Penalty: Penalty matrix constructor

Description

Build a penalty matrix that can be adapted to a graph with affilation structure in case of available node classification. If no classification is available, a uniformly designed matrix is given.

Usage

Penalty(X, ...)

Arguments

a $n\times p$ matrix of data, taken from a i.i.d. size-$n$ sample.

...

Additional arguments are available, see Details

Value

Return a $p\times p$ matrix of penalties.

Details

The Penalty function construct a penalty matrix according to the arguments passed by the user.

Additional arguments are : [object Object],.,[object Object],[object Object],[object Object] If rho is not specified, a default value is computed, function of the data variance, the risk and the size $n$ of the sample. This default value is very conservative and leads to very sparse graphs. As a matter of fact, the probability of misclassification holds for the $p^2$ potential edges. Thus, a correction can be applied by multiplying the risk by the expected number of edges. For instance, when one expects as many edges as nodes, a typical risk to apply is $0.05 /p^2 \times p = 0.05 \times p$.

If classes is NULL, a uniform penalty matrix is returned. If a vector of classes belonging is specified, a classified version of the penalty matrix is built that enforces an affiliation structure, by penalizing more intra-class connections. The multpliers argument is a list with inter, intra and dust that permits to adjust the penalty according to the involved nodes' classes.

Examples

Run this code

library(simone)

  ## Data set generation
  p <- 100 # number of nodes
  n <- 200 # sample size
  proba.in  <- 0.15
  proba.out <- 0.005
  alpha <- c(.3,.2,.5)
  X <- SimDataAffiliation (p, n, proba.in, proba.out, alpha, proba.dust=0.2)

  ## Build a penalty matrix with an arbitrary base-value of rho and
  ## multiplier values that encourage affiliation structure
  P <- Penalty(X$data, rho = 0.1, classes = X$cl.theo,
               multipliers = list(intra=1,inter=1.5,dust=2))
	
  par(mfrow=c(1,2))
  Mplot(P, main="Penalty matrix")	
  Mplot(P, X$cl.theo, main="Ordered penalty matrix")