Isomap: Isomap

In RDRToolbox: A package for nonlinear dimension reduction with Isomap and LLE.

Description

Computes the Isomap embedding as introduced in 2000 by Tenenbaum, de Silva and Langford.

Usage

Isomap(data, dims = 2, k, mod = FALSE, plotResiduals = FALSE, verbose = TRUE)

Arguments

data	N x D matrix (N samples, D features)
dims	vector containing the target space dimension(s)
k	number of neighbours
mod	use modified Isomap algorithm
plotResiduals	show a plot with the residuals between the high and the low dimensional data
verbose	show a summary of the embedding procedure at the end

Details

Isomap is a nonlinear dimension reduction technique, that preserves global properties of the data. That means, that geodesic distances between all samples are captured best in the low dimensional embedding.
This R version is based on the Matlab implementation by Tenenbaum and uses Floyd's Algorithm to compute the neighbourhood graph of shortest distances, when calculating the geodesic distances.
A modified version of the original Isomap algorithm is included. It respects nearest and farthest neighbours.
To estimate the intrinsic dimension of the data, the function can plot the residuals between the high and the low dimensional data for a given range of dimensions.

Value

It returns a N x dim matrix (N samples, dim features) with the reduced input data (list of several matrices if more than one dimension was specified)

Author(s)

Christoph Bartenhagen

References

Tenenbaum, J. B. and de Silva, V. and Langford, J. C., "A global geometric framework for nonlinear dimensionality reduction.", 2000; Matlab code is available at http://waldron.stanford.edu/~isomap/

Examples

## two dimensional Isomap embedding of a 1.000 dimensional dataset using k=5 neighbours
d = generateData(samples=20, genes=1000, diffgenes=100, blocksize=10)
d_low = Isomap(data=d[[1]], dims=2, k=5)
## Isomap residuals for target dimensions 1-10
d_low = Isomap(data=d[[1]], dims=1:10, k=5, plotResiduals=TRUE)	

## three dimensional Isomap embedding of a 1.000 dimensional dataset using k=10 (nearest and farthest) neighbours
d = generateData(samples=20, genes=1000, diffgenes=100, blocksize=10)
d_low = Isomap(data=d[[1]], dims=3, mod=TRUE, k=10)

Example output

Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 
Computing distance matrix ... done
Building graph with shortest paths (using 5 nearest neighbours) ... done
Computing low dimensional embedding ... done
number of samples: 20
reduction from 1000 to 2 dimensions
number of connected components in graph: 1
Computing distance matrix ... done
Building graph with shortest paths (using 5 nearest neighbours) ... done
Computing low dimensional embedding ... done
number of samples: 20
reduction from 1000 to 12345678910 dimensions
number of connected components in graph: 1
Computing distance matrix ... done
Building graph with shortest paths (using 5 nearest and 5 farthest neighbours) ... done
Computing low dimensional embedding ... done
number of samples: 20
reduction from 1000 to 3 dimensions
number of connected components in graph: 1

RDRToolbox documentation built on Nov. 8, 2020, 11:10 p.m.