KMeans initial k centers

[Mark Hall]

Hi,

I'm very new to Mahout so please forgive any unintentional stupidity on 
my part :-) I was just browsing the clustering code for KMeans and have 
a couple of questions.

The initial random selection of k cluster centers generated by 
RandomSeedGenerator looks like it is using reservoir sampling in order 
to give each input instance equal chance of being selected as a center. 
However, the code is not correct (if it is supposed to be reservoir 
sampling). After the first k instances have been added to the reservoir, 
the chance of an instance being selected to randomly replace a reservoir 
entry should be k / n, where n is the number of instances seen so far. 
The code uses constant probability 1/k.

Another observation. I see that arbitrary distance functions can be used 
with KMeans, but, as far as I can see, the centroid is always computed 
by taking the component-wise mean of the instances in a cluster. The 
mean minimizes the squared error (i.e. Euclidean distance) but does not 
minimize the intra-cluster distance for other distance functions. E.g. 
for the Manhattan distance you need to take the median as the cluster 
center in order to minimize the distance.

Cheers,
Mark.