ManifoldLearning

A Julia package for manifold learning and nonlinear dimensionality reduction.

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Methods

• Isomap
• Diffusion maps
• Locally Linear Embedding (LLE)
• Hessian Eigenmaps (HLLE)
• Laplacian Eigenmaps (LEM)
• Local tangent space alignment (LTSA)
• t-Distributed Stochastic Neighborhood Embedding (t-SNE)

Installation

The package can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add ManifoldLearning

Examples

A simple example of using the Isomap reduction method.

julia> X, _ = ManifoldLearning.swiss_roll();

julia> X
3×1000 Array{Float64,2}:
  -3.19512  3.51939   -0.0390153  …  -9.46166   3.44159
  29.1222   9.99283    2.25296       25.1417   28.8007
 -10.1861   6.59074  -11.037         -1.04484  13.4034

julia> M = fit(Isomap, X)
Isomap(outdim = 2, neighbors = 12)

julia> Y = transform(M)
2×1000 Array{Float64,2}:
 11.0033  -13.069   16.7116  …  -3.26095   25.7771
 18.4133   -6.2693  10.6698     20.0646   -24.8973

Performance

Most of the methods use k-nearest neighbors method for constructing local subspace representation. By default, neighbors are computed from a distance matrix of a dataset. This is not an efficient method, especially, for large datasets.

Consider using a custom k-nearest neighbors function, e.g. from NearestNeighbors.jl or FLANN.jl.

See example of custom knn function here.