uniscale function

Fit an Unidimensional Scaling for a Seriation Order

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

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.

Returns

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.

Examples

data(SupremeCourt)
d <- as.dist(SupremeCourt)
d

# embedding-based methods return "configuration" attribute
# plot_config visualizes the configuration
o <- seriate(d, method = "sammon")
get_order(o)
plot_config(o)

# the configuration (Note: objects are in the original order in d)
get_config(o)

# angle methods return a 2D configuration
o <- seriate(d, method = "MDS_angle")
get_order(o)
get_config(o)
plot_config(o, )

# calculate a configuration for a seriation method that does not
# create a configuration
o <- seriate(d, method = "ARSA")
get_order(o)
get_config(o)

# find the minimum-stress configuration for the ARSA order
sc <- uniscale(d, o)
sc

plot_config(sc)

References

Mair P., De Leeuw J. (2015). Unidimensional scaling. In Wiley StatsRef: Statistics Reference Online, Wiley, New York. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.18637/jss.v031.i03")

See Also

register_smacof()

Author(s)

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