Hindawi Publishing Corporation
Journal of Artificial Evolution and Applications
Volume 2009, Article ID 179680, 9 pages
doi:10.1155/2009/179680
Research Article
Evolutionary Selection of Features for
Neural Sleep/Wake Discrimination
Peter Du¨rr, Walter Karlen, Je´re´mie Guignard, Claudio Mattiussi, and Dario Floreano
Laboratory of Intelligent Systems, Ecole Polytechnique Fe´de´rale de Lausanne, 1015 Lausanne, Switzerland
Correspondence should be addressed to Peter Du¨rr, peter.duerr@epfl.ch
Received 15 November 2008; Accepted 19 February 2009
Recommended by Janet Clegg
In biomedical signal analysis, artificial neural networks are often used for pattern classification because of their capability for
nonlinear class separation and the possibility to efficiently implement them on a microcontroller. Typically, the network topology is
designed by hand, and a gradient-based search algorithm is used to find a set of suitable parameters for the given classification task.
In many cases, however, the choice of the network architecture is a critical and difficult task. For example, hand-designed networks
often require more computational resources than necessary because they rely on input features that provide no information or are
redundant. In the case of mobile applications, where computational resources and energy are limited, this is especially detrimental.
Neuroevolutionary methods which allow for the automatic synthesis of network topology and parameters offer a solution to these
problems. In this paper, we use analog genetic encoding (AGE) for the evolutionary synthesis of a neural classifier for a mobile
sleep/wake discrimination system. The comparison with a hand-designed classifier trained with back propagation shows that the
evolved neural classifiers display similar performance to the hand-designed networks, but using a greatly reduced set of inputs,
thus reducing computation time and improving the energy efficiency of the mobile system.
Copyright © 2009 Peter Du¨rr et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1. Introduction
The traditional way to craft an artificial neural network
(ANN) for a classification task is to hand design a network
topology and to find a set of network parameters using a
gradient-based error-minimization algorithm such as back
propagation [1]. However, in real-world applications, such as
the classification of biomedical signals, the network topology
can be difficult to design by hand. Additionally, in many
cases, it is desirable to minimize the computational cost
of the network, for example, by reducing the number of
inputs used by the classifier. Evolutionary methods for the
design of ANNs can provide an answer to both issues [2]. In
this paper, we study the application of a neuroevolutionary
method called analog genetic encoding (AGE) [3] to the
problem of synthesis and optimization of neural networks
for the processing of biological signals aimed at sleep and
wake classification.
Continuous monitoring of the sleep/wake state of high-
risk professionals such as pilots, truck drivers, or shift work-
ers can potentially decrease the risk of accidents and help
scheduling breaks and resting times. However, implementing
such a classification in a wearable device is a challenging
task. Limited energy and processing resources as well as
the increased noise level due to movement artifacts and a
constantly changing environment put tight restrictions on
the choice of sensors and algorithms. Traditionally, the states
of sleep and wake are classified based on the analysis of brain
wave patterns (EEG) [4]. EEG recording requires gluing
electrodes to the scalp and is typically susceptible to different
sources of noise. Methods relying on EEG measurements
are thus more suited for sleep analysis in controlled hospital
environments than for mobile applications.
For mobile sleep/wake pattern screening, a commonly
used technique is actigraphy [5]. In actigraphy, the accel-
eration of the wrist of the subject is recorded, and phases
of weak activity—as judged by the levels of acceleration—
are classified as sleep. Actigraphy devices can be small,
inexpensive, and low power, which makes them suitable for
mobile applications. However, as the signals provided by
actigraphy devices are not directly linked to physiological
states, it is difficult to derive a reliable prediction from

2 Journal of Artificial Evolution and Applications
them. Activities characterized by low levels of motion, such
as reading or watching TV, are often misclassified as sleep
[6]. In [7, 8], we have suggested to use electrocardiogram
(ECG) and respiratory effort (RSP) signals for wearable
sleep/wake classification (see Figure 1). Both signals depend
on properties of the activity of the autonomous nervous
system, which differ in sleep and wake [9]. Furthermore,
they are measurable with portable sensor systems such as the
Heally system (see Figure 2, Koralewski Industrie Elektronik,
Celle, Germany).
