The slide-vector model is a multidimensional scaling model for asymmetric proximity data. In this model, an asymmetric distance matrix is fitted to the data, representing the distances between data points based on their coordinates within an objective space.
The slide-vector model introduces an additional vector, referred to as slide vector, to account for asymmetry. The asymmetry in the data is represented by the projections of the coordinates of the objects onto the slide-vector. The slide-vector points in the direction of large asymmetries in the data. The interpretation of asymmetry in this model is aided by the use of projections of points onto the slide-vector. The distance from i to j is larger if the point i has a higher projection onto the slide-vector than the distance from j to i. If the line connecting two points is perpendicular to the slide-vector the difference between the two projections is zero. In this case the distance between the two points is symmetric. The algorithm for fitting this model is derived from the majorization approach to multidimensional scaling. $$d_{ij}(X)=\sqrt{\sum_{s=1}^p(x_{is}-x_{js}+z_{s})^2}.$$
slidevector(data, weight = NULL, ndim = 2, verbose = FALSE, itmax = 125,
eps = 1e-12, rotate = TRUE)
Number of dimensions
The raw stress for this model
Returns the configuration matrix of this multidimensional scaling model
The number of iterations for the algorithm to converge
The number of observations in this model
A matrix with raw residuals
Coordinates of the slide-vector
Name of this asymmetric multidimensional scaling model
Asymmetric dissimilarity matrix
Optional non-negative matrix with weights, if no weights are given all weights are set equal to one
Number of dimensions
If TRUE, print the history of iterations
Maximum number of iterations
Convergence criterion for the algorithm
If TRUE, the slide-vector is aligned with the first dimension of the configuration
The slide-vector model is a special case of the unfolding model. Therefore, the algorithm for fitting this model is a constrained unfolding model. The coordinates of the objects are calculated by minimizing a least squares loss function. This loss function is called stress in the multidimensional scaling literature. The stress is minimized by a version of the SMACOF algorithm. The main output are the configuration of points and the slide-vector.
Zielman, B., and Heiser, W. J. (1993), The analysis of asymmetry by a slide-vector, Psychometrika, 58, 101-114.
plot.slidevector
## asymmetric distances between English towns
data(Englishtowns)
v <- slidevector(Englishtowns, ndim = 2, itmax = 250, eps = .001, rotate = TRUE)
plot(v)
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