Computational Intelligence Techniques for Classification in Microarray Analysis - Computational Intelligence in Healthcare: Advanced Methodologies - page 286

'

. x

6. Calculate the value for

7. Establish the confidence interval for the variance, which is established as

⎡ ⎤

2 2

( n − 1 ⋅ S ( n − 1 ⋅ S

2

σ ' ∈ , α = 0 . 05 n = # x '

⎢
⎣

⎥
⎦

with and and the

⋅ j ⋅ j

2 2

χ χ

n − 1 − α / 2 n − 1 α / 2

x '

, S is the sampling variance. number of elements for

j

'

i x not belonging to the set

8. Establish the set of elements form

{ }

Q = x ' / x ' ∉ I

j ij ij

'

σ

⋅ j

9. Go to step 11.
10. Select those values up to the percentile

P from every x '

and establish the

α j

{ }

/'
11. Select the probe j+1 in the case of more probes needing revision and go to
step 2.
12. Create the new set of probes

Q = x x ' > P

set

j ij ij α

' ∪
13. Finalize and return the new set of individuals with the filtered probes

I = x ' / ∃ x ' ∈ Q / i > # x ' ⋅ u ∧ i < # x ' − # x ' ⋅ u

⋅ j ij j

I

4.1.6 Correlations
At the last stage of the filtering process, correlated variables are eliminated so that
only the independent variables remain. To this end, the linear correlation index of
Pearson is calculated and the probes meeting the following condition are eliminated.

r

> α

(5)

i y

· · j

σ

1

n

) (

)

(

x x

∑
=

α = 0 . 95

r

= σ = μ − x u − x

· i . j

given: , where

y x x j . i si . j sj

σ σ

N

· i · j · i ·

s 1

x x

· i · j

σ

is the covariance between probes i and j.

x

i x

· . j

4.2 Classification

There are several algorithms for clustering, but the most common are the hierarchical
algorithms [35] and those based on partitioning [16]. Within the hierarchical algo-
rithms the most common is the dendrogram [35]. The dendrograms are hierarchical
methods that initially define conglomerates for each available case. At each stage the
method joins the conglomerates with a smaller distance, and calculates the distance of
the conglomerate with respect to the others. The new distances are updated in the
distance matrix. The process finishes when there is only one conglomerate (agglom-
erative method) remaining.
Among the partition-based methods it is possible to find alternatives based on
RNAs such as SOM [36] (Self-Organizing Map), GNG [37] (Growing Neural Gas) or