An additional difficulty is that the generation of a set of
labeled data for the training of the classifier is typically a
time-consuming activity for both the subjects from whom
data is collected and the technicians who must label the data
[7]. It is thus desirable to design a classifier that can be
trained on a set of data and can then be used on further
subjects without additional training. In [7], we have shown
that using the frequency content of the ECG and RSP
signals as input features for a single layer ANN, a mean
accuracy of 86.7% can be achieved when the network was
trained and tested on data obtained from different subjects.
A limitation of the hand-designed ANN used in [7] is its
large number of inputs. Some of these inputs are presumably
redundant and might not contribute significantly to the
classifier performance. For the targeted mobile application,
the power consumption of the classifier is critical. In order
to reduce processing time and thus power consumption
for mobile applications, it would be desirable to minimize
the number of inputs. In this paper, we show how to
automatically synthesize networks that use a small subset of
the spectral components associated with the signals as inputs
while maintaining the performance of the classifier.
2. Evolutionary Synthesis of Neural Networks
Neural networks can be described as directed graphs, where
the nodes represent a neuron model, and the edges of the
graph are associated with the weighted connections between
the neurons, the so-called synaptic weights. The design of
a network for a particular task thus involves the choice of
the topology of the graph (i.e., the network architecture)
and a suitable set of numerical parameters (i.e., the synaptic
weights and the parameters of the neuron model). The
automatic synthesis of the topology and parameters of a
neural network requires a computer representation for both
aspects of the network, combined with an algorithm capable
of performing a search in the space defined by this rep-
resentation. Evolutionary algorithms have been extensively
used to evolve neural classifiers because these algorithms can
combine a flexible representation with a high potential of
stochastic exploration of the search space [10–13].
The simplest approach to this, the so-called direct
encoding, represents all the neurons, synaptic connections,
and parameters of the network explicitly (see, e.g. [14–16]).
This has the advantage that the resulting networks can easily
be decoded from the genome. However, with increasing size
of the network, the length of the corresponding genome
grows rapidly, which can affect the evolvability. In order to
mitigate this problem, it has been suggested to encode a
program or a sequence of instructions that, when executed,
builds the network. This developmental encoding can lead
to very compact representations of large networks (see, e.g.,
[17, 18]). However, the definition of a set of mutation and
recombination operators which guarantees that only valid
networks are generated during the search is typically very
difficult.
A promising alternative to direct and developmental
representations that is getting more and more popular is
implicit encoding [19–23]. In this paper, we use an implicit
representation called analog genetic encoding (AGE). AGE
has been shown to be very effective for the automatic
synthesis of various kinds of networks and, in particular, of
neural networks [2, 3, 24–26].
The concept of implicit encodings like AGE is loosely
inspired by the working of biological gene regulatory net-
works (GRNs). In biological GRNs, the interactions between
the genes are not explicitly encoded in the genome but follow
implicitly from the physical and chemical environment
in which the genome is immersed. Simplifying a bit the
picture, the activation of a biological gene depends on
the interaction of molecules produced by another gene
with parts of the activated gene called regulatory regions
(Figure 3(a)). AGE abstracts this picture and defines an
artificial genome composed of sequences of characters, for
example, the uppercase ASCII set (Figure 3(b)). Similar to
the function of promoter and terminal regions in GRNs,
special sequences (the so-called tokens) identify regions
of the artificial genome as artificial genes, which encode
individual neurons. The sequences delimited by the tokens
are interpreted analogous to coding regions and regulatory
regions in biological GRNs. The strength of the connection
between two neurons is implicitly determined by the coding
region of one neuron and the regulatory region of another
neuron via a function called interaction map. The interaction
map can be seen as an abstraction of the biochemical
process of gene regulation. It takes sequences of characters
as arguments and outputs a real-valued connection strength.
