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.LLE
— TypeLLE{NN <: AbstractNearestNeighbors, T <: Real} <: NonlinearDimensionalityReduction
The LLE
type represents a locally linear embedding model constructed for T
type data constructed with a help of the NN
nearest neighbor algorithm.
StatsAPI.fit
— Methodfit(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 ofdata
is an observation.
Keyword arguments
k
: a number of nearest neighbors for construction of local subspace representationmaxoutdim
: a dimension of the reduced space.nntype
: a nearest neighbor construction class (derived fromAbstractNearestNeighbors
)tol
: an algorithm regularization tolerance
Examples
M = fit(LLE, rand(3,100)) # construct LLE model
R = transform(M) # perform dimensionality reduction
StatsAPI.predict
— Methodpredict(R::LLE)
Transforms the data fitted to the LLE model R
into a reduced space representation.
References
- 1Roweis, S. & Saul, L. "Nonlinear dimensionality reduction by locally linear embedding", Science 290:2323 (2000). DOI:10.1126/science.290.5500.2323