SpectralMap {SpectralMap}

Diffusion Map and Spectral Map

Description

Implements the diffusion map method of dimensionality reduction and spectral method of combining multiple diffusion maps, including creation of the spectra and visualization of maps.

Usage

SpectralMap(data, epsilon=0.1, range=1, Plot2D=FALSE, Plot3D=FALSE)

Arguments

data

a list of datasets and each column in each dataset is a variable

epsilon

parameter in the Gaussian kernel

range

indexes of the datasets in the data list to be combined and computed. If length(range)==1, only diffusion map will be computed. Otherwise, spectral map will be computed

Plot2D

a logical value indicating whether a 2-D map should be plotted

Plot3D

a logical value indicating whether a 3-D map should be plotted

Value

singularvector

the spectra of either diffusion map or spectral map

Examples

#generate two datasets
n <- 100
theta <- 2*pi*seq(from=0, to=1-1/n, by=1/n)
r = (1 + cos(6*theta)/4)

# X is a circle
X1 = cos(theta)
X2 = sin(theta)
X<-data.frame(X1,X2)

#Y is a hexagon
Y1 = r*cos(theta)
Y2 = r*sin(theta)
Y<-data.frame(Y1,Y2)

#create data list
Data<-list(X,Y)

#create the diffusion map of X
example1<-SpectralMap(Data, epsilon=0.1, range=1, Plot2D=TRUE, Plot3D=FALSE)
#create the spectral map from X to Y
example2<-SpectralMap(Data, epsilon=0.1, range=1:2, Plot2D=TRUE, Plot3D=FALSE)