1d:T75f,# The radius of a point from one class with respect to points from the other class Returns the radius for the ball centered at point `p` with radius=min distance to `Y` points. That is, for the point `p` $radius= \min_{y \in Y}d(p,y)$ (i.e., distance from `p` to the closest `Y` point). The point `p` and `Y` points must be of same dimension. ```r radius(p, Y) ``` ## Arguments - `p`: A $d$-dimensional point for which radius is computed. Radius of `p` equals to the distance to the closest `Y` point to `p`. - `Y`: A set of $d$-dimensional points representing the reference points for the balls. That is, radius of the point `p` is defined as the minimum distance to the `Y` points. ## Returns A `list` with three elements - **rad**: Radius value for the point, `p` defined as $\min_{y in Y} d(p,y)$ - **index.of.clYpnt**: Index of the closest `Y` points to the point `p` - **closest.Ypnt**: The closest `Y` point to the point `p` ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); ny<-10 Y<-cbind(runif(ny),runif(ny)) radius(A,Y) nx<-10 X<-cbind(runif(nx),runif(nx)) rad<-rep(0,nx) for (i in 1:nx) rad[i]<-radius(X[i,],Y)$rad Xlim<-range(X[,1]-rad,X[,1]+rad,Y[,1]) Ylim<-range(X[,2]-rad,X[,2]+rad,Y[,2]) xd<-Xlim[2]-Xlim[1] yd<-Ylim[2]-Ylim[1] plot(rbind(Y),asp=1,pch=16,col=2,xlab="",ylab="", main="Circles Centered at Class X Points with \n Radius Equal to the Distance to Closest Y Point", axes=TRUE, xlim=Xlim+xd*c(-.05,.05),ylim=Ylim+yd*c(-.05,.05)) points(rbind(X)) interp::circles(X[,1],X[,2],rad,lty=1,lwd=1,col=4) #For 1D data ny<-5 Y<-runif(ny) Ym = as.matrix(Y) radius(1,Ym) #this works as Y is treated as 1D data sets #but will give error if radius(1,Y) is used #as Y is treated as a vector (i.e., points) #For 3D data ny<-5 X<-runif(3) Y<-cbind(runif(ny),runif(ny),runif(ny)) radius(X,Y) ``` ## See Also `radii` ## Author(s) Elvan Ceyhan

radius function