dst (version 1.8.0)

peeling: The peeling algorithm

Description

An implementation of the peeling algorithm based on its description in terms of hypergraphs by R. Almond [1989].

Usage

peeling(vars_def, hgm, hg_rel_names, elim_order, verbose = FALSE)

Value

A bca class object.

Arguments

vars_def

A list of variables and their possible values. Concatenate the valuenames parameter of all the variables of the hypergraph to obtain this list.

hgm

The incidence matrix of the hypergraph (bipartite graph), which is the description of the relations between the variables. The variables are the nodes of the hypergraph, and the relations are the edges. Each column describes a relation between the variables by a (0,1) vector. A "1" indicates that a variable belongs to the relation and a "0" not. This matrix must have row and column names. These names are used to show the graph eventually. They need not be the same as variables and relations names of the set of bca's to be analyzed. Use short names to obtain a clear graph.

hg_rel_names

The names of the relations, which are objects of class "bcaspec".

elim_order

The order of elimination of the variables. A vector of length nrow(hgm). Variables are identified by numbers. The first number gives the first variable to eliminate. The variable of interest comes last.

verbose

= TRUE: print steps on the console. Default = FALSE.

Author

Claude Boivin

Details

The peeling algorithm works on an undirected graph. Nodes of the graph (variables) are removed one by one until only the variable of interest remains. An order of elimination (peeling) of the variables must be chosen by the user. No algorithm is provided for that matter. At each step, a procedure of extension is applied to the bca's to merge, and marginalization is applied to eliminate a variable. The marginalization has the effect to integrate in the remaining nodes the information of the eliminated variable.

References

• Almond, R. G. (1989) Fusion and Propagation of Graphical Belief Models: An Implementation and an Example. Ph. D. Thesis, the Department of Statistics, Harvard University. 288 pages (for the description of the peeling algorithm, see pages 52-53).

Examples

# Zadeh's Example
# 1. Defining variables and relations 
# (for details, see vignette: Zadeh_Example)
e1 <- bca(tt = matrix(c(1,0,0,1,1,1), ncol = 2, byrow = TRUE),
 m = c(0.99, 0.01, 0), cnames = c("M", "T"), 
 varnames = "D1", idvar = 1)
e2 <- bca(tt = matrix(c(1,0,0,1,1,1), ncol = 2, byrow = TRUE),
m = c(0.99, 0.01, 0), cnames = c("C", "T"), 
varnames = "D2", idvar = 2)
p_diag <- bca(tt = matrix(c(1,1,1), ncol = 3, byrow = TRUE), 
m = 1, cnames = c("M", "T", "C"), 
varnames = "D", idvar = 3)
# Defining the relation between the variables
# tt matrix
tt_r1 <- matrix(c(1,0,1,0,1,0,0,1,0,1,0,0,0,1,
1,0,0,1,1,0,0,1,0,0,1,0,1,0,0,1,1,0,0,1,0,
0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1), 
ncol = 7,byrow = TRUE)
colnames(tt_r1) = c("M", "T", "C", "T", "M", "T", "C")
# The mass function
spec_r1 <- matrix(c(rep(1,7),2, rep(1,7), 0), ncol = 2, dimnames = list(NULL, c("specnb", "mass"))) 
# Variables numbers and dimension of their frame
info_r1 <- matrix(c(1:3, 2,2,3), ncol = 2, dimnames = list(NULL, c("varnb", "size")) )
#  The relation between e1, e2 and a patient p
r1 <- bcaRel(tt = tt_r1, spec = spec_r1, infovar = info_r1,
 varnames = c("D1", "D2", "D"), relnb = 1)

# 2. Setting the incidence matrix of the grapph
rel1 <- 1*1:3 %in% r1$infovar[,1]
ev1 <- 1*1:3 %in% e1$infovar[,1]
ev2 <- 1*1:3 %in% e2$infovar[,1]
meddiag_hgm <- matrix(c(ev1,ev2, rel1), ncol = 3, 
dimnames = list(c("D1", "D2", "D"), c("e1","e2", "r1")))

# 3. Setting the names of the variables and their frame of discernment
meddiag_vars1 <- c(e1$valuenames, e2$valuenames, p_diag$valuenames)

# 4. Names of bca specifications (evidence and relations)
meddiag_rel_names <- c("e1", "e2", "r1")

# 5. Order of elimination of variables
elim_order <- c(1,2,3)

tabresul(peeling(vars_def = meddiag_vars1, hgm = meddiag_hgm,
hg_rel_names = meddiag_rel_names, elim_order = c(1, 2, 3)) )