Locally Linear Embedding

Locally Linear Embedding (LLE) technique builds a single global coordinate system of lower dimensionality. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds [1].

This package defines a LLE type to represent a LLE results, and provides a set of methods to access its properties.

ManifoldLearning.LLEType
LLE{NN <: AbstractNearestNeighbors, T <: Real} <: AbstractDimensionalityReduction

The LLE type represents a locally linear embedding model constructed for T type data constructed with a help of the NN nearest neighbor algorithm.

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StatsBase.fitMethod
fit(LLE, data; k=12, maxoutdim=2, nntype=BruteForce, tol=1e-5)

Fit a locally linear embedding model to data.

Arguments

  • data: a matrix of observations. Each column of data is an observation.

Keyword arguments

  • k: a number of nearest neighbors for construction of local subspace representation
  • maxoutdim: a dimension of the reduced space.
  • nntype: a nearest neighbor construction class (derived from AbstractNearestNeighbors)
  • tol: an algorithm regularization tolerance

Examples

M = fit(LLE, rand(3,100)) # construct LLE model
R = transform(M)          # perform dimensionality reduction
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References