dimRed (version 0.2.5)

LaplacianEigenmaps-class: Laplacian Eigenmaps

Description

An S4 Class implementing Laplacian Eigenmaps

Slots

fun

A function that does the embedding and returns a dimRedResult object.

stdpars

The standard parameters for the function.

General usage

Dimensionality reduction methods are S4 Classes that either be used directly, in which case they have to be initialized and a full list with parameters has to be handed to the @fun() slot, or the method name be passed to the embed function and parameters can be given to the ..., in which case missing parameters will be replaced by the ones in the @stdpars.

Parameters

LaplacianEigenmaps can take the following parameters:

ndim

the number of output dimensions.

sparse

A character vector specifying hot to make the graph sparse, "knn" means that a K-nearest neighbor graph is constructed, "eps" an epsilon neighborhood graph is constructed, else a dense distance matrix is used.

knn

The number of nearest neighbors to use for the knn graph.

eps

The distance for the epsilon neighborhood graph.

t

Parameter for the transformation of the distance matrix by \(w=exp(-d^2/t)\), larger values give less weight to differences in distance, t == Inf treats all distances != 0 equally.

norm

logical, should the normed laplacian be used?

Implementation

Wraps around spec.emb.

Details

Laplacian Eigenmaps use a kernel and were originally developed to separate non-convex clusters under the name spectral clustering.

References

Belkin, M., Niyogi, P., 2003. Laplacian Eigenmaps for Dimensionality Reduction and Data Representation. Neural Computation 15, 1373.

Examples

dat <- loadDataSet("3D S Curve")
emb <- embed(dat, "LaplacianEigenmaps")
plot(emb@data@data)