compute_transition

Compute Normalized Transition Matrix from Connectivity Matrix

Usage

compute_transition(connectivity)

Arguments

connectivity

A symmetric numeric or sparse matrix representing pairwise affinities (e.g., k-NN graph).

Value

A symmetric matrix representing the normalized transition matrix.

Details

Converts a symmetric connectivity matrix into a double-normalized transition matrix suitable for diffusion-based analyses. The output matrix is scaled such that it preserves local affinities and is symmetric with unit row and column scaling.

The transition matrix is computed as: $$T = Z D^{-1} A D^{-1} Z$$ where \(A\) is the input matrix, \(D\) is the row sum diagonal matrix, and \(Z\) rescales the result for symmetry.

Examples

library(Matrix)
mat <- Matrix::rsparsematrix(5, 5, density = 0.6)
mat <- 0.5 * (mat + t(mat))  # ensure symmetry
trans <- compute_transition(mat)
#> Warning: NaNs produced
print(trans)
#> 5 x 5 sparse Matrix of class "dgCMatrix"
#>                                            
#> [1,] .          0.02096412 NaN .        NaN
#> [2,] 0.02096412 0.18876807 NaN .        NaN
#> [3,]        NaN        NaN NaN      NaN NaN
#> [4,] .          .          NaN 1.025801 NaN
#> [5,]        NaN        NaN NaN      NaN   .