=Paper=
{{Paper
|id=None
|storemode=property
|title=Self-Advising SVM for Sleep Apnea Classification
|pdfUrl=https://ceur-ws.org/Vol-944/cihealth3.pdf
|volume=Vol-944
}}
==Self-Advising SVM for Sleep Apnea Classification==
https://ceur-ws.org/Vol-944/cihealth3.pdf
Self-Advising SVM for Sleep Apnea Classification
Yashar Maali1, Adel Al-Jumaily1 and Leon Laks2
1
University of Technology, Sydney (UTS)
Faculty of Engineering and IT, Sydney, Australia
Yashar.Maali@student.uts.edu.au, Adel.Al-Jumaily@uts.edu.au
2
Respiratory Physician, Concord Hospital
Sydney, Australia
leonlaks@bigpond.com
Abstract. In this paper Self-Advising SVM, a new proposed version of SVM,
is investigated for sleep apnea classification. Self-Advising SVM tries to trans-
fer more information from training phase to the test phase in compare to the
traditional SVM. In this paper Sleep apnea events are classified to central, ob-
structive or mixed, by using just three signals, airflow, abdominal and thoracic
movement, as inputs. Statistical tests show that self-advising SVM performs
better than traditional SVM in sleep apnea classification.
Keywords: Sleep apnea, Support vector machines, Particle swarm optimiza-
tion.
1 Introduction
Sleep disorders are common and sleep apnea (SA) is one of the most common and
critical types of sleep disorders. SA can be recognized by the repeated temporary ces-
sation of breathing during sleep [1]. More precisely, apnea is defined as the total or
near-total absence of airflow. This becomes significant once the reduction of the
breathing signal amplitude is at least around 75% with respect to the normal respiration
and occurs for a period of 10 seconds or longer[2]. A sleep apnea event can also be
classified into three groups as: central sleep apnea, obstructive sleep apnea, and mixed
sleep apnea. In case of the first, sleep apnea is originated by the central nervous sys-
tem. In the case of the second, the reason for the pauses in the breathing lie in a respira-
tory tract obstruction, while in the third case, both of these reasons may be present.
The manual scoring of sleep apnea is costly and time-consuming. Therefore, many
efforts have been made to develop systems that score the records automatically [11-
13]. For this reason several Artificial Intelligent (AI) algorithms are used in this area
such as fuzzy rule-based system [14], genetic SVM [15], and PSO-SVM [16] which
have been proposed in our previous works. Classification of apneic events to apnea or
hypopnea is also so important for severity calculation of the sleep disorder. The clas-
sification of apneic events is also considered in many studies, such as [17-19].
In this study an improved version of SVM, named self-advising SVM, is used to
classify sleep apnea to central, obstructive and mixed. The second section of this work
24
covers some preliminaries about SVM and partial swarm optimization. We introduce
the self-advising SVM algorithm in the third section of this paper; fourth section co-
vers proposed methodology for classifying sleep apnea be the self-advising SVM
which is followed by experimental results in section five, and the conclusion in sec-
tion six.
2 Preliminaries
2.1 Support vector machine
Support vector machine (SVM) is a machine learning method proposed by Vapnik
in 1995 [20]. The idea of SVM is to construct a maximized separating hyperplane. The
optimization criterion of SVM is the width of the margin between the classes, i.e., the
empty area around the decision boundary defined by the distance to the nearest training
patterns. SVM shows it ability for classification in many applications even with high
dimension. In addition, SVMs avoid over fitting by choosing a specific hyperplane
among the many that can separate the data in the feature space.
The brief math description can be shown as follows. For a binary classification,
from a training set of samples( ) ( ) ( ) * +, where
is the input vector corresponding to the sample and labeled by depending on
its class. SVM aim is, separating the binary labeled training data with a hyperplane
that has maximum distance from them, known as maximum margin hyperplane. Fig-
ure 1 shows the basic idea of the SVM graphically. The pair ( ) defines the hyper-
plane with equation . So, this hyperplane can linearly separate the
train data if
( ) ( )
Distance of each training data from the hyperplane is given by
( )
‖ ‖
combining inequality (1) and (2), for all result in
( )
‖ ‖
Therefore, ‖ ‖ is the lower bound on the distance between the training data and
the separating hyperplane.
The maximum margin hyperplane can be considered as the solution of the problem
of maximizing the ‖ ‖ subject to the constraint (1), or equivalently by solving the
following problem
( )
( )
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If we denote ( ) the nonnegative Lagrange multipliers associated
with the constraints (1), and without considering few steps the resulting decision func-
tion is given by [21],
( ) (∑ ) ( )
Note that the nonzero are those for which the constraints (1) are satisfied with
the equality sign. This has an important consequence. Since most of the are usually
zero the vector is a linear combination of a relatively small percentage of the train-
ing data . These points are termed support vectors because they are the closest
points from the separating hyperplane and the only points needed to determine the
hyperplane. The support vectors are the training patterns that lie on the margin
boundaries. An advantage of SVM is this fact that only small subset of the training
samples, support vectors, is finally retained for the classifier.
