TESI DOCTORAL - La Salle

C.1. Configuration of a random hierarchical consensus architecture
l
b⌊logb (l)⌉
l
b⌊logb (l)⌉−1
l =7 0.875 1.75
s
⌊logb (l)⌉−1=2
l =8 1 2 ⌊logb (l)⌉ =3
l =9 1.125 2.25 ⌊logb (l)⌉ =3
Table C.1: Examples of computation of the number of stages s of a RHCA on cluster
ensembles of size l =7, 8 and 9, being the mini-ensembles size b =2.
which is designated by Ki (where the subindex i denotes the stage number), is computed
according to equation (C.2).
l
Ki =max
bi
, 1
(C.2)
The number of consensus processes per stage of the three RHCA examples discussed
are presented in table C.2.
1
Stage number
2 3
l =7 K1 =max(⌊3.5⌋ , 1) = 3
as
K2 =max(⌊1.75⌋ , 1) = 1
–
l
b1 =3.5 as l
b2 l =8
=1.75
K1 =max(⌊4⌋ , 1) = 4
as
K2 =max(⌊2⌋ , 1) = 2 K3 =max(⌊1⌋ , 1) = 1
l
b1 =4 as l
b2 =2 as l
b3 l =9
=1
K1 =max(⌊4.5⌋ , 1) = 4
as
K2 =max(⌊2.25⌋ , 1) = 2 K3 =max(⌊1.125⌋ , 1) = 1
l
b1 =4.5 as l
b2 =2.25 as l
b3 =1.125
Table C.2: Examples of computation of the number of consensus per stage (Ki) ofaRHCA
on cluster ensembles of size l =7, 8 and 9, being the mini-ensembles size b =2.
And finally, the real mini-ensembles size bij, ∀i ∈ [1,s]and∀j ∈ [1,Ki] mustbecomputed.
Recall that the effective size of all the mini-ensembles of the RHCA is equal to the
user-defined mini-ensemble size (i.e bij = b ∀i, j) if and only if l is an integer power of b. In
practice, the effective mini-ensembles size is computed according to equation (C.3), which
adjusts this factor so that all the original and intermediate clusterings are subject to a consensus
process. The bij values corresponding to the three RHCA examples are presented
in table C.3 along with the corresponding number of consensus Ki at each RHCA stage in
brackets.
⎧
⎪⎨
b if i