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

radii function