Classical (metric) multidimensional scaling
Source:R/spatial_voting.R
morie_spatial_voting_classical_mds.RdTorgerson scaling via eigendecomposition of the double-centred matrix.
Examples
D <- as.matrix(dist(matrix(rnorm(40), 10)))
morie_spatial_voting_classical_mds(D, n_dims = 2)
#> $coordinates
#> [,1] [,2]
#> [1,] -0.9045227 1.23253240
#> [2,] 1.7367469 0.01038171
#> [3,] 0.6379009 -0.67999362
#> [4,] -1.6597743 -0.01264046
#> [5,] -0.3107453 -1.49452728
#> [6,] 0.2688576 -0.75337274
#> [7,] 0.2681814 1.33214099
#> [8,] -2.1940883 -0.21622109
#> [9,] 0.9576449 1.16389811
#> [10,] 1.1997989 -0.58219802
#>
#> $eigenvalues
#> [1] 14.407612 8.297942
#>
#> $stress
#> [1] 0.210684
#>
#> $fit
#> [1] 0.7562131
#>
#> $B_matrix
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 2.8934831 -1.8930816 -1.7523402 2.1499344 -1.4343077 -0.59505879
#> [2,] -1.8930816 3.7236957 1.2765714 -2.7047302 -0.5421181 -0.66062549
#> [3,] -1.7523402 1.2765714 1.0752580 -1.4841512 0.7364102 0.37589062
#> [4,] 2.1499344 -2.7047302 -1.4841512 4.2090525 0.7881009 -0.63114011
#> [5,] -1.4343077 -0.5421181 0.7364102 0.7881009 2.3748196 1.03718948
#> [6,] -0.5950588 -0.6606255 0.3758906 -0.6311401 1.0371895 2.41796630
#> [7,] 0.9769299 0.7413524 -0.4790602 -0.9579661 -2.1691534 -1.38073793
#> [8,] 0.7109137 -3.4133292 -0.6307025 2.2048828 0.7389656 -1.15495204
#> [9,] 0.6653337 1.2614786 -0.2201654 -1.8946300 -2.0777852 0.02415205
#> [10,] -1.7218065 2.2107866 1.1022893 -1.6793530 0.5478786 0.56731591
#> [,7] [,8] [,9] [,10]
#> [1,] 0.9769299 0.7109137 0.66533369 -1.7218065
#> [2,] 0.7413524 -3.4133292 1.26147858 2.2107866
#> [3,] -0.4790602 -0.6307025 -0.22016542 1.1022893
#> [4,] -0.9579661 2.2048828 -1.89462998 -1.6793530
#> [5,] -2.1691534 0.7389656 -2.07778524 0.5478786
#> [6,] -1.3807379 -1.1549520 0.02415205 0.5673159
#> [7,] 2.1674253 -0.1145517 1.72844291 -0.5126811
#> [8,] -0.1145517 6.7694873 -2.38293219 -2.7277818
#> [9,] 1.7284429 -2.3829322 2.53845296 0.3576526
#> [10,] -0.5126811 -2.7277818 0.35765262 1.8556994
#>