## Creating Neighbours using sf objects

### Introduction

This vignette tracks the legacy nb vignette, which was based on part of the first (2008) edition of ASDAR. It adds hints to the code in the nb vignette to use the sf vector representation instead of the sp vector representation to create neighbour objects. .

### Summary

This is a summary of the results below:

• In general, if you need to reproduce results from using "Spatial" objects in spdep, coerce sf objects to sp objects before constructing neighbour objects (particularly if polygon centroids are used for point representation).

• However, for new work, you should use "sf" objects read in using sf.

• From spdep 1.1-7, a number of steps have been taken to choose more efficient approaches especially for larger data sets, using functions in sf and the approximate nearest neighbour (ANN) implementation in dbscan rather than RANN.

### Data set

We’ll use the whole NY 8 county set of boundaries, as they challenge the implementations more than just the Syracuse subset. The description of the input geometries from ADSAR is: New York leukemia: used and documented extensively in Waller and Gotway (2004) and with data formerly made available in Chap. 9 of http://web1.sph.emory.edu/users/lwaller/ch9index.htm; the data import process is described in the help file of NY_data in spData; geometries downloaded from the CIESIN server at https://sedac.ciesin.columbia.edu/data/set/acrp-boundary-1992/data-download, file /pub/census/usa/tiger/ny/bna_st/t8_36.zip, and extensively edited; a zip archive NY_data.zip of shapefiles and a GAL format neighbours list is on the book website. Further, the zipfile is now at a new location requiring login. The object listw_NY is directly imported from nyadjwts.dbf on the Waller & Gotway (2004) chapter 9 website.

The version of the New York 8 counties geometries used in ASDAR and included as a shapefile in spdep was converted from the original BNA file using an external utility program to convert to MapInfo format and converted on from there using GDAL 1.4.1 (the OGR BNA driver was not then available; it entered OGR at 1.5.0, release at the end of 2007), and contains invalid geometries. What was found in mid-2007 was that included villages were in/excluded by in-out umbilical cords to the boundary of the enclosing tract, when the underlying BNA file was first converted to MapInfo (holes could not exist then).

Here we will use a GPKG file created as follows (rgdal could also be used with the same output; GDAL here is built with GEOS, so the BNA vector driver will use geometry tests: The BNA driver supports reading of polygons with holes or lakes. It determines what is a hole or a lake only from geometrical analysis (inclusion, non-intersection tests) and ignores completely the notion of polygon winding (whether the polygon edges are described clockwise or counter-clockwise). GDAL must be built with GEOS enabled to make geometry test work.):

library(sf)
table(st_is_valid(sf_bna))
sf_bna$AREAKEY <- gsub("\\.", "", sf_bna$Primary.ID)
data(NY_data, package="spData")
key <- as.character(nydata$AREAKEY) sf_bna1 <- sf_bna[match(key, sf_bna$AREAKEY), c("AREAKEY")]
sf_bna2 <- merge(sf_bna1, nydata, by="AREAKEY")
sf_bna2_utm18 <- st_transform(sf_bna2, "+proj=utm +zone=18 +datum=NAD27")
st_write(sf_bna2_utm18, "NY8_bna_utm18.gpkg")

### nb and listw objects (copied from the nb_igraph vignette)

Since the spdep package was created, spatial weights objects have been constructed as lists with three components and a few attributes, in old-style class listw objects. The first component of a listw object is an nb object, a list of n integer vectors, with at least a character vector region.id attribute with n unique values (like the row.names of a data.frame object); n is the number of spatial entities. Component i of this list contains the integer identifiers of the neighbours of i as a sorted vector with no duplication and values in 1:n; if i has no neighbours, the component is a vector of length 1 with value 0L. The nb object may contain an attribute indicating whether it is symmetric or not, that is whether i is a neighbour of j implies that j is a neighbour of i. Some neighbour definitions are symmetric by construction, such as contiguities or distance thresholds, others are asymmetric, such as k-nearest neighbours. The nb object redundantly stores both i-j and j-i links.