In our implementation, this is obtained by mapping the local
alignment score [27] of the two sequences exponentially to
the interval that spans all possible weight values (see [24]).
In summary, the AGE genome can be decoded first
by extracting the neurons with the associated (coding and
regulatory) sequences of characters. This is realized by
scanning the genome for tokens which indicate the presence
of a neuron (GN). Together with predefined terminator
sequences (TE), these tokens delimit the part of the
genome associated with the respective neuron. The enclosed
sequences of characters are interpreted as the coding and
regulatory sequences of the respective neuron. Subsequently,
the interaction map I can be applied to all pairs of coding
and regulatory sequences to obtain the synaptic weights wij
connecting the neurons (see Figure 4).
In this framework, there are several different possibilities
to implement connections from external inputs to external
outputs (see [28] for more details). Here, we encoded the
coding sequences associated to the input neurons and the
regulatory sequences associated to the output neurons in

Journal of Artificial Evolution and Applications 3
2
4
6
8
10
2
4
6
8
−4 0 4
−1
0
1
Wake Sleep Wake
Raw signalsA FFT pre-processing ANN classifierC
OutputD
B
E
C
G
fr
eq
ue
n
cy
(
H
z)
R
SP
fr
eq
ue
n
cy
(
H
z)
−120 −100 −80 −60 −40 −20 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Experiment duration (hours)
−1.49
−1.47
R
SP
(
m
V
)
−0.4
0
0.4
E
C
G
(
m
V
)
0 2 4 6 8 10
(Seconds)
log(̂S(ω))
log(̂S(ω))
∑
Threshold
Wake: y(x) < 0
Sleep: y(x) ≥ 0
wECG
wResp
Figure 1: Overview of the sleep/wake classification system. (a) The raw electrocardiogram (ECG) and respiratory effort (RSP) signals are cut
into windows of 40.06 seconds. (b) A short-time fast Fourier transformation (FFT) is used to calculate the spectral power of the windowed
signals. (c) The resulting frequency data are fed to a feed-forward artificial neural network (ANN) and (d) a symmetric threshold classifies
the ANN output into sleep or wake state estimates.
1
4
2
3
Figure 2: Portable Heally recording system mounted on a shirt.
(1) ECG gel electrodes; (2) inductive belt sensor; (3) electronics
modules; (4) NiMH battery.
separated parts of the genome (see Figure 5). In this case,
the connections from the input neurons to the network can
be obtained by applying the interaction map to all pairs of
coding sequences (associated with the input neurons and
the hidden neurons) and regulatory regions (associated to
the hidden neurons and the output neuron). Note that
the interaction map can associate a null weight value, thus
leaving the respective neurons unconnected. When this
feature is applied to the connections stemming from the
input neurons, it gives evolution the freedom to select a
subset of the set of inputs that contains the information
necessary to realize the classification task.
As the sequences which define the strength of the synaptic
connections can have a variable length and the interaction
map is defined to operate on sequences of arbitrary length,
a large class of genetic operators can be used to alter the
network. In particular, we use the biologically plausible
insertion, substitution, and deletion of characters and the
transposition, duplication, and deletion of fragments of
genome. The changes in the genome caused by these muta-
tion operators can reflect both changes in the parameters of
the network as well as changes in the network structure. For
example, the insertion of a character in the genome can lead
to a change of the synaptic weight connecting a particular
input to the output neuron. The deletion of a fragment of
genome associated with an input of the network can lead
to the removal of this particular input from the network.
Furthermore, the number of hidden neurons in the network
can increase (e.g., after a genome fragment duplication) or
decrease (e.g., after a character substitution) over the course
of evolution. Given the fact that parts of the genome can
be noncoding (i.e., they are not part of the description of a
neuron) and that the interaction map is defined to be highly
redundant, many mutations do not have an effect on the
decoded networks. This allows for a high neutrality in the
search space, which can improve evolvability [29].
