Fit an Unidimensional Scaling for a Seriation Order

Fits an (approximate) unidimensional scaling configuration given an order.

Usage

uniscale(d, order, accept_reorder = FALSE, warn = TRUE, ...)

MDS_stress(d, order, refit = TRUE, warn = FALSE)

get_config(x, dim = 1L, ...)

plot_config(x, main, pch = 19, labels = TRUE, pos = 1, cex = 1, ...)

Arguments

d: a dissimilarity matrix.
order: a precomputed permutation (configuration) order.
accept_reorder: logical; accept a configuration that does not preserve the requested order. If FALSE, the initial configuration stored in order or, an equally spaced configuration is returned.
warn: logical; produce a warning if the 1D MDS fit does not preserve the given order.
...: additional arguments are passed on to the seriation method.
refit: logical; forces to refit a minimum-stress MDS configuration, even if order contains a configuration.
x: a scaling returned by uniscale() or a ser_permutation with a configuration attribute.
dim: The dimension if x is a ser_permutation object.
main: main plot label
pch: print character
labels: add the object names to the plot
pos: label position for 2D plot (see text()).
cex: label expansion factor.

Value

A vector with the fitted configuration.

Details

This implementation uses the method describes in Maier and De Leeuw (2015) to calculate the minimum stress configuration for a given (seriation) order by performing a 1D MDS fit. If the 1D MDS fit does not preserve the given order perfectly, then a warning is produced indicating for how many positions order could not be preserved. The seriation method which is consistent to uniscale is "MDS_smacof" which needs to be registered with register_smacof().

The code is similar to smacof::uniscale() (de Leeuw, 2090), but scales to larger datasets since it only uses the permutation given by order.

MDS_stress() calculates the normalized stress of a configuration given by a seriation order. If the order does not contain a configuration, then a minimum-stress configuration if calculates for the given order.

All distances are first normalized to an average distance of close to 1 using \(d_{ij} \frac{\sqrt{n(n-1)/2}}{\sqrt{\sum_{i<j}{d_{ij}}^2}}\).

Some seriation methods produce a MDS configuration (a 1D or 2D embedding). get_config() retrieved the configuration attribute from the ser_permutation_vector. NULL is returned if the seriation did not produce a configuration.

plot_config() plots 1D and 2D configurations. ... is passed on to plot.default and accepts col, labels, etc.

References

Mair P., De Leeuw J. (2015). Unidimensional scaling. In Wiley StatsRef: Statistics Reference Online, Wiley, New York. doi:10.1002/9781118445112.stat06462.pub2

Jan de Leeuw, Patrick Mair (2009). Multidimensional Scaling Using Majorization: SMACOF in R. Journal of Statistical Software, 31(3), 1-30. doi:10.18637/jss.v031.i03

Author

Michael Hahsler with code from Patrick Mair (from smacof::uniscale()).

Examples

data(SupremeCourt)
d <- as.dist(SupremeCourt)
d
#>            Breyer Ginsburg Kennedy OConnor Rehnquist  Scalia  Souter Stevens
#> Ginsburg  0.11966                                                           
#> Kennedy   0.25000  0.26709                                                  
#> OConnor   0.20940  0.25214 0.15598                                          
#> Rehnquist 0.29915  0.30769 0.12179 0.16239                                  
#> Scalia    0.35256  0.36966 0.18803 0.20726   0.14316                        
#> Souter    0.11752  0.09615 0.24790 0.22009   0.29274 0.33761                
#> Stevens   0.16239  0.14530 0.32692 0.32906   0.40171 0.43803 0.16880        
#> Thomas    0.35897  0.36752 0.17735 0.20513   0.13675 0.06624 0.33120 0.43590

# embedding-based methods return "configuration" attribute
# plot_config visualizes the configuration
o <- seriate(d, method = "sammon")
get_order(o)
#>   Stevens  Ginsburg    Breyer    Souter   OConnor   Kennedy Rehnquist    Thomas 
#>         8         2         1         7         4         3         5         9 
#>    Scalia 
#>         6 
plot_config(o)


# the configuration (Note: objects are in the original order in d)
get_config(o)
#>      Breyer    Ginsburg     Kennedy     OConnor   Rehnquist      Scalia 
#> -0.14684990 -0.19296373  0.08295749  0.02409039  0.14664491  0.25573152 
#>      Souter     Stevens      Thomas 
#> -0.10664196 -0.28273598  0.21976725 

# angle methods return a 2D configuration
o <- seriate(d, method = "MDS_angle")
get_order(o)
#>   Stevens    Souter  Ginsburg    Breyer   OConnor Rehnquist   Kennedy    Scalia 
#>         8         7         2         1         4         5         3         6 
#>    Thomas 
#>         9 
get_config(o)
#>                  [,1]          [,2]
#> Breyer    -0.14049676  5.127010e-02
#> Ginsburg  -0.15882157 -9.597189e-05
#> Kennedy    0.07540714 -1.955142e-03
#> OConnor    0.05058155  8.506621e-02
#> Rehnquist  0.14235840  3.586661e-02
#> Scalia     0.19613081 -4.444093e-02
#> Souter    -0.12683772 -6.267484e-03
#> Stevens   -0.23446211 -6.798782e-02
#> Thomas     0.19614026 -5.145556e-02
plot_config(o, )



# calculate a configuration for a seriation method that does not
# create a configuration
o <- seriate(d, method = "ARSA")
get_order(o)
#>   Stevens  Ginsburg    Breyer    Souter   OConnor   Kennedy Rehnquist    Thomas 
#>         8         2         1         7         4         3         5         9 
#>    Scalia 
#>         6 
get_config(o)
#> NULL

# find the minimum-stress configuration for the ARSA order
sc <- uniscale(d, o)
sc
#>     Breyer   Ginsburg    Kennedy    OConnor  Rehnquist     Scalia     Souter 
#> -0.5502170 -0.6888976  0.3206014  0.1179750  0.5502213  0.8861084 -0.4412820 
#>    Stevens     Thomas 
#> -1.0148850  0.8203757 

plot_config(sc)