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

D <- as.matrix(dist(matrix(rnorm(40), 10)))
morie_spatial_voting_classical_mds(D, n_dims = 2)
#> $coordinates
#>             [,1]       [,2]
#>  [1,]  0.4324050 -0.7145873
#>  [2,] -1.5082069  0.5011667
#>  [3,] -1.0021574 -0.2538114
#>  [4,]  1.4226743 -1.6612207
#>  [5,]  2.2656658  2.2531028
#>  [6,] -2.1548952  0.6026057
#>  [7,] -0.5504315  0.4059818
#>  [8,]  0.4347682 -1.0406272
#>  [9,]  0.4255145  0.3420170
#> [10,]  0.2346633 -0.4346273
#> 
#> $eigenvalues
#> [1] 15.99493 10.57909
#> 
#> $stress
#> [1] 0.2912767
#> 
#> $fit
#> [1] 0.6893002
#> 
#> $B_matrix
#>             [,1]       [,2]         [,3]       [,4]       [,5]        [,6]
#>  [1,]  1.1500336 -1.4466125 -0.459914484  1.6574752 -0.5390116 -0.48054698
#>  [2,] -1.4466125  3.1786662  1.205244368 -2.5310559 -2.6244684  2.45163926
#>  [3,] -0.4599145  1.2052444  1.785292419 -1.4407142 -2.4779087  2.01013360
#>  [4,]  1.6574752 -2.5310559 -1.440714192  5.2376776 -0.8781933 -4.68027076
#>  [5,] -0.5390116 -2.6244684 -2.477908746 -0.8781933 10.4942456 -3.07885597
#>  [6,] -0.4805470  2.4516393  2.010133600 -4.6802708 -3.0788560  6.99480093
#>  [7,] -1.7407389  2.8170191  0.001559705 -0.2556445 -1.2346597 -1.59413971
#>  [8,]  0.8517918 -1.6682687  0.794372778  1.6198372 -0.7674159 -1.10770797
#>  [9,]  0.2045281 -0.3453699 -1.257510789  0.4568086  1.3806722 -0.60430051
#> [10,]  0.8029958 -1.0367935 -0.160554659  0.8140801 -0.2744041  0.08924812
#>               [,7]       [,8]        [,9]       [,10]
#>  [1,] -1.740738855  0.8517918  0.20452809  0.80299576
#>  [2,]  2.817019099 -1.6682687 -0.34536991 -1.03679347
#>  [3,]  0.001559705  0.7943728 -1.25751079 -0.16055466
#>  [4,] -0.255644467  1.6198372  0.45680856  0.81408007
#>  [5,] -1.234659724 -0.7674159  1.38067223 -0.27440413
#>  [6,] -1.594139712 -1.1077080 -0.60430051  0.08924812
#>  [7,]  5.342426293 -1.9508445  0.20137673 -1.58635456
#>  [8,] -1.950844509  2.6766281 -1.14920420  0.70081142
#>  [9,]  0.201376728 -1.1492042  1.07720838  0.03579142
#> [10,] -1.586354559  0.7008114  0.03579142  0.61518002
#>