Augmentation of diffusion maps that produces a full-rank embedding. Based on the following paper.
Chen, Yu-Chia & Meilă, Marina. (2019). Selecting the independent coordinates of manifolds with large aspect ratios. https://arxiv.org/abs/1907.01651
julia> using IES
julia> using Plots; gr()
julia> import Random
julia> Random.seed!(1234);
julia> X = rand(2,1000)
2×1000 Array{Float64,2}:
0.842877 0.383266 0.415927 0.660104 0.704336 … 0.768678 0.938344 0.458261 0.0464189
0.512672 0.979221 0.154317 0.560282 0.386316 0.432986 0.466662 0.617414 0.239659
julia> X[1,:] *= 6;
julia> DM = DiffMap(X, m=20, σ=0.1);
Laplacian sparsity = 0.958968
julia> mfd = rmetric(DM, d=2);
julia> S = ies(mfd, :ag, s=2, ζ=0.1, q=true)
2-element Array{Int64,1}:
1
8
julia> scatter(DM.Y[1,:], DM.Y[8,:], zcolor=X[1,:], legend=:none)
