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Table 9.1 Means and standard deviations of correct classi cation rate for the classi cation
methods on the slope criterion
K nearest
neighbors
Binary
decision tree
Random
forests
Discriminant
PLS
Sparse
discriminant
PLS
Mean
37.28
33.98
32.03
40.63
36.25
Standard
deviation
10.47
5.15
6.46
8.55
7.96
rates. Speci
cally, a GA has been used as a feature selection process, to determine
the electrode and the frequencies that provide the best discrimination for the slope
criterion.
9.6
Feature Selection with a Genetic Algorithm
In this section, a GA is used to improve the slope criterion. So far, previous work in
the
field, which suggested to focus on the alpha waves, was used. For this reason,
the regression was done using frequencies between 4 and 16 Hz. Given the results,
this approach will be fre-
ned. The algorithm searches for the best range of fre-
quencies (not necessarily adjacent) to perform the regression. Similarly, so far all
electrodes were kept. However, one objective of this work is to remove some
electrodes to reduce the time required for the installation of the cap. Thus, the best
combination electrode/frequencies based on the quality of the prediction is searched
for. In this work, 58 electrodes and 15 decomposition levels are available. Then,
58 * 2 15 = 1,900,544 ways exist to choose an electrode and a frequency range. To
avoid an exhaustive search, the proposed approach is to use a GA to perform a
feature selection (Broadhursta et al. 1997 ; Cavill et al. 2009 ).
9.6.1 General Principle of a Genetic Algorithm
These optimization algorithms (De Jong 1975 ; Holland 1975 ) are based on a
simpli
ed abstraction of Darwinian evolution theory. The general idea is that a
population of potential solutions will improve its characteristics over time, through
a series of basic genetic operations called selection, mutation and genetic recom-
bination or crossing. From an algorithmic point of view, the general principle is
depicted in Fig. 9.18 .
The purpose of these algorithms is to optimize a function (
(fitness) within a given
search space of candidate solutions. Solutions (called individuals) correspond to
points within the search space, a random set of which are generated, this seeds the
algorithm with an initial Population (set of individuals). They are represented by the
genomes (binary codes or reals, with a
fixed or variable size). All individuals are
 
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