shipunov (version 1.17.1)

Overlap: Calculates overlap between polygons

Description

Calculates overlaps between polygons (typically, convex hulls or confidence ellipses from some scatterplot). Requires 'PBSmapping' package.

Usage

Overlap(ppts, symmetric=FALSE, negative=FALSE)
# S3 method for Overlap
summary(object, ...)

Value

Object (square matrix) of class 'Overlap', or nothing.

Arguments

ppts

List with hulls information (e.g., output from Hulls())

symmetric

Make overlaps symmetric (like in distance matrix)?

negative

Calculate "negative overlaps" (relative distance between non-overlapped hulls)?

object

Object of the class 'Overlap'

...

Additional arguments

Author

Alexey Shipunov

Details

The main idea of Overlap() is to provide the measurement of the separation between groups in 2D space.

Overlap() employs calculations of areas of polygons and their intersects provided by 'PBSmapping' package. Initially, it was based on the code provided by J. Oksanen for his "ordihulldist" function.

By default, overlaps are asymmetric, so overlap between a and b is not necessarily equal to the overlap between b and a. If 'symmetric=TRUE', then Overlap() will calculate symmetric overlaps, less precise but more suitable, e.g., for interpreting overlaps as distances.

When 'negative=TRUE', Overlap() calculates also negative polygon-based distances between non-overlapping polygons. They are symmetric and might be used as similarities too (please look on examples).

summary.Overlap() provides some general numbers, including mean and total overlaps for each hull. In these calculations, hulls without overlaps are ignored. Note that summary.Overlap() calculates the arithmetic, not geometric, mean (whereras symmetric Overlap() uses geometric mean). The average of all overlaps could serve as the reliable measure of the quality of dimension reduction.

Please also check out vegan::ordiareatest() function; this studies the one-side hypothesis that actuall hull areas are smaller than with randomized groups (i.e., that actuall hulls are better than random).

References

Serebryanaya A., Shipunov A. 2009. Morphological variation of plants on the uprising islands of northern Russia. Annales Botanici Fennici. 2009. 46: 81-89.

See Also

Hulls, Ellipses

Examples

iris.p <- prcomp(iris[, -5])$x[, 1:2]
iris.h <- Hulls(iris.p, iris$Species, plot=FALSE)

Overlap(iris.h)
Overlap(iris.h, negative=TRUE)
Overlap(iris.h, symmetric=TRUE)

(iris.o <- Overlap(iris.h, symmetric=TRUE, negative=TRUE))
as.dist(1 - iris.o) # how to convert overlaps into distance-like objects

summary(Overlap(iris.h))
summary(Overlap(iris.h, negative=TRUE))
summary(Overlap(iris.h, symmetric=TRUE))
summary(iris.o)

iris.e <- Ellipses(iris.p, iris$Species, plot=FALSE, centers=TRUE)
Overlap(iris.e, negative=TRUE)