Composite UMAP

Combining multiple 'views' of the same dataset into a single projection.

As a simple example, we can split the Fashion MNIST dataset in two: one with the top half of the images and the other with the bottom half.

using UMAP

using Distances

using MLDatasets

using CairoMakie

n_points = 10_000;

fmnist_x = FashionMNIST.traintensor(Float64, 1:n_points);

First, run on full images for baseline.

full_res = @time UMAP.fit(reshape(fmnist_x, :, n_points), 2);

fmnist_x_top = reshape(fmnist_x[1:14, :, :], :, n_points);

fmnist_x_bot = reshape(fmnist_x[15:28, :, :], :, n_points);

fmnist_y = FashionMNIST.trainlabels(1:n_points);

Run UMAP on the top and bottom halves separately.

top_res = @time UMAP.fit(fmnist_x_top, 2);

bot_res = @time UMAP.fit(fmnist_x_bot, 2);

Pass both top and bottom halves as separate views using the advanced API.

The configuration for each view is the same as when run separately.

knn_params = (v1=UMAP.DescentNeighbors(15, Euclidean()),
              v2=UMAP.DescentNeighbors(15, Euclidean()));

src_params = (v1=UMAP.SourceViewParams(1., 1, 1.),
              v2=UMAP.SourceViewParams(1., 1, 1.));

gbl_params = UMAP.SourceGlobalParams(0.5);

memb_params = UMAP.MembershipFnParams(.1, 1.);

tgt_params = UMAP.TargetParams(UMAP._EuclideanManifold{2}(), SqEuclidean(), UMAP.SpectralInitialization(), memb_params);

opt_params = UMAP.OptimizationParams(300, 1., 1., 5);

comp_res = @time UMAP.fit((v1=fmnist_x_top, v2=fmnist_x_bot), knn_params, src_params, gbl_params, tgt_params, opt_params);