\name{cccd}
\alias{cccd}
\alias{cccd.rw}
\alias{cccd.classify}
\alias{cccd.classifier}
\alias{cccd.classifier.rw}
\alias{cccd.multiclass.classifier}
\alias{cccd.multiclass.classify}
\alias{plot.cccd}
\title{
Class Cover Catch Digraph
}
\description{
Constructs a class cover catch digraph from points or interpoint distance matrices.
}
\usage{
cccd(x = NULL, y = NULL, dxx = NULL, dyx = NULL, method = NULL)
cccd.rw(x=NULL,y=NULL,dxx=NULL,dyx=NULL,method=NULL,m=1,d=2)
cccd.classifier(x,y,method=NULL)
cccd.classify(data, C,method=NULL)
cccd.classifier.rw(x,y,m=1,d=2)
cccd.multiclass.classifier(data, classes)
cccd.multiclass.classify(data,C,method=NULL)
\method{plot}{cccd}(x, ..., plot.circles = FALSE, dominate.only = FALSE, 
          D = NULL, vertex.size = 2, vertex.label = NA, 
			 vertex.color = "SkyBlue2", dom.color = "Blue", 
			 ypch = 20, ycex = 1.5, ycol = 2, 
			 use.circle.radii = FALSE, balls = FALSE, 
			 ball.color = gray(0.8), square = FALSE, xlim, ylim)
}
\arguments{
    \item{x,y}{
	    the target class and non-target class points. Either x,y
		 or dxx,dyx must be provided. In the case of \code{plot}, x is
		 an object of class cccd.
    }
    \item{dxx,dyx}{
	    interpoint distances (x against x and y against x). If these
		 are not provided they are computed using x and y.
    }
  \item{method}{ the method used for the distance. 
     See \code{\link[proxy]{dist}}.}
	 \item{m}{slope of the null hypothesis curve}
	 \item{data}{data to be classified}
	 \item{d}{dimension of the data}
	 \item{classes}{class labels of the data}
	 \item{C}{cccd object}
  \item{plot.circles}{ logical. Plot the circles around the points if TRUE.}
  \item{dominate.only}{ logical. Only plot the digraph induced by the
      dominating set.}
  \item{D}{ a dominating set. Only used if dominate.only is TRUE. If
         dominate.only is TRUE and D is NULL, then \code{dominate}
			is called.}
  \item{vertex.size,vertex.color,vertex.label, dom.color}{parameters controling
		  the plotting of the vertices. \code{dom.color} is the color
		  of the vertices in the dominating set.}
  \item{balls, ball.color}{if \code{balls}=TRUE, the cover is plotted
        as filled balls, with
        \code{ball.color} controling their color}.
  \item{ypch,ycex,ycol}{ parameters for plotting the non-target points.}
  \item{use.circle.radii}{ logical. Ensure that the circles fit
      within the plot.}
  \item{square}{logical. Make the plot square.}
  \item{xlim,ylim}{if present, these control the plotting region.}
  \item{\dots}{ arguments passed to \code{plot} or \code{plot.cccd}.}
}
\details{
   The class cover catch digraph is a graph with vertices defined by the
	points of \code{x} and edges defined according to the balls
	\eqn{B(x,d(x,Y))}. There is an edge between vertices
	\eqn{x_1,x_2} if \eqn{x_2\in B(x_1,d(x_1,Y))}.
}
\value{
   an object of class igraph. In addition, it contains the attributes:
	\item{R}{a vector of radii.}
	\item{Y}{the y vectors.}
	\item{layout}{the x vectors.}
 }
\note{
    The plotting assumes the cccd used Euclidean distance, and so the
	 balls/circles will be Euclidean balls/circles. If the 
	 method used in the distance was some other metric, you'll have
	 to plot the balls/circles yourself if you want them to be correct
	 on the plot.
 }
\references{
D.J. Marchette,
"Class Cover Catch Digraphs",
Wiley Interdisciplinary Reviews: Computational Statistics, 
2, 171-177, 2010.

D.J. Marchette, Random Graphs for Statistical Pattern Recognition,
John Wiley & Sons, 2004.

C.E. Priebe, D.J. Marchette, J. DeVinney and D. Socolinsky, 
"Classification Using Class Cover Catch Digraphs",
Journal of Classification,
20, 3-23, 2003.
}
\author{
David J. Marchette, david.marchette@navy.mil
}
\seealso{
\code{\link{ccd}}, \code{\link{rng}}, \code{\link{gg}}, \code{\link[proxy]{dist}},
\code{\link{plot.cccd}}
}
\examples{
set.seed(456330)
z <- matrix(runif(1000),ncol=2)
ind <- which(z[,1]<.5 & z[,2]<.5)
x <- z[ind,]
y <- z[-ind,]
g <- cccd(x,y)
C <- cccd.classifier(x,y)
z2 <- matrix(runif(1000),ncol=2)
ind <- which(z2[,1]<.5 & z2[,2]<.5)
cls <- rep(0,nrow(z2))
cls[ind] <- 1
out <- cccd.classify(z2,C)
sum(out != cls)/nrow(z2)
\dontrun{
plot(g,plot.circles=TRUE,dominate.only=TRUE)
points(z2,col=2*(1-cls)+1,pch=20)
}
}
\keyword{graphs}