Hessian Locally Linear Embedding

An S4 Class implementing Hessian Locally Linear Embedding (HLLE)

Details

HLLE uses local hessians to approximate the curvines and is an extension to non-convex subsets in lowdimensional space.

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

HLLE can take the following parameters:

knn: neighborhood size
ndim: number of output dimensions

Implementation

Own implementation, sticks to the algorithm in Donoho and Grimes (2003). Makes use of sparsity to speed up final embedding.

References

Donoho, D.L., Grimes, C., 2003. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. PNAS 100, 5591-5596. doi:10.1073/pnas.1031596100

Examples

if(requireNamespace(c("RSpectra", "Matrix", "RANN"), quietly = TRUE)) {

dat <- loadDataSet("3D S Curve", n = 300)
emb <- embed(dat, "HLLE", knn = 15)
plot(emb, type = "2vars")

}
#> 2023-03-21 13:05:24: Finding nearest neighbors
#> 2023-03-21 13:05:24: Calculating Hessian
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#> as(<dsCMatrix>, "dgCMatrix") is deprecated since Matrix 1.5-0; do as(., "generalMatrix") instead
#> 2023-03-21 13:05:24: Embedding
#> Eigenvalues:  5.515692e-04  4.675215e-05 -5.137594e-17
#> 2023-03-21 13:05:24: DONE