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.LTSAType
LTSA{NN <: AbstractNearestNeighbors, T <: Real} <: AbstractDimensionalityReduction

The LTSA type represents a local tangent space alignment model constructed for T type data with a help of the NN nearest neighbor algorithm.

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StatsBase.fitMethod
fit(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 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)

Examples

M = fit(LTSA, rand(3,100)) # construct LTSA model
R = transform(M)           # perform dimensionality reduction
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MultivariateStats.transformMethod
transform(R::LTSA)

Transforms the data fitted to the local tangent space alignment model R into a reduced space representation.

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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