isomap: Isometric Feature Mapping Ordination

In pattakosn/Rworkshop: Community Ecology Package

Description

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).

Usage

isomap(dist, ndim=10, ...)
isomapdist(dist, epsilon, k, path = "shortest", fragmentedOK =FALSE, ...)
## S3 method for class 'isomap'
summary(object, axes = 4, ...)
## S3 method for class 'isomap'
plot(x, net = TRUE, n.col = "gray", type = "points", ...)
rgl.isomap(x, web = "white", ...)

Arguments

dist	Dissimilarities.
ndim	Number of axes in metric scaling (argument k in cmdscale).
epsilon	Shortest dissimilarity retained.
k	Number of shortest dissimilarities retained for a point. If both epsilon and k are given, epsilon will be used.
path	Method used in stepacross to estimate the shortest path, with alternatives "shortest" and "extended".
fragmentedOK	What to do if dissimilarity matrix is fragmented. If TRUE, analyse the largest connected group, otherwise stop with error.
x, object	An isomap result object.
axes	Number of axes displayed.
net	Draw the net of retained dissimilarities.
n.col	Colour of drawn net segments.
type	Plot observations either as "points", "text" or use "none" to plot no observations. The "text" will use ordilabel if net = TRUE and ordiplot if net = FALSE, and pass extra arguments to these functions.
web	Colour of the web in rgl graphics.
...	Other parameters passed to functions.

Details

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 xdiss in 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, function rgl.isomap can make dynamic 3D plots that can be rotated on the screen. The functions is based on ordirgl, but it adds the connecting lines. The function passes extra arguments to scores or ordirgl functions so that you can select axes, or define colours and sizes of points.

Value

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.

Note

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.

Author(s)

Jari Oksanen

References

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.

See Also

The underlying functions that do the proper work are stepacross, distconnected and cmdscale. Package mvpart provides a parallel (but a bit different) implementation (xdiss). Moreover, vegan 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.

Examples

## 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)
## The following command requires user interaction
## Not run: 
rgl.isomap(ord, size=4, color="hotpink")

## End(Not run)

pattakosn/Rworkshop documentation built on May 24, 2019, 8:22 p.m.