The second component of a listw object is a list of n numeric vectors, each of the same length as the corresponding non-zero vectors in the nbobject. These give the values of the spatial weights for each i-j neighbour pair. It is often the case that while the neighbours are symmetric by construction, the weights are not, as for example when weights are row-standardised by dividing each row of input weights by the count of neighbours or cardinality of the neighbour set of i. In the nb2listwfunction, it is also possible to pass through general weights, such as inverse distances, shares of boundary lengths and so on.

The third component of a listw object records the style of the weights as a character code, with "B" for binary weights taking values zero or one (only one is recorded), "W" for row-standardised weights, and so on. In order to subset listw objects, knowledge of the style may be necessary.

### Comparison of sp and sf approaches

First some housekeeping and setup to permit this vignette to be built when packages are missing or out-of-date:

if (!suppressPackageStartupMessages(require(sf, quietly=TRUE))) {
message("install the sf package")
dothis <- FALSE
}
if (dothis) sf_extSoftVersion()
##           GEOS           GDAL         proj.4 GDAL_with_GEOS     USE_PROJ_H
##       "3.11.0"        "3.5.2"        "9.1.0"         "true"         "true"
##           PROJ
##        "9.1.0"

Let us read the GPKG file with valid geometries in to ‘sf’ and ‘sp’ objects:

NY8_sf <- st_read(system.file("shapes/NY8_bna_utm18.gpkg", package="spData"), quiet=TRUE)
table(st_is_valid(NY8_sf))
##
## TRUE
##  281

#### Contiguity neighbours for polygon support

Here we first generate a queen contiguity nb object using the legacy spdep approach. This first either uses a pre-computed list of vectors of probable neighbours or finds intersecting bounding boxes internally. Then the points on the boundaries of each set of polygons making up an observation are checked for a distance less than snap to any of the points of the set of polygons making up an observation included in the set of candidate neighbours. Because contiguity is symmetric, only i to j contiguities are tested. A queen contiguity is found as soon as one point matches, a rook contiguity as soon as two points match:

suppressPackageStartupMessages(library(spdep))
reps <- 10
eps <- sqrt(.Machine\$double.eps)
system.time(for(i in 1:reps) NY8_sf_1_nb <- poly2nb(NY8_sf, queen=TRUE, snap=eps))/reps
##    user  system elapsed
##  0.2088  0.0098  0.2208

Using spatial indices to check intersection of polygons is much faster than the legacy method in poly2nb. From spdep 1.1-7, use is made of GEOS through sf to find candidate neighbours when foundInBox=NULL, the default value. Because contiguity is symmetric by definition, foundInBox= only requires intersections for higher indices, leading to a slight overhead to remove duplicates, as st_intersects() reports both i j ans j i relationships. As st_intersects() does not report whether neighbours are queen or rook, a further step is needed to distinguish the two cases.

NY8_sf_1_nb
## Neighbour list object:
## Number of regions: 281
## Number of nonzero links: 1632
## Percentage nonzero weights: 2.066843
## Average number of links: 5.807829

spdep::poly2nb uses two heuristics, first to find candidate neighbours from intersecting polygons (st_intersects()), and second to use the symmetry of the relationship to halve the number of remaining tests. This means that performance is linear in n, but with overhead for identifying candidates, and back-filling symmetric neighbours. Further, spdep::poly2nb() stops searching for queen contiguity as soon as the first neighbour point is found within snap distance (if not identical, which is tested first); a second neighbour point indicates rook contiguities. For details of alternatives for spherical geometries, see section @ref(spher-poly2nb) below.

