Reducing the dimensionality of a vector

How can I reduce the size of a vector to a lower dimension?

Say for example X:=(1,2,3,4,5,6,7,8,9,10) is a 10-D vector. Suppose I want to reduce it to a 5 dimensional space. Is there any way to do this?

开发者_C百科I have a situation where I need to compare an N-d vector with a corresponding vector of a lower dimension.

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There are an infinite number of ways to convert a 10d vector into a 5d vector.

This is like saying "I want a function that takes two integer parameters and returns an integer, can I make such a function". There an infinite many such functions.

It really depends on what you want to do with the vector. What are the meanings of your 10d and 5d vectors?

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If my assumption is right, the OP would like to convert a vector of 10 values to a matrix with 2 columns.

This could be done easily in R:

# make up the demo data
> v <- c(1,2,3,4,5,6,7,8,9,10)

# modify the dimensions of 'v' to have 2 columns
> dim(v) <- c(5,2)

# and check the result
> v
     [,1] [,2]
[1,]    1    6
[2,]    2    7
[3,]    3    8
[4,]    4    9
[5,]    5   10