R: Class of Point Matchings

pppmatching.object {spatstat} | R Documentation

## Class of Point Matchings

### Description

A class `"pppmatching"` to represent a matching of two planar point patterns. Optionally includes information about the construction of the matching and its associated distance between the point patterns.

### Details

This class represents a (possibly weighted and incomplete) matching between two planar point patterns (objects of class `"ppp"`).

A matching can be thought of as a bipartite weighted graph where the vertices are given by the two point patterns and edges of positive weights are drawn each time a point of the first point pattern is "matched" with a point of the second point pattern.

If `m` is an object of type `pppmatching`, it contains the following elements

`pp1, pp2` | the two point patterns to be matched (vertices)
`matrix` | a matrix specifying which points are matched
| and with what weights (edges)
`type` | (optional) a character string for the type of
| the matching (one of `"spa"`, `"ace"` or `"mat"`)
`cutoff` | (optional) cutoff value for interpoint distances
`q` | (optional) the order for taking averages of
| interpoint distances
`distance` | (optional) the distance associated with the matching

The element `matrix` is a "generalized adjacency matrix". The numbers of rows and columns match the cardinalities of the first and second point patterns, respectively. The `[i,j]`-th entry is positive if the `i`-th point of `X` and the `j`-th point of `Y` are matched (zero otherwise) and its value then gives the corresponding weight of the match. For an unweighted matching all the weights are set to 1.

The optional elements are for saving details about matchings in the context of optimal point matching techniques. `type` can be one of `"spa"` (for "subpattern assignment"), `"ace"` (for "assignment only if cardinalities differ") or `"mat"` (for "mass transfer"). `cutoff` is a positive numerical value that specifies the maximal interpoint distance and `q` is a value in [1,Inf] that gives the order of the average applied to the interpoint distances. See the help files for `pppdist` and `matchingdist` for detailed information about these elements.

Objects of class `"pppmatching"` may be created by the function `pppmatching`, and are most commonly obtained as output of the function `pppdist`. There are methods `plot`, `print` and `summary` for this class.

### Author(s)

Dominic Schuhmacher dominic.schuhmacher@stat.unibe.ch http://www.dominic.schuhmacher.name

### See Also

`matchingdist`, `pppmatching`, `plot.pppmatching`

### Examples

      # a random complete unweighted matching
      X <- runifpoint(10)
      Y <- runifpoint(10)
      am <- r2dtable(1, rep(1,10), rep(1,10))[[1]]
            # generates a random permutation matrix
      m <- pppmatching(X, Y, am)
      summary(m)
      m$matrix
      ## Not run:
        plot(m)

    ## End(Not run)

      # an optimal complete unweighted matching
      m2 <- pppdist(X,Y)
      summary(m2)
      m2$matrix
      ## Not run:
        plot(m2)

    ## End(Not run)

[Package spatstat version 1.63-3 Index]