#### Contiguity neighbours from invalid polygons

Next, we explore a further possible source of differences in neighbour object reproduction, using the original version of the tract boundaries used in ASDAR, but with some invalid geometries as mentioned earlier:

NY8_sf_old <- st_read(system.file("shapes/NY8_utm18.shp", package="spData"), quiet=TRUE)
table(st_is_valid(NY8_sf_old))
##
## FALSE  TRUE
##     5   276

We can see that there are a number of differences between the neighbour sets derived from the fully valid geometries and the older partly invalid set:

try(NY8_sf_old_1_nb <- poly2nb(NY8_sf_old), silent = TRUE)
all.equal(NY8_sf_old_1_nb, NY8_sf_1_nb, check.attributes=FALSE)
## [1] "Component 57: Numeric: lengths (4, 5) differ"
## [2] "Component 58: Numeric: lengths (5, 6) differ"
## [3] "Component 66: Numeric: lengths (7, 11) differ"
## [4] "Component 73: Numeric: lengths (4, 5) differ"
## [5] "Component 260: Numeric: lengths (8, 9) differ"

Using st_make_valid() to make the geometries valid:

NY8_sf_old_val <- st_make_valid(NY8_sf_old, dist=0)
table(st_is_valid(NY8_sf_old_val))
##
## TRUE
##  281

we also see that the geometry type of the geometry column changes:

class(st_geometry(NY8_sf_old))
## [1] "sfc_POLYGON" "sfc"
class(st_geometry(NY8_sf_old_val))
## [1] "sfc_GEOMETRY" "sfc"

and checking the "sfg" objects, two now have objects of different topological dimensions.

table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]]))
##
## MULTIPOLYGON      POLYGON
##            3          278

This can be remedied using st_collection_extract() to get the polygon objects:

NY8_sf_old_val <- st_collection_extract(NY8_sf_old_val, "POLYGON")
table(sapply(st_geometry(NY8_sf_old_val), function(x) class(x)[[2]]))
##
## MULTIPOLYGON
##          281

However, in making the geometries valid, we change the geometries, so the new sets of neighbours still differ from those made with the valid geometries in the same ways as before imposing validity:

try(NY8_sf_old_1_nb_val <- poly2nb(NY8_sf_old_val), silent = TRUE)
all.equal(NY8_sf_old_1_nb_val, NY8_sf_1_nb, check.attributes=FALSE)
## [1] "Component 57: Numeric: lengths (4, 5) differ"
## [2] "Component 58: Numeric: lengths (5, 6) differ"
## [3] "Component 66: Numeric: lengths (7, 11) differ"
## [4] "Component 73: Numeric: lengths (4, 5) differ"
## [5] "Component 260: Numeric: lengths (8, 9) differ"

The neighbour sets are the same for the old boundaries with or without imposing validity:

all.equal(NY8_sf_old_1_nb_val, NY8_sf_old_1_nb, check.attributes=FALSE)
## [1] TRUE

### Planar point-based neighbours

#### Finding points for polygon objects

knearneigh() and dnearneigh() require point support, so decisions must be taken about how to place the point in the areal object. We can use st_centroid() to get the centroids, using the of_largest_polygon=TRUE argument to make sure that the centroid is that of the largest polygon id the observation is made up of more than one external ring:

NY8_ct_sf <- st_centroid(st_geometry(NY8_sf), of_largest_polygon=TRUE)

or st_point_on_surface() which guarantees that the point will fall on the surface of a member polygon:

NY8_pos_sf <- st_point_on_surface(st_geometry(NY8_sf))

or indeed taking the centre of the largest inscribed circle (the function returns a radius line segment, so we choose the central point, not the point on the circle):

if (unname(sf_extSoftVersion()["GEOS"] >= "3.9.0"))
NY8_cic_sf <- st_cast(st_inscribed_circle(st_geometry(NY8_sf), nQuadSegs=0), "POINT")[(1:(2*nrow(NY8_sf)) %% 2) != 0]

We need to check whether coordinates are planar or not:

st_is_longlat(NY8_ct_sf)
## [1] FALSE

#### Graph-based neighbours

From this, we can check the graph-based neighbours (planar coordinates only):

suppressPackageStartupMessages(require(deldir))
NY84_nb <- tri2nb(NY8_ct_sf)
if (require(dbscan, quietly=TRUE)) {
NY85_nb <- graph2nb(soi.graph(NY84_nb, NY8_ct_sf))
} else NY85_nb <- NULL
NY86_nb <- graph2nb(gabrielneigh(NY8_ct_sf))
NY87_nb <- graph2nb(relativeneigh(NY8_ct_sf))

