Classical (metric) multidimensional scaling

Torgerson scaling via eigendecomposition of the double-centred matrix.

Usage

morie_spatial_voting_classical_mds(D, n_dims = 2L)

Arguments

D

Symmetric numeric distance matrix.

n_dims

Number of dimensions to extract.

Value

A list with coordinates, eigenvalues, stress, fit, B_matrix.

References

Torgerson, W. S. (1952); Armstrong et al. (2021).

Examples

set.seed(1)
D <- as.matrix(dist(matrix(rnorm(40), 10)))
morie_spatial_voting_classical_mds(D, n_dims = 2)
#> $coordinates
#>               [,1]        [,2]
#>  [1,]  1.979418648 -0.92650417
#>  [2,]  0.596186447  0.42784593
#>  [3,] -0.001047182 -0.41902581
#>  [4,] -3.383827884 -0.31586046
#>  [5,]  0.720001600  1.71989288
#>  [6,]  0.165637607  0.39229188
#>  [7,] -0.414873379  0.50475630
#>  [8,] -0.640556965  0.03933409
#>  [9,]  0.134002868 -0.90457015
#> [10,]  0.845058240 -0.51816048
#> 
#> $eigenvalues
#> [1] 17.584180  5.771801
#> 
#> $stress
#> [1] 0.2457221
#> 
#> $fit
#> [1] 0.7816266
#> 
#> $B_matrix
#>             [,1]        [,2]        [,3]       [,4]         [,5]        [,6]
#>  [1,]  4.8111596  0.82636970  0.18505116 -6.3907206 -0.104262760 -0.22984620
#>  [2,]  0.8263697  0.91119402 -0.04142596 -1.9325303  1.158520509  0.10033190
#>  [3,]  0.1850512 -0.04142596  1.80836735  0.2944681 -1.196142503  1.05077817
#>  [4,] -6.3907206 -1.93253030  0.29446808 11.6836556 -3.006439173 -0.72049034
#>  [5,] -0.1042628  1.15852051 -1.19614250 -3.0064392  3.617590743  0.41549072
#>  [6,] -0.2298462  0.10033190  1.05077817 -0.7204903  0.415490715  1.28690238
#>  [7,] -1.2650732  0.07575998 -0.25528272  1.3035909  0.592617088  0.01364144
#>  [8,] -1.2124708 -1.05509506 -1.51781774  1.6872745 -0.009357381 -0.78883774
#>  [9,]  1.2360549 -0.43084321 -0.73764436 -0.2927678 -1.137370174 -1.14208135
#> [10,]  2.1437383  0.38771842  0.40964853 -2.6260409 -0.330647064  0.01411103
#>              [,7]         [,8]       [,9]       [,10]
#>  [1,] -1.26507323 -1.212470837  1.2360549  2.14373828
#>  [2,]  0.07575998 -1.055095064 -0.4308432  0.38771842
#>  [3,] -0.25528272 -1.517817742 -0.7376444  0.40964853
#>  [4,]  1.30359092  1.687274479 -0.2927678 -2.62604091
#>  [5,]  0.59261709 -0.009357381 -1.1373702 -0.33064706
#>  [6,]  0.01364144 -0.788837739 -1.1420813  0.01411103
#>  [7,]  0.46216454  0.153418568 -0.4908652 -0.58997134
#>  [8,]  0.15341857  2.670592941  0.9509361 -0.87864332
#>  [9,] -0.49086525  0.950936091  1.6020598  0.44252129
#> [10,] -0.58997134 -0.878643316  0.4425213  1.02756508
#>