Compute the differential co-localization operator

Computes the differential operator \(P_{\text{diff}} = P_{\text{proj}}^{-1/2} P_{\text{comp}} P_{\text{proj}}^{-1/2}\) using regularisation. The regularisation parameter is chosen automatically at the knee point of the eigenvalue spectrum of gene_graph_proj.

ComputeDifferentialOperator(
  gene_graph_comp,
  gene_graph_proj,
  regulator_min = 0.01
)

Arguments

gene_graph_comp

A symmetric positive semi-definite matrix representing the comparison graph operator (e.g., from ComputeGraphOperator()).

gene_graph_proj

A symmetric positive semi-definite matrix representing the projection/reference graph operator.

regulator_min

Numeric. Minimum allowed regularisation parameter to avoid numerical instability. Default 1e-2.

Value

A symmetric numeric matrix — the differential operator — with the same dimensions as the input matrices.

Examples

if (FALSE) {
P_diff <- ComputeDifferentialOperator(gene_graph_comp, gene_graph_proj)
}