#### K-nearest neighbours

K-nearest neighbours use the coordinate matrices, and can handle Great Circle distances, but this is not demonstrated here, as the data set used is planar, in which case dbscan::kNN() in 2D or 3D building a kd-tree is used:

system.time(for (i in 1:reps) NY88_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1)))/reps
##    user  system elapsed
##  0.0805  0.0035  0.0845

Legacy code may be used omitting the kd-tree:

system.time(for (i in 1:reps) NY89_nb_sf <- knn2nb(knearneigh(NY8_ct_sf, k=1, use_kd_tree=FALSE)))/reps
##    user  system elapsed
##  0.0834  0.0036  0.0875

#### Distance neighbours

Distance neighbours need a threshold - nbdists shows the maximum distance to first nearest neighbour:

dsts <- unlist(nbdists(NY88_nb_sf, NY8_ct_sf))
summary(dsts)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
##    82.85   912.85  1801.11  3441.04  4461.26 17033.11
max_1nn <- max(dsts)

dnearneigh can also handle Great Circle distances, but this is not demonstrated here, as the data set used is planar:

system.time(for (i in 1:reps) NY810_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn))/reps
##    user  system elapsed
##  0.0996  0.0041  0.1042

By default, the function uses dbscan::frNN() to build a kd-tree in 2D or 3D which is then used to find distance neighbours. For small n, the argument use_kd_tree=FALSE may speed up computation a little by reverting to legacy code not building a kd-tree first, but in general the differences are so small that the user will not notice:

system.time(for (i in 1:reps) NY811_nb <- dnearneigh(NY8_ct_sf, d1=0, d2=0.75*max_1nn, use_kd_tree=FALSE))/reps
##    user  system elapsed
##  0.0800  0.0037  0.0843

### Spherical point-based neighbours

Spherical point-based neighbours may be found using Great Circle distances. These have been used for many years, but the switch of sf 1.0-0 to use s2 by default has opened up new opportunities where spatial indexing on the sphere may help.

pts_ll <- st_transform(NY8_ct_sf, "OGC:CRS84")
st_is_longlat(pts_ll)
## [1] TRUE

#### K-nearest neighbours

If the input geometries are in geographical coordinates, and sf_use_s2() is TRUE, knearneigh() will use spatially indexed points and s2::s2_closest_edges() (see https://github.com/r-spatial/s2/issues/125#issuecomment-860107442)

(old_use_s2 <- sf_use_s2())
## [1] TRUE

and performs well with also with larger data sets:

sf_use_s2(TRUE)
system.time(for (i in 1:reps) pts_ll1_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps
##    user  system elapsed
##  0.0299  0.0000  0.0301

For this smaller data set, the legacy approach without spatial indexing is adequate, but slows down as the number of observations increases:

sf_use_s2(FALSE)
## Spherical geometry (s2) switched off
system.time(for (i in 1:reps) pts_ll2_nb <- knn2nb(knearneigh(pts_ll, k=6)))/reps
##    user  system elapsed
##  0.0233  0.0000  0.0235

The WGS84 ellipsoid Great Circle distances differ a very little from the s2 spherical distances, yielding output that here diverges for two tract centroids:

all.equal(pts_ll1_nb, pts_ll2_nb, check.attributes=FALSE)
## [1] "Component 52: Mean relative difference: 1.466667"
## [2] "Component 124: Mean relative difference: 0.0251046"
pts_ll1_nb[[52]]
## [1] 15 38 48 49 50 53
pts_ll2_nb[[52]]
## [1] 37 38 48 49 50 53
pts_ll1_nb[[124]]
## [1] 117 122 123 125 133 134
pts_ll2_nb[[124]]
## [1] 116 117 123 125 133 134
sf_use_s2(old_use_s2)
## Spherical geometry (s2) switched on

#### Distance neighbours

Distance neighbours are more problematic. While nbdists() works well with s2 spherical coordinates, none of the tried adaptations for dnearneigh() work adequately yet. An argument use_s2= is set to TRUE if s2 > 1.0-7, using s2::s2_closest_edges() or the legacy brute-force approach, then only calculating distances from i to j and copying those to j to i through symmetry. The distance metric is alway "km".

