TESI DOCTORAL - La Salle

l =7
l =8
l =9
Appendix C. Experiments on hierarchical consensus architectures
1
Stage number
2 3
[K1 =3] [K2 =1]
b11 = b =2
b12 = b =2
b13 = b + l mod b =3
b21 = K1 =3
–
[K1 =4] [K2 =2] [K3 =1]
b11 = b =2
b12 = b =2
b21 = b =2
b13 = b =2
b14 = b + l mod b =2
b22 = b + K1 mod b =2
[K1 =4] [K2 =2] [K3 =1]
b11 = b =2
b12 = b =2
b21 = b =2
b13 = b =2
b14 = b + l mod b =3
b22 = b + K1 mod b =2
b31 = K2 =2
b31 = K2 =2
Table C.3: Examples of computation of the mini-ensembles size of a RHCA on cluster
ensembles of size l =7, 8 and 9, being the mini-ensembles size b =2.
cluster ensemble of an arbitrarily chosen size of l = 30 using the following predefined miniensembles
sizes: b = {2, 3, 5, 15}.
It can be observed that the larger the mini-ensemble size b, the smaller the number of
stages s. Moreover, notice that, for any given RHCA, the number of consensus per stage Ki
progressively converges to unity, i.e. Ks = 1, giving rise to a regular pyramidal hierarchy of
consensus processes. Last, it is worth observing how the effective size of the mini-ensembles
bij is determined. Notice bij is regularly set to b maybe except for the last (i.e. the Kith)
consensus of each stage and/or the only consensus of the final stage, which may vary their
size so as to accomodate the necessary number of clusterings into the associated consensus
process.
l =30
2
mini-ensemble size b
3 5 15
#ofstages s =4 s =3 s =2 s =2
#of
consensus
per stage
Ki = {15, 7, 3, 1} Ki = {10, 3, 1} Ki = {6, 1} Ki = {2, 1}
miniensembles
size bij
b1j =2∀j
∈ [1, 15]
2 ∀j ∈ [1, 6]
b2j =
3 j =7
2 ∀j ∈ [1, 2]
b3j =
3 j =3
b41 =3
b1j =3∀j ∈ [1, 10]
3 ∀j ∈ [1, 2]
b2j =
4 j =3
b31 =3
b1j =5∀j ∈ [1, 6] b1j =15∀j ∈ [1, 2]
b21 =6 b21 =2
Table C.4: Configuration of RHCA topologies on a cluster ensemble of size l =30with
varying mini-ensembles sizes b = {2, 3, 5, 15}.
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