ls_fit_sum_of_ultrametrics {clue} | R Documentation |
Least Squares Fit of Sums of Ultrametrics to Dissimilarities
Description
Find a sequence of ultrametrics with sum minimizing square distance (Euclidean dissimilarity) to a given dissimilarity object.
Usage
ls_fit_sum_of_ultrametrics(x, nterms = 1, weights = 1,
control = list())
Arguments
x |
a dissimilarity object inheriting from or coercible to class
|
nterms |
an integer giving the number of ultrametrics to be fitted. |
weights |
a numeric vector or matrix with non-negative weights
for obtaining a weighted least squares fit. If a matrix, its
numbers of rows and columns must be the same as the number of
objects in |
control |
a list of control parameters. See Details. |
Details
The problem to be solved is minimizing the criterion function
L(u(1), \dots, u(n)) =
\sum_{i,j} w_{ij} \left(x_{ij} - \sum_{k=1}^n u_{ij}(k)\right)^2
over all u(1), \ldots, u(n)
satisfying the ultrametric
constraints.
We provide an implementation of the iterative heuristic suggested in
Carroll & Pruzansky (1980) which in each step t
sequentially
refits the u(k)
as the least squares ultrametric fit to the
“residuals” x - \sum_{l \ne k} u(l)
using
ls_fit_ultrametric
.
Available control parameters include
maxiter
an integer giving the maximal number of iteration steps to be performed. Defaults to 100.
eps
a nonnegative number controlling the iteration, which stops when the maximal change in all
u(k)
is less thaneps
. Defaults to10^{-6}
.reltol
the relative convergence tolerance. Iteration stops when the relative change in the criterion function is less than
reltol
. Defaults to10^{-6}
.method
a character string indicating the fitting method to be employed by the individual least squares fits.
control
a list of control parameters to be used by the method of
ls_fit_ultrametric
employed. By default, if the SUMT method method is used, 10 inner SUMT runs are performed for each refitting.
It should be noted that the method used is a heuristic which can not be guaranteed to find the global minimum.
Value
A list of objects of class "cl_ultrametric"
containing
the fitted ultrametric distances.
References
J. D. Carroll and S. Pruzansky (1980). Discrete and hybrid scaling models. In E. D. Lantermann and H. Feger (eds.), Similarity and Choice. Bern (Switzerland): Huber.