ls_fit_sum_of_ultrametrics {clue} | 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
"dist" . |
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 x , and the lower diagonal part is used.
Otherwise, it is recycled to the number of elements in x . |
control |
a list of control parameters. See Details. |
The problem to be solved is minimizing the criterion function
L(u(1), ..., u(n)) = sum_{i,j} w_{ij} (x_{ij} - sum_{k=1}^n u_{ij}(k))^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 - sum_{l ne k} u(l) using
ls_fit_ultrametric
.
Available control parameters include
maxiter
eps
eps
.
Defaults to 10^{-6}.reltol
reltol
.
Defaults to 10^{-6}.method
control
ls_fit_ultrametric
employed. By default,
if the SUMT method method is ised, 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.