3. Experiments
To compare the performance of the classical approach to
classifier synthesis and training with the state-of-the-art
neuroevolution method based on AGE, we performed a set
of experiments, where we compared the performance of
a neural network with fixed hand-designed topology and
variable weights trained with back propagation, with that of
neural networks synthesized with an evolutionary algorithm-
based on AGE. As anticipated, we are interested in the
performance in a sleep/wake detection task, where data from
a set of users is available for network synthesis and training,
but the performance is expected to generalize to additional
users. We thus investigated the performance of the two
methods when trained on ECG and RSP data collected on
multiple subjects, and tested on data from a different subject.
3.1. Data. The data used in the following experiments are
identical with those described in [8], where a hand-designed
classifier with back propagation was used. They stem from

4 Journal of Artificial Evolution and Applications
· · ·
DNA
Promoter Coding region Terminator Regulatory region Non-coding
· · ·
Transcription
mRNA
Translation Protein
Binding
Regulation
+/−
RNAP
(a) Transcriptional regulation
XOVJWPGNBMJHDBTEOODFODDPWXXTEKCMRSIZZKJUWPOXCGNJJYXXVISTEVUBYCPTESSOOXI
JJYXXVISOODFODDPWXX ,
· · ·
AGE
genome
Coding region Scod Non-coding Regulatory region Sreg Non-coding
· · ·
Tokens
Iw
( )
Arbitrary character sequences
(b) The AGE abstraction
Figure 3: (a) In biological gene networks, the link between genes is realized by molecules that are synthesized from the coding region of
one gene and interact with the regulatory region of another gene. (b) Analog genetic encoding abstracts this mechanism using an artificial
genome containing markers that identify the artificial genes, and an interaction map that creates links between pairs of artificial genes by
associating with them a numerical value that represents the strength of the link.
XOVJWPGNBMJHDBTEOODFODDPWXXTEKCMRSIZZKJUWPOXCGNJJYXXVISTEVUBYCPTESSOOXI
JJYXXVIS
JJYXXVIS
OODFODDPWXX
BMJHDB
BMJHDB
OODFODDPWXX
VUBYCP
VUBYCP
,
,
,
,
· · · · · ·
Decoding
1 2w11 w22
w12
w21
w12 = I
( )
w22 = I
( )
w11 = I
( )
w21 = I
( )
Figure 4: A simple artificial neural network represented with analog genetic encoding. The interaction strengths wij are computed by the
interaction map I(si, s j) which takes the sequence of characters si associated to the output of neuron i and the sequence of characters s j
associated to the input of neuron j as inputs.
recording sessions with six young healthy male subjects of a
mean(± SD) age of 26(± 3) years. The subjects wore a Heally
recording device (see Figure 2) for a total of 18 recording
sessions which lasted 16 hours each and contained an
overnight sleep. The datasets are composed of ECG and RSP
recordings sampled at 100 Hz and 50 Hz, respectively. The a
priori sleep and wake states of the subjects were determined
by a trained technician who labeled the signals in 10-second
intervals based on electromyogram, electrooculogram, and
video recordings. The data were preprocessed and fed to
the ANN. As in [7], the preprocessing step consisted of
calculating the power spectrum of each signal using a short-
time fast Fourier transform with a window length of 40.96
seconds (see Figure 1(b)). For each of these segments, we
calculated a feature vector as v = log(̂S(ω)), where ̂S(ω) is
the periodogram of the segment. Experiments described in
[8] revealed that frequency components above 10 Hz for ECG
and 8 Hz for RSP do not contribute to the hand-designed
classifier performance and can be removed. The resulting
two input vectors are thus composed of 409 spectral inputs

Journal of Artificial Evolution and Applications 5
AAGSTURYNIO AIZRUG
OODFODDPWXX
OODFODDPWXX
AIZRUG
BIUNSTEWQOAPPNNET
BIUNSTEWQOAPPNNET
BIUNSTEWQOAPPNNET
AIZRUG
AIZRUG
AAGSTURYNIO
AAGSTURYNIO
BMJHDB
BMJHDB
BMJHDB
XOVJWPGNBMJHDBTEOODFODDPWXXTEKCMRSIZZKJUWPOXC
,
, ,
,
,
,
A B C
...
