Solved – Compute BIC clustering criterion (to validate clusters after K-means)

Question

I'm wondering if there is a good way to calculate the clustering criterion based on BIC formula, for a k-means output in R? I'm a bit confused as to how to calculate that BIC so that I can compare it with other clustering models. Currently I'm using the stats package implementation of k-means.

Answer 1

To calculate the BIC for the kmeans results, I have tested the following methods:

1. The following formula is from: [ref2]

The r code for above formula is:

  k3 <- kmeans(mt,3)
  intra.mean <- mean(k3$within)
  k10 <- kmeans(mt,10)
  centers <- k10$centers
  BIC <- function(mt,cls,intra.mean,centers){
    x.centers <- apply(centers,2,function(y){
      as.numeric(y)[cls]
    })
    sum1 <- sum(((mt-x.centers)/intra.mean)**2)
    sum1 + NCOL(mt)*length(unique(cls))*log(NROW(mt))
  }
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the problem is when i using the above r code, the calculated BIC was monotone increasing. what's the reason?

[ref2] Ramsey, S. A., et al. (2008). "Uncovering a macrophage transcriptional program by integrating evidence from motif scanning and expression dynamics." PLoS Comput Biol 4(3): e1000021.

2. I have used the new formula from https://stackoverflow.com/questions/15839774/how-to-calculate-bic-for-k-means-clustering-in-r

   BIC2 <- function(fit){
   m = ncol(fit$centers)
       n = length(fit$cluster)
   k = nrow(fit$centers)
       D = fit$tot.withinss
   return(data.frame(AIC = D + 2*m*k,
                     BIC = D + log(n)*m*k))
   }
   

This method given the lowest BIC value at cluster number 155.

3. using @ttnphns provided method, the corresponding R code as listed below. However, the problem is what the difference between Vc and V? And how to calculate the element-wise multiplication for two vectors with different length?

   BIC3 <- function(fit,mt){
   Nc <- as.matrix(as.numeric(table(fit$cluster)),nc=1)
   Vc <- apply(mt,2,function(x){
       tapply(x,fit$cluster,var)
    })
   V <- matrix(rep(apply(mt,2,function(x){
   var(x)
   }),length(Nc)),byrow=TRUE,nrow=length(Nc))
   LL = -Nc * colSums( log(Vc + V)/2 ) ##how to calculate this? elementa-wise multiplication for two vectors with different length?
   BIC = -2 * rowSums(LL) + 2*K*P * log(NRoW(mt))
   return(BIC)
   }