Connectivity Matrix Seriation via Relaxation
Fig 4
Comparison of the smooth-index (‘SI’) algorithm with feedback arc set (‘FAS’) sorting.
A Original connectivity matrix of 50 neurons with 50% density in the lower and 4% density in the upper triangle. B Same as A, but after scrambling. C Resulting matrix after removing recurrent connections identified by the FAS algorithm. Note that the ordering of the scrambled matrix is retained. D FAS reduced matrix, reordered applying the Schur decomposition. E Full, scrambled matrix reordered applying the permutation matrix as obtained from applying the Schur decomposition to the FAS-reduced matrix. F Scrambled matrix after SI-sorting. Note that it has fewer entries in the upper triangle than the one in E. G-I Performance of the SI and the FAS algorithm for matrices with three different densities in the lower triangle, from p = 50% to p = 20%. The density in the upper triangle was held constant at 4%. Plotted is the fraction of non-zero entries in the upper triangle of the matrix in case of the original connectivity matrix before scrambling (in gray), after FAS sorting (in red) and after smooth-index sorting (in blue). Data represent the mean +- standard deviation obtained from 10 sorting runs.