· · · · · ·
w(1,N + 1) = I
w(1, 1) = I w(M + 1,N + 1) = I
w(M + 1, 1) = I
w(M, 1) = I
w(M,N + 1) = I
Figure 5: There are different ways to implement external inputs and outputs in AGE [28]. Here, the genome is split in three parts: (a)
contains the coding sequences of the M input neurons, (b) contains the definition of the N hidden neurons, and (c) contains the regulatory
sequence of the output neuron. In the decoding process, the coding sequences and the regulatory sequences of all neurons present in the
genome are identified. The connection weights w(x, y) can then be obtained by applying the interaction map to all pairs of coding sequences
x and regulatory sequences y.
MU 561 (6)
N
um
be
r
of
re
co
rd
in
g
se
ss
io
n
s
0
2
4
6
8
10
TR VA TE
Subject
A
B
C
D
E
F
Figure 6: Distribution of the experimental data used for the train-
ing, validation, and test of the hand-designed and the evolutionary
synthesized neural classifiers. The numbers indicate users in the
training set (TR), users in the validation set (VA), and users in the
test set (TE). There are six repetitions with different combinations
of users/sessions in training, validation, and test sets.
from ECG and 327 spectral inputs from RSP. Together, they
compose the set of 736 inputs that were fed to the ANN
classifier (see Figure 1(c)).
3.2. Experimental Design. In order to evaluate the perfor-
mance of the two classifiers, we divided the data into three
different sets: a training set (TR), a validation set (VA), and a
test set (TE) (see Figure 6). The training set contains a subset
Evolved network
Output neuron
ECG inputs RSP inputs Bias
Figure 7: The neural classifier is automatically synthesized with
analog genetic encoding. The evolved network can connect to an
arbitrary subset of the 409 inputs from the ECG data, the 327 inputs
from the RSP data and a bias unit. As the size of the network is
not fixed, the number of hidden units in the network can increase
or decrease over the course of evolution. The output unit indicates
sleep or wake states using a simple threshold at an activation level
of zero.
of the data from five of the six subjects. The validation set
is composed of 2 hours of data from each subject, randomly
sampled over the two available sessions and containing an
equal amount of samples labeled as sleep and wake. This data
is not used for training or for testing. The test set contains
data from the subject that has not been used in the training.
Five independent runs of each experiment are performed
from different randomly assigned initial conditions. In order
to prevent performance biases due to the choice of sessions,
we repeat each experiment with all possible combinations
of users in the test and trainingsets, making sure that the
same sessions do not appear both in the training and in the

6 Journal of Artificial Evolution and Applications
C
la
ss
ifi
ca
ti
on
ac
cu
ra
cy
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
0.9
0.92
AGE
+
Fixed topology
Figure 8: The average classification accuracy of the evolved
networks (AGE) and the fixed topology networks trained with
back propagation (fixed topology). The midline in each box is the
median, the borders of the box represent the upper and the lower
quartiles. The whiskers outside the box represent the minimum and
maximum values obtained, except when there are outliers which
are shown as small crosses. We define outliers as data points which
differ more than 1.5 times the interquartile range from the border
of the box. The notches permit the assessment of the significance
of the differences of the medians. When the notches of two boxes
overlap, the corresponding medians are not significantly different
at (approximately) the 95% confidence level [34].
