan et al. (2007)) of for two-dimensional data.

The pcds package also contains the functions for generating patterns of segregation, association, CSR (complete spatial randomness) and Uniform data in one, two and three dimensional cases, for testing these patterns based on two invariants of various families of the proximity catch digraphs (PCDs), (see (Ceyhan (2005)).

Moreover, the package has visualization tools for these digraphs for 1D-3D vertices. The AS-PCD and CS-PCD tools are provided for 1D and 2D data and PE-PCD related tools are provided for 1D-3D data.

The pcds functions

The pcds functions can be grouped as Auxiliary Functions, AS-PCD Functions, PE-PCD Functions, and CS-PCD Functions.

Auxiliary Functions

Contains the auxiliary (or utility) functions for constructing and visualizing Delaunay tessellations in 1D and 2D settings, computing the domination number, constructing the geometrical tools, such as equation of lines for two points, distances between lines and points, checking points inside the triangle etc., finding the (local) extrema (restricted to Delaunay cells or vertex or edge regions in them).

Arc-Slice PCD Functions

Contains the functions used in AS-PCD construction, estimation of domination number, arc density, etc in the 2D setting.

Proportional-Edge PCD Functions

Contains the functions used in PE-PCD construction, estimation of domination number, arc density, etc in the 1D-3D settings.

Central-Similarity PCD Functions

Contains the functions used in CS-PCD construction, estimation of domination number, arc density, etc in the 1D and 2D setting.

Point Generation Functions

Contains functions for generation of points from uniform (or CSR), segregation and association patterns.

In all these functions points are vectors, and data sets are either matrices or data frames.

Author(s)

Maintainer: Elvan Ceyhan [e-mail]

References

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2011). “Spatial Clustering Tests Based on Domination Number of a New Random Digraph Family.” Communications in Statistics - Theory and Methods, 40(8), 1363-1395.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

Ceyhan E, Priebe CE, Wierman JC (2006). “Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.” Computational Statistics & Data Analysis, 50(8), 1925-1964.