R function to find the vector with the highest correlation with all the remaining vectors

user_9721314 0
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I want to find which vector (or row) in a matrix has the highest correlation value to the other vectors (rows). Is there another solution than doing this in a loop like this :

mat <- matrix(rnorm(100), 5, 5)
for (i in 1:nrow(mat)){
  for (j in 1:nrow(mat)){
    # the correlation coefficients of each row
    cor_val[[i]][[j]] <- cor(mat[i,], mat[j,])
    # the average of the correlation coefficients of each row 
    cor_mean[[i]] <- mean(unlist(cor_val[[i]]))
  }
}

# the index of the row with the highest correlation
Indx <- which.max(cor_mean)
correlation r
3 Answers

One approach is with cor. As pointed out by @Darren Tsai, cor calculates correlation by columns, but you can use t to transpose. 

set.seed(3)
mat <- matrix(rnorm(100),5,5)

cor.mat <- cor(t(mat),t(mat))
max.cor <- max(abs(cor.mat[lower.tri(cor.mat)]))
which(abs(cor.mat) == max.cor, arr.ind = TRUE)
#     row col
#[1,]   3   2
#[2,]   2   3

Edit Forgot the call to abs in which, fixed.

user_130953260

From your loop code, the corresponding shorter version is

which.max(rowMeans(cor(t(mat))))

However, correlation coefficients can be positive or negative. Computing the average will balance the strength of correlation. I think it's better to compute the mean of absolute correlation or squared correlation. I.e.

which.max(rowMeans(abs(cor(t(mat)))))

or

which.max(rowMeans(cor(t(mat))^2))
user_100689850

You can just do cor(mat) to obtain a matrix of correlation indexes. Since Cor() returns the correlation between columns, you would have to first transpose your matrix. 

mat <- matrix(rnorm(100),5,4)

mat <- t(mat)

cor(mat)
user_95754350
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