eigenmap  R Documentation 
Function to calculate spatial eigenvector maps of a set of locations in a space with an arbitrary number of dimension.
eigenmap(
x,
alt.coord = NA,
weighting = wf.sqrd,
boundaries,
wpar,
tol = .Machine$double.eps^0.5
)
eigenmap.score(emap, target)
x 
A set of coordinates defined in one (numeric vector) or many (a
coordinate x dimension matrix) dimensions or, alternatively, a distance
matrix provided by 
alt.coord 
Coordinates to be used when a distance matrix is provided as x. Used for plotting purposes. 
weighting 
The function to obtain the edge weighting matrix (see details). 
boundaries 
When required by argument 
wpar 
Shape parameter for argument 
tol 
The smallest absolute eigenvalue for a spatial eigenfunctions to
be considered as a suitable predictor. Default:

emap 
An eigenmapclass object. 
target 
A (generally rectangular) distance matrix between a set of
target locations for which spatiallyexplicit predictions are being made
(rows), and the reference locations given to function 
When function eigenmap
is given coordinates as its argument
x
, they are treated as Cartesian coordinates and the distances between
them are assumed to be Euclidean. Otherwise (e.g., when geodesic distances
are used), distances have to be provided as the argument x
and
plotting coordinates have to be supplied as argument alt.coord
.
The weighting function (see weightingfunctions) must have the
distances as its first argument, optionally an argument named
boundaries
giving the boundaries within which locations are regarded
as neighbours and/or an argument wpar
containing any other weighting
function parameters.
Default values for argument boundaries
are 0 for the minimum value and
NA
for the maximum. For weighting functions with an argument
bounraries
, The upper value NA
indicates the function to take
the minimum value that allow every locations to form a single cluster
following single linkage clustering as a maximum value (obtained internally
from a call to hclust
.
eigenmap()
: Main function for generating an eigenmapclass object from Cartesian
coordinates or pairwise distances.
eigenmap.score()
: Generate scores for arbitrary locations within the scope of an existing
eigenvector map.
Guillaume Guenard and Pierre Legendre, Bertrand Pages Maintainer: Guillaume Guenard <guillaume.guenard@gmail.com>
Borcard, D. and Legendre, P. 2002. Allscale spatial analysis of ecological data by means of principal coordinates of neighbour matrices. Ecol. Model. 153: 5168
Dray, S.; Legendre, P. and PeresNeto, P. 2006. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbor matrices (PCNM). Ecol. Modelling 196: 483493
Legendre, P. and Legendre, L. 2012. Numerical Ecology, 3rd English edition. Elsevier Science B.V., Amsterdam, The Netherlands.
### Example 1: A linear transect.
data(salmon)
## A warning is issued when no boundaries are provided for a function that
## requires them.
## Example:
map < eigenmap(x = salmon[,"Position"], weighting = wf.binary)
map
## plot(map)
## In the following examples, boundaries are provided; they are needed by the
## functions.
map < eigenmap(x = salmon[,"Position"], weighting = wf.binary,
boundaries = c(0,20))
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.Drayf1,
boundaries = c(0,20))
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.Drayf2,
boundaries = c(0,20))
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.Drayf3,
boundaries = c(0,20), wpar = 2)
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.PCNM,
boundaries = c(0,20))
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.sqrd)
map
## plot(map)
map < eigenmap(x = salmon[,"Position"], weighting = wf.RBF, wpar = 0.001)
map
## plot(map)
### Example 2: Using predictor scores
smpl < c(4,7,10,14,34,56,61,64) # A sample to be discarded
map < eigenmap(x = salmon[smpl,"Position"], weighting = wf.sqrd)
scr < eigenmap.score(
map, target = as.matrix(dist(salmon[,"Position"]))[,smpl]
)
## Scores of sampling points are the eigenvectors
scr[smpl,]
wh < 5L # You can try with other vectors.
plot(map$U[,wh] ~ salmon[smpl,"Position"], ylab = expression(U[5]),
xlab = "Position along transect")
points(y = scr[smpl,wh], x = salmon[smpl,"Position"], pch = 21L,
bg = "black")
map < eigenmap(x = salmon[smpl,"Position"], weighting = wf.binary,
boundaries = c(0,20))
scr < eigenmap.score(
map, target = as.matrix(dist(salmon[,"Position"]))[smpl,smpl])
## Plot the 8 prediction sites along particular eigenvectors, here
## eigenvector #1:
wh < 1L # One could try the other vectors.
plot(map$U[,wh] ~ salmon[smpl,"Position"], ylab = expression(U[1L]),
xlab = "Position along transect (m)")
points(y = scr[,wh], x = salmon[smpl,"Position"], pch=21L, bg = "black")
map < eigenmap(x = salmon[smpl,"Position"], weighting = wf.PCNM,
boundaries = c(0,100))
scr < eigenmap.score(
map, target = as.matrix(dist(salmon[,"Position"]))[smpl,smpl]
)
wh < 1L # You can try with other vectors.
plot(map$U[,wh] ~ salmon[smpl,"Position"], ylab = expression(U[1]),
xlab = "Position along transect (m)")
points(y = scr[,wh], x = salmon[smpl,"Position"], pch = 21L, bg = "black")
### Example 3: A unevenly sampled surface.
data(mite)
## Example using the principal coordinates of the square root of the
## (Euclidean) distances:
map < eigenmap(x = as.matrix(mite.geo), weighting = wf.sqrd)
map
## plot(map)
## Example using the radial basis functions (RBF):
map < eigenmap(x = as.matrix(mite.geo), weighting = wf.RBF)
map
## plot(map)
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