allow diffusion map to take as input a Gram matrix?

[SimonEnsemble]

hi. wanting to learn a diffusion map with a custom kernel.
I have my own Gram matrix. (can't explicitly build the feature vectors...)
are you able / can I make a PR to allow this to take as input a Gram matrix whose element (i,j) is k(x_i, x_j) with k the kernel?

https://github.com/wildart/ManifoldLearning.jl/blob/master/src/diffmaps.jl#L66

something like the below?

function fit(::Type{DiffMap}, X::AbstractMatrix{T}; maxoutdim::Int=2, t::Int=1, α::Real=0.0, ɛ::Real=1.0, custom_gram::Bool=false) where {T<:Real}
    if ! custom_gram
      sumX = sum(X.^ 2, dims=1)
      K = exp.(-( transpose(sumX) .+ sumX .- 2*transpose(X) * X ) 
   else
      @assert size(K)[1] == size(K)[2] "Gram matrix must be square!"
      @assert all(K .>= 0.0)
      @assert K == K'
   end
   L = K ./ convert(T, ɛ))

https://inside.mines.edu/~whereman/talks/delaPorte-Herbst-Hereman-vanderWalt-DiffusionMaps-PRASA2008.pdf
going off of the above reference.

edit

I now understand that

    D = Diagonal(vec(sum(L, dims=1)))
    M = inv(D)*L

will normalize the rows :)

thx!

[wildart]

Sure, PR is quite welcome. I think the better design for custom kernel would be similar to how KernelPCA fit handles different kernels, see here: https://github.com/JuliaStats/MultivariateStats.jl/blob/99ee965df3a8e136ff2d0fcb10456b434e1f9001/src/kpca.jl#L157-L165

[SimonEnsemble]

thx, wanted to change this for our research project anyway so glad I could try to help out. let me know if you want me to change anything or have improvements you want me to make.

[we are using it for when the gram matrix is from a graph kernel so the X input argument does not work for us.]

https://github.com/wildart/ManifoldLearning.jl/pull/28/files

[wildart]

This is included in the new release.