SEMINARIESCHEMA FÖR MATEMATISK STATISTIK 

Fredag    8/3  15.15          Timo Koski,
                              Institutionen för matematik, KTH

                              CLUSTERING OF BINARY VECTORS BY MINIMIZATION
                              OF STOCHASTIC COMPLEXITY



Abstract

The operation of partitioning some data set into separate subsets is
called clustering or classification. The clusters considered here can
be represented by certain probability distributions over the binary
hypercube.  Thus the  clustering  forms in a sense a statistical theory
for  any underlying  data base of binary vectors. 

One basic problem is to determine the  number of clusters to be formed.
More clusters  can always explain the data better, so we shall limit the
number of classes to be found by minimization of stochastic complexity,
which also determines the clusters themselves. 

Intuitively this corresponds to the most concise explanation or the
briefest possible binary recording of the data. 
We shall  also  mention and comment the related minimum message  length
and the autoclass (i.e. Bayesian) techniques of clustering or
classification.

Stochastic complexity is here evaluated by means of the statistical model
for the clusters, which is in fact  a finite mixture of multivariate
Bernoulli distributions. 

Given a clustering  there are both explicit  and asymptotic expressions         (related to the maximum likelihood classification estimate) for stochastic
complexity. Our aim is  to  find the clustering  with the minimal stochastic
complexity using these formulae.       

Applications of the method  to a data base of some several thousands strains
of Enterobacteria i.e. to numerical taxonomy of bacteria will be discussed.
This  is joint work with prof. Mats Gyllenberg from  University of Turku. 


The talk will be in Swedish.

Lokal: Rum 227 i Mattehuset.