Isomap: Isomap

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)

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

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)

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.

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

Run this code

## 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)

Run the code above in your browser using DataCamp Workspace