Zoning with GeoFIS

Loading data

The zoning process accepts input dataset of class SpatialPointsDataFrame or SpatialMultiPointsDataFrame of the sp R package.
It keeps only the attributes that can be used in the zoning process, meaning numeric attributes, without missing values and with a range that is not limited to a unique value. The last condition is required by the min-max standardization process.
The input dataset must be in a projected coordinate reference system.

In this example the conductivity_2014 input dataset is used. It is included in the GeoFIS R package, each location is described by a single numeric attribute conduct:

data(conductivity_2014)
zoning <- NewZoning(conductivity_2014)

The zonable dataset used by the zoning process is available through the zonable_data method. In this example zonable_data is identical to conductivity_2014.

zonable_data <- zoning$zonable_data()

Main parameters

The border

The border is a polygon used to limit the processed area. Only data points within the border are processed.

If NULL the Convex Hull polygon of the input dataset will be used (computed with st_convex_hull function of the sf R package).

zoning$border <- NULL

An object of class SpatialPolygons can be used as border:

data(conductivity_border)
zoning$border <- conductivity_border

Show the Voronoi diagram

zoning$perform_voronoi()
vm <- zoning$voronoi_map()
par(mar = c(0, 0, 0, 0))
plot(vm)
plot(zoning$zonable_data(), add = TRUE)

The neighborhood

The neighborhood relation can be filtered by a minimal common edge length.

If NULL all contiguous Voronoi polygons are considered as neighbors:

zoning$neighborhood <- NULL

The user can define the minimum edge length (in the same unit as the input dataset coordinate system) shared by two Voronoi polygons for being considered as neighbors:

zoning$neighborhood <- 5

Show the neighborhood relations

The red lines shows the pairs of Voronoi polygons that are no longer considered as neighbors.

zoning$perform_neighborhood()
nm <- zoning$neighborhood_map()
par(mar = c(0, 0, 0, 0))
plot(vm)
plot(subset(nm, filtered == FALSE), add = TRUE, col = "green")
plot(subset(nm, filtered == TRUE), add = TRUE, col = "red")

Attribute distance

This distance function is used for a given attribute. It computes the distance between two data points in the monodimensional attribute space. As many distance functions as there are attributes in the zonable dataset are needed (in a list if multiple attributes).
Two univariate distances are available: EuclideanDistance (the default) or FuzzyDistance. Or NULL if the attribute should not be used in the zoning process.

The fuzzy distance function is based on a fuzzy partition that allows for integrating expert knowledge into distance calculations (Guillaume, Charnomordic, and Loisel 2013; Guillaume and Charnomordic 2013). The partition must be a standardized fuzzy partition based on a FisIn object of the FisPro R package.

The following command-line sets the fuzzy distance based on 3 Mfs-partition defined by the following breakpoints: 20, 30, 100. The range of the conduct attribute is [12, 116]:

zoning$attribute_distance <- FuzzyDistance(NewFisIn(c(20, 30, 100), 12, 116))

The default value, used in this example, is the euclidean distance:

zoning$attribute_distance <- EuclideanDistance()

Zone distance aggregation

To compute the distance between two zones, all the data points included in the two zones are considered and the aggregation is done using the aggreg parameter:

\[ d(z_i,z_j) = (Aggreg) d(x,y), \forall x \in z_i, y \in z_j\] Three aggreg operators are available: MinimumDistance, MaximumDistance (the default) or MeanDistance.
The two zones to be merged at a given iteration are the ones for which the zone distance is minimum.

zoning$zone_distance <- MaximumDistance()

Combine distance

The combination function distance is needed when the zoning is done according to several attributes. In this case, each univariate or elementary distance is computed and normalized in a unit interval. These partial distances are then aggregated to yield the distance between two data points in the multidimensional attribute space. The distance combination is done before computing the between-zones distance.
Two combinations are proposed: EuclideanDistance (the default) or MinkowskiDistance.

zoning$combine_distance <- EuclideanDistance()

Smallest zone

This criterion is used to determine the smallest size for a zone (number of points or area) to be kept in the final map. The zones with a size less than the threshold are included in the most compatible neighboring zone.
The two available parameters are: ZoneSize or ZoneArea.
The default value is ZoneSize with 1 point.

zoning$smallest_zone <- ZoneSize(1)

Perform zoning

zoning$perform_zoning()

Get the map with 5 zones:

map5 <- zoning$map(5)

The result map contains for each zone:

the id
the number of points
the area
the mean of the attribute
the std of the attribute

print(map5@data)
#>    id size      area conduct_mean conduct_std
#> 1 282   13  1691.965     93.15385   11.700402
#> 2 101   31  2442.451     87.29032    9.395241
#> 3   1  107 13123.461     36.40187   11.362226
#> 4  10  175 21098.067     60.05714   11.161011
#> 5 106   27  2683.125     41.77778   10.897955

Plot the map:

library(RColorBrewer)

palette <- brewer.pal(3, "Blues")
breaks <- c(30, 50, 70, 100)
colors <- palette[findInterval(map5$conduct_mean, vec = breaks)]
par(mar = c(0, 0, 2, 0))
plot(map5, col = colors, main = "Map 5 zones")
legend("bottomright",
  legend = levels(cut(map5$conduct_mean, breaks)),
  fill = palette, title = "Conductivity mean"
)

Save the map

Any map can be exported to various common file format, e.g. Shapefile (sf package is required): replace tempdir() with the directory you want to export the map

if (require(sf)) {
  write_sf(st_as_sf(map5), dsn = tempdir(), layer = "map5", driver = "ESRI Shapefile")
}