Fr
eq
ue
n
cy
0
1
2
3
4
5
6
7
8
Number of input features used
0 100 200 300 400 500 600 700
Figure 9: Histogram of the number of input features used by the
evolved networks in the five repetitions of each of the six training
cases. From the 30 networks, 8 used from 3 to 45 inputs, 2 used from
95 to 113 inputs, 3 used from 162 to 196 inputs, 4 used from 231 to
282 inputs, 1 used 411 and 1 used 484 inputs, 2 networks used from
522 to 533 inputs, 6 networks used from 602 to 647 inputs, and 3
networks used from 628 to 732 inputs.
testsets. This leads to a total of six different cases with five
independent replications for each case.
3.3. Algorithms
3.3.1. Hand-Designed Fixed Topology Network. As a baseline
for the classification accuracy, we used a feed-forward ANN
with no hidden layers and a single output unit with a
tangent-sigmoid transfer function. Additional experiments
not reported here showed that the use of ANNs with a hidden
layer does not improve the performance of the classifier.
A similar finding has been reported by [30]. The synaptic
weights of this fixed topology network were initialized
with the Nguyen-Widrow method [31] and trained with a
Levenberg-Marquardt back-propagation algorithm [32].
3.3.2. Network Synthesized with AGE. For the automatic
synthesis of the network topology and parameters, the
AGE representation was combined with a standard genetic
algorithm (see [24] for more details). Using the above-
mentioned possibility of feature selection, the evolved
network could connect to an arbitrary subset of the 409
inputs from the ECG data, the 327 inputs from the RSP
data, and a constant bias unit (see Figure 7). Additionally,
the evolutionary process might insert hidden neurons in
the network in order to generate more complex network
structures. The activation yi of the hidden neuron i was
computed as
yi = σi
( N
∑
k=1
w(i, k)yk +
M
∑
l=1
w(i,N + l)Il + w(i,N + M + 1)
)
,
(1)
where N is the number of hidden neurons in the network,
w(x, y) = wxy are the entries of the weight matrix, M = 736
is the number of available inputs, Il is the value of input l,
and
σi(z) = 21 + e−αiz − 1, (2)
is a sigmoid transfer function with slope parameter αi. The
activation of the output neuron was computed analogously
to the activation of the hidden neurons. The slope parameters
αi for the hidden neurons were encoded using the center of
mass encoding [33].
Selection was performed using tournament selection and
elitism. The algorithm parameters and mutation probabil-
ities are listed in Table 1. In order to prevent bootstrap
problems, the population was initialized with the best 100
networks out of 1000 randomly created genomes. Addition-
ally, to save computation time, only a randomly selected
subset of 10% of each training set was used for training.
However, validation and testingwere always performed using
100% of the respective dataset. For each evolutionary run,
the synthesized network was the network with the best
performance on the validation set, in the collection of all
the best performing networks observed at each of the 1000
generations that compose a run.
For both the back-propagation training and the evolu-
tionary process, the measure of quality of the classifier was
the sum over the data points of the squares of the difference
between the actual and the desired classifier output.
4. Results and Discussion
As shown in Figure 8, the evolved networks and the
fixed topology networks trained with back propagation do
not display a significantly different classification accuracy
(Wilcoxon rank sum test P = .48). However, while the
hand-designed fixed topology networksemploy all of the
736 input features, many of the evolved networks used a

Journal of Artificial Evolution and Applications 7
Table 1: The parameters used in the evolutionary algorithm.
Parameter Value
Population size 100
Tournament size 2
Elite size 1
Recombination probability .1
Probability of character substitution (per character) .001
Probability of character insertion (per character) .001
Probability of character deletion (per character) .0015
Probability of fragment transposition .01
Probability of fragment duplication .01
Probability of fragment deletion .015
Probability of neuron insertion .01
C
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0.65
0.7
0.75
0.8
0.85
0.9
0.95
Number of input features used
0 100 200 300 400 500 600 700
Figure 10: The performance of the evolved networks in the five
repetitions of each of the six training cases. The horizontal axis
represents the number of input features used by the network and
the vertical axis gives the corresponding classification performance.
