Local Tangent Space Alignment
Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates [1].
This package defines a LTSA
type to represent a local tangent space alignment results, and provides a set of methods to access its properties.
ManifoldLearning.LTSA
— TypeLTSA{NN <: AbstractNearestNeighbors, T <: Real} <: NonlinearDimensionalityReduction
The LTSA
type represents a local tangent space alignment model constructed for T
type data with a help of the NN
nearest neighbor algorithm.
StatsAPI.fit
— Methodfit(LTSA, data; k=12, maxoutdim=2, nntype=BruteForce)
Fit a local tangent space alignment 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
)
Examples
M = fit(LTSA, rand(3,100)) # construct LTSA model
R = transform(M) # perform dimensionality reduction
StatsAPI.predict
— Methodpredict(R::LTSA)
Transforms the data fitted to the local tangent space alignment model R
into a reduced space representation.
References
- 1Zhang, Zhenyue; Hongyuan Zha. "Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment". SIAM Journal on Scientific Computing 26 (1): 313–338, 2004. DOI:10.1137/s1064827502419154