max_1nn_ll <- max(unlist(nbdists(knn2nb(knearneigh(pts_ll, k=1)), pts_ll)))
args(dnearneigh)
## function (x, d1, d2, row.names = NULL, longlat = NULL, bounds = c("GE",
##     "LE"), use_kd_tree = TRUE, symtest = FALSE, use_s2 = packageVersion("s2") >
##     "1.0.7", k = 200, dwithin = TRUE)
## NULL

If we permit s2 methods to run, without other arguments set, and s2 > 1.0-7, s2::s2_dwithin_matrix() is run:

if (packageVersion("s2") > "1.0.7") {
system.time(for (i in 1:(reps/5)) pts_ll3_nb <- dnearneigh(pts_ll, d1=0,
d2=0.75*max_1nn_ll))/(reps/5)
}
##    user  system elapsed
##  0.0515  0.0000  0.0515

Alternatively, spherical distances can be used with dwithin=FALSE and s2::s2_closest_edges(); although running in similar time, s2::s2_closest_edges() depends on the additional k= argument, which, if mis-set, may miss valid neighbours:

system.time(for (i in 1:(reps/5)) pts_ll5_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, dwithin=FALSE))/(reps/5)
##    user  system elapsed
##  0.0345  0.0000  0.0350
if (packageVersion("s2") > "1.0.7") all.equal(pts_ll3_nb, pts_ll5_nb, check.attributes=FALSE)
## [1] TRUE

Using s2::s2_closest_edges() respects d1 > 0 without requiring a second pass in R, so is faster than s2::s2_dwithin_matrix():

if (packageVersion("s2") > "1.0.7") {
system.time(for (i in 1:(reps/5)) pts_ll3a_nb <- dnearneigh(pts_ll, d1=5,
d2=0.75*max_1nn_ll, dwithin=FALSE))/(reps/5)
}
##    user  system elapsed
##  0.0385  0.0005  0.0395

Using s2::s2_dwithin_matrix() requires a second pass, one for the lower bound, another for the upper bound, and a set difference operation to find neighbours in the distance band:

if (packageVersion("s2") > "1.0.7") {
system.time(for (i in 1:(reps/5)) pts_ll5a_nb <- dnearneigh(pts_ll, d1=5,
d2=0.75*max_1nn_ll))/(reps/5)
}
##    user  system elapsed
##  0.0890  0.0000  0.0895
if (packageVersion("s2") > "1.0.7") all.equal(pts_ll3a_nb, pts_ll5a_nb, check.attributes=FALSE)
## [1] TRUE

Setting use_s2=FALSE falls back to the legacy version, which uses symmetry to reduce time:

system.time(for (i in 1:reps) pts_ll6_nb <- dnearneigh(pts_ll, d1=0, d2=0.75*max_1nn_ll, use_s2=FALSE))/reps
##    user  system elapsed
##  0.0122  0.0000  0.0122

Minor differences may occur between the legacy ellipsoid and s2 spherical approaches:

