ls_fit_sum_of_ultrametrics  R Documentation 
Find a sequence of ultrametrics with sum minimizing square distance (Euclidean dissimilarity) to a given dissimilarity object.
ls_fit_sum_of_ultrametrics(x, nterms = 1, weights = 1, control = list())
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 nonnegative 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. 
The problem to be solved is minimizing the criterion function
L(u(1), …, u(n)) = ∑_{i,j} w_{ij} ≤ft(x_{ij}  ∑_{k=1}^n u_{ij}(k)\right)^2
over all u(1), …, 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  ∑_{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 than
eps
.
Defaults to 10^{6}.
reltol
the relative convergence tolerance. Iteration
stops when the relative change in the criterion function is less
than reltol
.
Defaults to 10^{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.
A list of objects of class "cl_ultrametric"
containing
the fitted ultrametric distances.
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.
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