How to predict cluster membership with cmeans?

cluster-analysis, r

Solution

The membership is defined as (Wikipedia)

Consider this example from the `cmeans` help page:

library("e1071")
set.seed(1)
x <- rbind(matrix(rnorm(100,sd=0.3), ncol=2),
           matrix(rnorm(100,mean=1,sd=0.3), ncol=2))
cl <- cmeans(x, 2, 20, verbose=TRUE, method="cmeans", m=2)

then the membership values can be computed as follows:

## compute distances between samples and cluster centers for default setting
## dist="euclidean"; use absolute values for dist="manhattan"
cc <- cl$centers
dm <- sapply(seq_len(nrow(x)),
             function(i) apply(cc, 1, function(v) sqrt(sum((x[i, ]-v)^2))))

m <- 2
## compute cluster membership values
ms <- t(apply(dm, 2,
              function(x) {
                tmp <- 1/((x/sum(x))^(2/(m-1)))  # formula above
                tmp/sum(tmp)  # normalization
              }))

Comparison:

R> head(cl$membership)
           1      2
[1,] 0.02669 0.9733
[2,] 0.01786 0.9821
[3,] 0.03622 0.9638
[4,] 0.13481 0.8652
[5,] 0.13708 0.8629
[6,] 0.20024 0.7998

R> head(ms)
           1      2
[1,] 0.02669 0.9733
[2,] 0.01786 0.9821
[3,] 0.03622 0.9638
[4,] 0.13481 0.8652
[5,] 0.13708 0.8629
[6,] 0.20024 0.7998

R> all.equal(ms, cl$membership, tolerance=1e-15)
[1] TRUE

Problem

I'm using the `cmeans` from the e1071 R package to cluster my data. I would like to predict cluster membership for new data, and I'm lost how to write the predict function. While it is simple to predict the hard cluster membership (just assign to the closest cluster centre), I don't know how to calculate the membership values as they are given in the `cl$membership`: ``` cl <- cmeans( train, centers= 10, m= 1.08 ) # cl$membership contains the "soft" cluster membership # the following line does not work, unfortunately cl.new <- predict( cl, test ) # getting the hard cluster assignments is easy predict.fclust <- function( cl, x ) { which.cl <- function( xx ) which.min( apply( cl$centers, 1, function( y ) sum( ( y - xx )^2 ) ) ) ret <- apply( x, 1, which.cl ) names( ret ) <- rownames( x ) ret } # this works, but only predicts hard clustering cl.new <- predict( cl, test ) ```

Original source