TESI DOCTORAL - La Salle

3.3. Deterministic hierarchical consensus architectures
processes conducted at each stage of a DHCA combine those clusterings stemming from a
single diversity factor (e.g. those ensemble components obtained by applying all the available
algorithms on a particular object representation with a specific dimensionality). Then,
quite obviously, the number of stages of a DHCA is equal to the number of diversity factors
employed in creating the cluster ensemble, i.e. s = f.
Besides selecting the diversity factors (and their cardinality) used in generating the cluster
ensemble, the user must make an additional choice that affects the DHCA configuration:
deciding which diversity factor is subject to consensus at each DHCA stage. This is specified
by means of an ordered list of diversity factors, O = {df1,df2,...,dff }, sothatdfi will
refer hereafter to the diversity factor which is subject to consensus at the ith stage of the
DHCA.
As regards the number of consensus executed on the ith DHCA stage (Ki), it is equal
to the product of the cardinalities of the diversity factors that have not been subject to
consensus neither in the present nor in the previous stages —except for the last stage,
where a single consensus is conducted, as defined in equation (3.13).
⎧
⎨
Ki =
⎩
f
k=i+1
|dfk| if 1 ≤ i