AGNES regularization parameter selection
Description
agnesLambdaSelection
is a function designed to select the regularization
parameter in graphical models. It selects the most clustered conditional dependence graph structure where clusters are
defined by the hierarchical algorithm agnes
(See details).
Usage
1 2 3 4  agnesLambdaSelection(obj, way = "direct", nite = 10, subsvec = NULL,
eps = 0.05, until = NULL, minNodes = 30,
distF = c("correlation","shortPath"))

Arguments
obj 
an object of class 
way 
name that uniquely identifies 
nite 
vector with the number of iterations used for each lambda (only if 
subsvec 
vector with the number of subsamples used for each lambda (only if 
eps 
acceptance tolerance for subsets of variables. 
until 
the last path used in 
minNodes 
minimum number of nodes with connections to compute the AGNES coefficient
(the coefficient is zero for paths with less nodes than 
distF 
distance function used to find the dissimilarity matrix from the graph: name that uniquely identifies

Details
AGNES algorithm finds λ by minimizing the risk function
R_{AGNES}(λ) = AC(λ)
where AC(λ) is the AGNES coefficient calculated using the R function
agnes
. Using AGNES we select the λ that maximizes the between
vs within cluster dissimilarities ratio given the dissimilarity matrix of the graph
(see graphCorr
and graphDist
for possible dissimilarities).
A variable subset selection algorithm is available to estimate AC(λ) for
very highdimensional data. It is recommended in order to save memory space and computational time.
Especially way = "int.sampling"
which tends to finds similar lambda selections to the default
procedure.
agnesLambdaSelection
gives a good recovery of global network characteristics when the true partial correlation matrix is block diagonal.
Value
An object of class lambdaSelection
containing the following components:
opt.lambda 
optimal lambda. 
crit.coef 
coefficients for each lambda given the criterion AGNES. 
criterion 
with value 
Author(s)
Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.
References
Caballe, A., N. Bochkina, and C. Mayer (2016). Selection of the Regularization Parameter in Graphical Models using network charactaristics. eprint arXiv:1509.05326, 125.
See Also
lambdaSelection
for other lambda selection approaches and agnes
for clustering implementation.
Examples
1 2 3 4 5 6 7 8 9 10  # example to use agnes function
EX1 < pcorSimulator(nobs = 70, nclusters = 3, nnodesxcluster = c(40,30,20),
pattern = "powerLaw")
y < EX1$y
Lambda.SEQ < seq(.25, 0.70, length.out=40)
out3 < huge(y, method = "mb", lambda = Lambda.SEQ)
AG.COEF < agnesLambdaSelection(out3, distF = "shortPath", way = "direct")
print(AG.COEF)
