[R] boundary check

[Greg Snow]

You did not originally define "ball", the other respondents have discussed using a convex hull, but here is another approach:

Use "ball" to mean sphere (or technically hypersphere) and find the sphere with the smallest radius that contains all the points, optim or other optimizers could be programmed to do this (or an approximation that may be good enough is to use the means as the center and the distance to the furthest point as the radius).

Then finding if a new point is within the sphere is just a matter of computing the Euclidean distance from the new point to the center and comparing that to the radius.

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Feng Li
> Sent: Friday, September 24, 2010 3:44 AM
> To: r-help at r-project.org
> Subject: [R] boundary check
> 
> Dear R,
> 
> I have a covariates matrix with 10 observations,  e.g.
> 
> > X <- matrix(rnorm(50), 10, 5)
> > X
>              [,1]        [,2]        [,3]        [,4]       [,5]
>  [1,]  0.24857135  0.30880745 -1.44118657  1.10229027  1.0526010
>  [2,]  1.24316806  0.36275370 -0.40096866 -0.24387888 -1.5324384
>  [3,] -0.33504014  0.42996246  0.03902479 -0.84778875 -2.4754644
>  [4,]  0.06710229  1.01950917 -0.09325091 -0.03222811  0.4127816
>  [5,] -0.13619141  1.33143821 -0.79958805  2.08274102  0.6901768
>  [6,] -0.45060357  0.19348831 -1.23793647 -0.72440163  0.5057326
>  [7,] -1.20740516  0.20231086  1.15584485  0.81777770 -1.2719855
>  [8,] -1.81166284 -0.07913113 -0.91080581 -0.34774436  0.9552182
>  [9,]  0.19131383  0.14980569 -0.37458224 -0.09371273 -1.7667203
> [10,] -0.85159276 -0.66679528  1.63019340  0.56920196 -2.4049600
> 
> And I define a boundary of X:  The smallest "ball" that nests all the
> observations of X. I wish to check if a particular point x_i
> 
> > x_i <- matrix(rnorm(5), 1, 5)
> > x_i
>            [,1]      [,2]       [,3]      [,4]      [,5]
> [1,] -0.1525543 0.4606419 -0.1011011 -1.557225 -1.035694
> 
> is inside the boundary of X or not. I know it's easy to do it with 1-D
> or
> 2-D, but I don't knot how to manage it when the dimension is large.
> 
> Can someone give a hint? Thanks in advance!
> 
> 
> Feng
> 
> --
> Feng Li
> Department of Statistics
> Stockholm University
> 106 91 Stockholm, Sweden
> http://feng.li/
> 
> 	[[alternative HTML version deleted]]
> 
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