A progress report on where I'm at on this question, with thanks to Lalit
Garg, Richard Sedcole, Stephen Senn, Brett Houlding, Brendan Murphy,
Allan Reese and Bill Venables.
Lalit Garg refers to some of his joint work on clustering classified
survival data including
1. Garg L, McClean SI, Meenan BJ, Millard PH (2011). Phase-type survival
trees and mixed distribution survival trees for clustering patients’
hospital length of stay. INFORMATICA. 22(1): 57-72. and
2. Garg L., McClean SI, Barton M, Meenan BJ and Fullerton K (2010). The
extended mixture distribution survival tree based analysis for
clustering and patient pathway prognostication in a stroke care unit.
International Journal of Information Sciences and Application. 2(4):
671-675.
I am always interested in mixture modelling approaches so I will try to
look at these papers, though the type of data is a lot different from
that I am thinking about. Brendan Murphy also mentions model-based
clustering. I am very keen on model-based clustering but I actually
think that this situation may be more amenable to a more traditional
approach.
Richard Sedcole suggests that Canonical Variate Analysis or Discriminant
Function Analysis would be a good approach. this indeed was the approach
that I had most in mind before asking anzstat and allstat.
Brett Houlding sent me a pre-print about Constrained Clustering. My
first thought was that this was not really what I was interested in but
in fact it may be. I will trickle out a few more details about the
application. I am considering the clustering of different geological
layers at a number of sites based on geochemical composition, with
several observations per layer-within-site. Now there are indeed some
constraints: one would not wish to cluster together two classes from
different layers at the same site, the interest is in which classes from
different sites cluster.
Stephen Senn referred me to the work of David Wishart on the clustering
of single-malt whisky by flavour. Unfortunately most of this work seems
to be in books that I don't have ready access too, though I have ordered
his 2006 book for our Library.
Allan Reese suggests Confirmatory Factor Analysis. In the clustering
situation the latent variables are discrete rather than continuous so
I'm not sure that CFA (let me admit, I've forgotten what that does!)
would be the way to go.
Bill Venables offers the following suggestions, which I will repeat for
the benefit of allstat:
Isn't this just a problem of clustering the clusters? In my naivete I
would have thought all you need to do is
a) define a distance measure between groups, (as opposed to the primary
entities), that reflects the importance you put on the separations that
exist already,
b) define an overall objective you want the clustering to achieve (e.g.
as an objective function to optimise, that balances costs and benefits) and
c) employ some appropriate clustering algorithm to see if there is any
advantage in merging any of your existing groups. Which one to use will
depend on your circumstances. (At this stage it might sometimes be
useful to look at a hierarchical clustering of your groups first, rather
than to go for a hard clustering straightaway - or it may not!)
My own thinking has evolved towards the following modest proposal (which
has some similarity to Bill's ideas, but which, I swear, was arrived at
independently.
1. Form a 'distance' matrix between the groups based on pairwise
Mahalanobis distance w.r.t. the pooled variance-covariance matrix.
2. Begin the hierarchical clustering process by merging the two groups
the smallest distance apart.
3. There is no need to bother about linkage methods, the changed
pairwise Mahalanobis distances are recomputed.
4. Continue merging until things you know shouldn't be merged start
getting merged.
5. Meditate on dendrogram.
Further comments welcome.
Regards, Murray Jorgensen
Cheers, Murray
--
Dr Murray Jorgensen http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
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