all.equal(pts_ll5_nb, pts_ll6_nb, check.attributes=FALSE)
##  [1] "Component 20: Numeric: lengths (6, 5) differ"
##  [2] "Component 28: Numeric: lengths (7, 6) differ"
##  [3] "Component 112: Numeric: lengths (109, 108) differ"
##  [4] "Component 116: Numeric: lengths (109, 108) differ"
##  [5] "Component 122: Numeric: lengths (105, 106) differ"
##  [6] "Component 123: Numeric: lengths (108, 107) differ"
##  [7] "Component 130: Numeric: lengths (108, 109) differ"
##  [8] "Component 134: Numeric: lengths (106, 105) differ"
##  [9] "Component 158: Numeric: lengths (101, 102) differ"
## [10] "Component 165: Numeric: lengths (101, 102) differ"
## [11] "Component 168: Numeric: lengths (101, 102) differ"
## [12] "Component 179: Numeric: lengths (89, 90) differ"
## [13] "Component 180: Numeric: lengths (96, 97) differ"
## [14] "Component 188: Numeric: lengths (46, 47) differ"
## [15] "Component 189: Numeric: lengths (55, 56) differ"
## [16] "Component 196: Numeric: lengths (47, 46) differ"
## [17] "Component 210: Numeric: lengths (106, 104) differ"
## [18] "Component 226: Numeric: lengths (88, 87) differ"
## [19] "Component 229: Numeric: lengths (55, 53) differ"
## [20] "Component 235: Numeric: lengths (40, 39) differ"
## [21] "Component 237: Numeric: lengths (14, 15) differ"
## [22] "Component 245: Numeric: lengths (16, 15) differ"
system.time(for (i in 1:reps) pts_ll6a_nb <- dnearneigh(pts_ll, d1=5, d2=0.75*max_1nn_ll, use_s2=FALSE))/reps
##    user  system elapsed
##  0.0122  0.0001  0.0125
if (packageVersion("s2") > "1.0.7") all.equal(pts_ll5a_nb, pts_ll6a_nb, check.attributes=FALSE)
##  [1] "Component 20: Numeric: lengths (6, 5) differ"
##  [2] "Component 28: Numeric: lengths (7, 6) differ"
##  [3] "Component 112: Numeric: lengths (62, 61) differ"
##  [4] "Component 113: Numeric: lengths (62, 63) differ"
##  [5] "Component 116: Numeric: lengths (56, 55) differ"
##  [6] "Component 119: Numeric: lengths (68, 69) differ"
##  [7] "Component 122: Numeric: lengths (43, 44) differ"
##  [8] "Component 123: Numeric: lengths (50, 49) differ"
##  [9] "Component 128: Numeric: lengths (65, 64) differ"
## [10] "Component 130: Numeric: lengths (61, 63) differ"
## [11] "Component 132: Numeric: lengths (45, 46) differ"
## [12] "Component 134: Numeric: lengths (46, 45) differ"
## [13] "Component 136: Numeric: lengths (61, 62) differ"
## [14] "Component 147: Numeric: lengths (50, 51) differ"
## [15] "Component 154: Numeric: lengths (56, 57) differ"
## [16] "Component 158: Numeric: lengths (49, 50) differ"
## [17] "Component 165: Mean relative difference: 0.02823018"
## [18] "Component 168: Numeric: lengths (54, 56) differ"
## [19] "Component 179: Numeric: lengths (77, 78) differ"
## [20] "Component 180: Numeric: lengths (85, 86) differ"
## [21] "Component 188: Numeric: lengths (39, 40) differ"
## [22] "Component 189: Numeric: lengths (48, 49) differ"
## [23] "Component 196: Numeric: lengths (45, 44) differ"
## [24] "Component 210: Numeric: lengths (68, 66) differ"
## [25] "Component 226: Numeric: lengths (82, 81) differ"
## [26] "Component 229: Numeric: lengths (48, 46) differ"
## [27] "Component 235: Numeric: lengths (38, 37) differ"
## [28] "Component 237: Numeric: lengths (14, 15) differ"
## [29] "Component 245: Numeric: lengths (15, 14) differ"

#### Contiguity neighbours for spherical polygon support

It also turns out that when sf functions are used to find contiguity neighbours, s2 spatial indexing functionality is accessed in finding candidate neighbours in intersecting geometries.

NY8_sf_ll <- st_transform(NY8_sf, "OGC:CRS84")
st_is_longlat(NY8_sf_ll)
## [1] TRUE

The timings are a little slower when st_intersects() hands off geometry predicates to s2_intersects_matrix(), but the results are the same, and because spatial indexing is used, this scales well for larger data sets:

system.time(for (i in 1:reps) NY8_sf_1_nb_ll <- poly2nb(NY8_sf_ll, queen=TRUE, snap=eps))/reps
##    user  system elapsed
##  0.1922  0.0041  0.1974
all.equal(NY8_sf_1_nb, NY8_sf_1_nb_ll, check.attributes=FALSE)
## [1] TRUE