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

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)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RDRToolbox)
> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/RDRToolbox/Isomap.Rd_%03d_medium.png", width=480, height=480)
> ### Name: Isomap
> ### Title: Isomap
> ### Aliases: 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)
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
> ## Isomap residuals for target dimensions 1-10
> d_low = Isomap(data=d[[1]], dims=1:10, k=5, plotResiduals=TRUE)	
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
> 
> ## 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)
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
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>