The symbols indicate the number neurons in the hidden layer of
the network. A cross indicates 0 hidden neurons, a circle indicates 1
hidden neuron, a star indicates 2 hidden neurons. Both the number
of inputs and the number of hidden neurons are not significantly
correlated with classification accuracy (see text).
drastically reduced set of inputs (see Figure 9, the median of
the number of inputs used is 244.5). Figure 10 shows that
there is no correlation between the number of inputs used
by the evolved networks and their performance (Spearman’s
rank correlation coefficient P = .02, P = .94). This
indicates that many input features are indeed redundant
and that it is possible to synthesize networks with a very
small number of inputs which perform as well as the hand-
designed network using all inputs. However, all networks use
input features from both ECG and RSP data (see Figure 11).
Given the results of [7], it is not surprising that the presence
of both types of data is beneficial for the classification
accuracy and thus selected during evolution. Note that in
the evolutionary experiments, no additional penalty term
was added to the objective function to bias the search
toward small networks. This explains the presence of both
networks using a significantly reduced set of inputs, and
networks using almost the whole set of available inputs in
the evolutionary results.
N
um
be
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of
in
pu
tf
ea
tu
re
s
us
ed
0
100
200
300
400
500
600
700
Evolved networks
ECG
RSP
Figure 11: The evolved networks for the five repetitions of each
of the six cases, sorted by the number of used input features. All
networks use input features from both ECG and RSP data.
As mentioned above, the fixed topology network has
no hidden layer. Of the 30 evolved networks, 19 feature
no hidden neurons, 7 feature one hidden neuron, and 4
feature two hidden neurons. However, there is no correlation
between the number of hidden neurons and the classification
accuracy (Spearman’s rank correlation coefficient P = −.06,
P = .74). This substantiates the conjecture formulated in [7]
that a hidden layer is not necessary for optimal performance
in this task. Note, however, that this conjecture applies to this
specific problem and does not extend to general classification
applications.
5. Conclusion
Portable devices for biomedical signal analysis, like
sleep/wake classification, have the potential to alleviate
health problems and prevent accidents. Recent advances
in sensor development and miniaturization allow for
the construction of small mobile devices which integrate
biomedical sensors and a microprocessor with sufficient
processing power for many applications. However, one of
the critical challenges, that remains, is the design of efficient
classifiers which can be implemented on these small mobile
systems. While the classification accuracy has to be as high
as possible, the computational effort and thus the energy
requirements for classification have to remain low. The
results presented in this paper demonstrate that analog
genetic encoding (AGE) permits the automatic evolutionary
synthesis of compact neural classifiers for the problem of
sleep/wake classification. Compared to a hand-designed
classifier trained with back propagation, the possibility of
the evolutionary selection of a subset of the available inputs
permits a drastic reduction of the number of inputs without
significant degradation of the classifier performance. For
example, in the experiments presented here, the evolutionary
synthesis with AGE found a classifier with the accuracy of
88.49%, using only 15 of the 736 input features used by
the hand-designed network. The implementation of this

8 Journal of Artificial Evolution and Applications
evolved solution on a digital signal controller of the dsPIC33
product family (Microchip Technology Inc., USA) requires
only 5.13% of the instructions used by an implementation
of the hand-designed network on the same processor. This
is a reduction of the computational cost of almost 95%.
Moreover, the savings in computational cost and energy can
be increased even further by adapting the sensory modalities
and preprocessing steps to the reduced set of input features.
Acknowledgments
This work was supported by the Swiss National Science
Foundation, Grant no. 200021-112060 and the Solar Impulse
Project grant of Ecole Polytechnique Fe´de´rale de Lausanne
(EPFL). Thanks to Daniel Marbach and Sara Mitri for their
comments on an earlier version of this manuscript and the
anonymous reviewers for their helpful suggestions.
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