This section demonstrates the data splitting procedure for selecting relevant features when there exists (or no) cluster structure under the Gaussian setting.

using SplitClusterTest
using Plots

Without cluster structure

x, cl = gen_data_normal(1000, 2000, 0.0, prop_imp=0.1);

Plot the first two PCs of X

pc1, pc2 = first_two_PCs(x)
scatter(pc1[cl .== 1], pc2[cl .== 1])
scatter!(pc1[cl .== 2], pc2[cl .== 2])

perform the data splitting procedure for selecting relevant features

ms = ds(x, ret_ms = true);

the mirror statistics are symmetric about zero since all features are null features.

histogram(ms, label = "")

With cluster structure

x, cl = gen_data_normal(1000, 2000, 0.5, prop_imp=0.1);

Plot the first two PCs of X

pc1, pc2 = first_two_PCs(x)
scatter(pc1[cl .== 1], pc2[cl .== 1])
scatter!(pc1[cl .== 2], pc2[cl .== 2])

the mirror statistics of relevant features tend to be larger and away from null features, where the null features still exhibit a symmetric distribution about zero.

ms = ds(x, ret_ms = true);

Then we can properly take the cutoff to control the FDR, as shown by the red vertical line.

τ = calc_τ(ms)
histogram(ms, label = "")
Plots.vline!([τ], label = "", lw = 3)