TrainSuperMDS: Find a set of configuration points that agree with a dissimilarity matrix D and a vector of class labels y

Description

Given a nxn dissimilarity matrix D and a n-vector of binary (1,2) class labels y, this function outputs a set of configuration points z1,...,zn, each a S-vector, such that the distances between the configuration points approximate the dissimilarity matrix D, AND such that zis >= zjs tends to occur when yi >= yj.

Usage

TrainSuperMDS(d = NULL, y, alpha = 0.5, S = 2, x = NULL, nstarts = 5, silent = FALSE)

Arguments

A nxn dissimilarity matrix. If NULL, then x, a nxp data matrix, must be input instead.

A n-vector of binary labels, in the form of 1's and 2's. For instance, c(1,1,1,2,2) could be input if D is a 5x5 matrix.

alpha

A scalar between 0 and 1. If alpha=0 then this is just least squares MDS, and if alpha=1 then it's completely supervised.

The number of dimensions of the configuration points z1,...,zn. Must be at least equal to 1.

A nxp data matrix, to be input only if D is NULL.

nstarts

The supervised MDS algorithm finds a local minimum for the objective. Here, specify the number of initial values to try. If nstarts>1 then the set of configuration points corresponding to the optimal (smallest) value of the objective will be reported.

silent

Set to TRUE in order to turn off printing output to screen.

Value

z: A nxS matrix of the configuration points obtained.
crits: The values of the criterion obtained at the iterations of the algorithm.
stress: The portion of the final criterion value that are due to the STRESS component of the objective function.
super: The portion of the final criterion value that are due to the SUPERVISED component of the objective function.

References

Witten and Tibshirani (2011) Supervised multidimensional scaling for visualization, classification, and bipartite ranking. Computational Statistics and Data Analysis.

Examples

Run this code

# Try ?superMDS for examples