TESI DOCTORAL - La Salle

1. Given a cluster ensemble E containing l components:
⎛ ⎞
λ1
⎜λ2⎟
⎜ ⎟
E = ⎜ ⎟
⎝ . ⎠
Chapter 4. Self-refining consensus architectures
compute the φ (ANMI) between each one of them and the cluster ensemble, that is:
l
φ (NMI) (λi, λk) , ∀k =1,...,l
φ (ANMI) (E, λk) = 1
l
i=1
2. Select the cluster ensemble component that maximizes its φ (ANMI) with respect to the whole
ensemble as the reference for the self-refining
process:
(ANMI)
λref =maxφ
(E, λk)
λk
3. Compute the φ (NMI) between λref and each of the components of the cluster ensemble, that
is:
φ (NMI) (λref, λk) , ∀k =1,...,l
4. Generate an ordered list Oφ (NMI) = {λφ (NMI) 1, λφ (NMI)2,...λφ (NMI)l} of cluster ensemble components
ranked in decreasing order according to their φ (NMI) with respect λref.
5. Create a set of P select cluster ensembles Epi by compiling the first ⌊ pi
100l⌉ components of
Oφ (NMI):
⎛
λφ (NMI)
⎜
Epi = ⎜
⎝
1
λφ (NMI) 2
⎞
⎟
.
⎟
⎠
where pi ∈ (0, 100) , ∀i =1,...,P.
λl
λ φ (NMI) ⌊ p i
100 l⌉
6. Run a (flat or hierarchical) consensus architecture based on a consensus function F on Epi,
obtaining a self-refined consensus clustering solution λc p i .
7. Apply the supraconsensus function on the selected cluster ensemble component λref and
the set of self-refined consensus clustering solutions λc p i , i.e. select as the final consensus
solution the one maximizing its φ (ANMI) with respect to the cluster ensemble E, i.e.:
λ final
c
= λ max φ (ANMI) (E, λ) , λ ∈{λref, λc p 1 ,...,λc p P }
Table 4.11: Methodology of the cluster ensemble component selection-based consensus selfrefining
procedure.
SLSAD consensus functions is applied on λref —see figures 4.3(b) and 4.3(g), respectively.
As in section 4.2, the consensus clustering solution deemed as the optimal one (across
a majority of experiment runs) by the supraconsensus function is identified by means of a
vertical green dashed line. As regards its performance, we can observe that it manages to
select the highest quality clustering solution in all cases except when self-refining is based
on the ALSAD and KMSAD consensus functions.
So as to provide the reader with a more comprehensive and quantitative analysis of the
performance of the proposed selection-based consensus self-refining procedure, the follow-
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