# Re: [R] fastest way to compute the squared Euclidean distance between two vectors in R

From: Hesen Peng <hesen.peng_at_gmail.com>
Date: Fri, 1 Feb 2008 14:51:25 +0800

Hi,

I wonder whether the following may help a little:

Since $\sum (x_i - y_i)^2 = \sum x_i^2 + \sum y_i^2 - 2 \sum x_i y_i$, we can modify the function as:

temp.distance<-function(x,y){
sum(x^2) + sum(y^2) - 2* x %*% y
}

I think this may be helpful when you need to compute the bootstrap distance for vectors from a matrix $X$. We simply need to pre-calculate sum(x^2) for each vector $x$, and access the resulted from designated vectors, say $xx$. Then we have:

xx<-RowSum(X^2)

another.distance<-function(i,j){ # i and j are the row index of vector x and y  xx[i] + xx[j] - 2*x[i,] %*% x[j,]
}

On Jan 31, 2008 10:28 AM, Jason Liao <jg_liao_at_yahoo.com> wrote:
> I have a program which needs to compute squared Euclidean distance
> between two vectors million of times, which the Rprof shows is the
> bottleneck. I wondered if there is any faster way than my own simple
> function
>
> distance2 = function(x1, x2)
> {
> temp = x1-x2
> sum(temp*temp)
> }
>
> I have searched the R-help archives and can not find anything except
> when the arguments are matrices. Thanks for any lead.
>
> Jason
>
> Jason Liao, http://www.geocities.com/jg_liao
> Associate Professor of Biostatistics
> Drexel University School of Public Health
> 1505 Race Street, Mail Stop 1033
> Bellet Building, 6th Floor
> phone 215-762-3934
>
>
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>

--

Hesen Peng
Department of Statistics
Fudan University
Shanghai, P. R. C.
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