Description Usage Arguments Details Value Note Author(s) References See Also Examples
The function performs isometric feature mapping which consists of three simple steps: (1) retain only some of the shortest dissimilarities among objects, (2) estimate all dissimilarities as shortest path distances, and (3) perform metric scaling (Tenenbaum et al. 2000).
1 2 3 4 5 6 |
dist |
Dissimilarities. |
ndim |
Number of axes in metric scaling (argument |
epsilon |
Shortest dissimilarity retained. |
k |
Number of shortest dissimilarities retained for a point. If
both |
path |
Method used in |
fragmentedOK |
What to do if dissimilarity matrix is
fragmented. If |
x, object |
An |
axes |
Number of axes displayed. |
net |
Draw the net of retained dissimilarities. |
n.col |
Colour of drawn net segments. |
type |
Plot observations either as |
... |
Other parameters passed to functions. |
The function isomap
first calls function isomapdist
for
dissimilarity transformation, and then performs metric scaling for the
result. All arguments to isomap
are passed to
isomapdist
. The functions are separate so that the
isompadist
transformation could be easily used with other
functions than simple linear mapping of cmdscale
.
Function isomapdist
retains either dissimilarities equal or shorter to
epsilon
, or if epsilon
is not given, at least k
shortest dissimilarities for a point. Then a complete dissimilarity
matrix is reconstructed using stepacross
using either
flexible shortest paths or extended dissimilarities (for details, see
stepacross
).
De'ath (1999) actually published essentially the same method before
Tenenbaum et al. (2000), and De'ath's function is available in function
xdiss
in non-CRAN package mvpart. The differences are that
isomap
introduced the k
criterion, whereas De'ath only
used epsilon
criterion. In practice, De'ath also retains
higher proportion of dissimilarities than typical isomap
.
The plot
function uses internally ordiplot
,
except that it adds text over net using ordilabel
. The
plot
function passes extra arguments to these functions. In
addition, vegan3d package has function
rgl.isomap
to make dynamic 3D plots that can
be rotated on the screen.
Function isomapdist
returns a dissimilarity object similar to
dist
. Function isomap
returns an object of class
isomap
with plot
and summary
methods. The
plot
function returns invisibly an object of class
ordiplot
. Function scores
can extract
the ordination scores.
Tenenbaum et al. (2000) justify isomap
as a tool of unfolding a
manifold (e.g. a 'Swiss Roll'). Even with a manifold structure, the
sampling must be even and dense so
that dissimilarities along a manifold are shorter than across the
folds. If data do not have such a manifold structure, the results are
very sensitive to parameter values.
Jari Oksanen
De'ath, G. (1999) Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data. Plant Ecology 144, 191–199
Tenenbaum, J.B., de Silva, V. & Langford, J.C. (2000) A global network framework for nonlinear dimensionality reduction. Science 290, 2319–2323.
The underlying functions that do the proper work are
stepacross
, distconnected
and
cmdscale
. Function metaMDS
may trigger
stepacross
transformation, but usually only for
longest dissimilarities. The plot
method of vegan
minimum spanning tree function (spantree
) has even
more extreme way of isomapping things.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ## The following examples also overlay minimum spanning tree to
## the graphics in red.
op <- par(mar=c(4,4,1,1)+0.2, mfrow=c(2,2))
data(BCI)
dis <- vegdist(BCI)
tr <- spantree(dis)
pl <- ordiplot(cmdscale(dis), main="cmdscale")
lines(tr, pl, col="red")
ord <- isomap(dis, k=3)
ord
pl <- plot(ord, main="isomap k=3")
lines(tr, pl, col="red")
pl <- plot(isomap(dis, k=5), main="isomap k=5")
lines(tr, pl, col="red")
pl <- plot(isomap(dis, epsilon=0.45), main="isomap epsilon=0.45")
lines(tr, pl, col="red")
par(op)
|
Loading required package: permute
Loading required package: lattice
This is vegan 2.4-4
Warning message:
In ordiplot(cmdscale(dis), main = "cmdscale") :
Species scores not available
Isometric Feature Mapping (isomap)
Call:
isomap(dist = dis, k = 3)
Distance method: bray shortest isomap
Criterion: k = 3
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