Support vectors
Margin
Fig.1. Basic ideas of support vector machines.
In order to use the SVM to produce nonlinear decision functions, the training data
is projected to a higher-dimensional inner product space , called feature space, using
a nonlinear map ( ) . In the feature space the optimal linear hyperplane
is computed. Nevertheless, by using kernels it is possible to make all the necessary
operations in the input space by using ( ) ( ) ( ) as ( ) is an
inner product in the feature space. The decision function can be written in terms of
these kernels as follows:
( ) (∑ ( ) ) ( )
There are 3 common kernel functions in SVM:
Polynomial kernel： ( ) ( )
| |
RBF kernel ： ( )
26
Sigmoid kernel： ( ) ( )
Here are kernel parameters.
2.2 Particle Swarm Optimization
Particle Swarm Optimization (PSO), was introduced by Kennedy and Eberhart in
1995 [22, 23] based on the movement of swarms and inspired by the social behaviors
of birds or fishes. Similar to the genetic algorithm, PSO is a population-based stochas-
tic optimization technique. In the PSO, each member is named particle, and each par-
ticle is a potential solution to the problem. In comparison with the genetic algorithms,
PSO updates the population of particles by considering their internal velocity and
position, which are obtained by the experience of all the particles.
In this study, we use the constriction coefficient PSO [24]. In this approach, the ve-
locity update equation is as (1),
( ) 0 ( ) . ( ) ( )/ .̂ ( ) ( )/1 ( )
where is the particle best and ̂ . And,
( )
√ ( )
with,
Equation (7) is used under the constraints that and , -
The parameter in the equation (8) controls the exploration and exploitation. For
, fast convergence is expected and for we can expect slow convergence with
a high degree of exploration [24].
The constriction approach has several advantages over traditional PSO model such
as; we do not need velocity clamping for constriction model and this model guaran-
tees convergence under the given constraints[25].
3 Self-Advising SVM
In current SVM methods, the only information that is used in the test phase from
the training is the hyperplane positions or SVs. Subsequent knowledge can be any
more information about the SVs, such as their distribution, and or the knowledge
extracted from the misclassified data in the training phase.
Self-advising SVM tries to generate subsequent knowledge from the misclassified
data of the training phase of the SVM. This misclassified data can come from 2 poten-
tial sources as outliers or as data that have not been linearly separated by using any
type of kernels. Classic SVM ignores the training data that has not been separated
linearly by kernels in the training phase. Self-advising SVM intended to deal with the
27
ignoring of the knowledge that can be extracted from the misclassified data. This can
be done by generating advice weights based on using of misclassified training data, if
possible, and use these weights together with decision values of the SVM in the test
phase. These weights help the algorithm to eliminate the outlier data.
To benefit from the misclassified data of the training phase, we must first find
them. Let’s define the misclassified data sets, MD, in the training phase as follows:
⋃ (∑ ( ) ) ( )
It must be considered that on the right hand side of the equation (9), we can use
any SVM decision function and kernel. The set can be null, but experimental
results revealed that the occurrence of misclassified data in training phase is common.
For each of MD the neighborhood length (NL) is defined as:
( ) ( | ) ( )
where are the training data.
Note: if the training data is mapped to a higher dimension by using a mapping
function, then the distance between and can be computed according to the fol-
lowing equation with reference to the related kernel ,
( ) ( ) ( ( ) ( ) ( )) ( )
Finally, based on finding of for each from the test set, the advised weight
(AW) is computed as follows,
| | ( )
{ ∑ ( )
| | ( )
∑ ( )
These AWs are between 0 and 1, and they represent how close the test data are to
the misclassified data. To conclude the above, the self-advising SVM (SA-SVM) is as
follows:
Training phase:
1- Finding the hyperplane by solving problem of equation (6) or related prob-
lem, it means normal SVM training.
2- Find the set using equation (9).
3- If the is null, go to the testing phase else compute for each member
of MD using equation (10).
Testing phase:
1- Compute the ( ) for each from the test set
28
2- Compute the absolute value of the SVM decision values for each from the
test set and scale the values to , -.
3- For each from the test set,
If ( ) ( ) then .∑ ( ) /
this means normal SVM labeling.
Else, ( ( ) )
Note: If the testing and training data are mapped to a higher dimension, then
in step 3 of the test phase should be computed by equation (11); further, as
mentioned previously, any SVM methods and kernels can be used in this algorithm.
4 Approach and Method
In this section, we present the proposed algorithm for the classification of the
sleep apnea events into central, obstructive or mixed. The proposed methodology is as
follows:
Feature generation: this stage generates several statistical features for each event
from the wavelet packet coefficients.
PSO-SVM classifier: In this stage PSO is used to select a best features subset inter-
actively with the SA SVM. PSO also is used for tuning the parameters of the SA
SVM. In the process, SA SVM is used as the fitness evaluator.
Final classification: the selected pattern is used for classification of the unseen
validation data in this stage. The accuracy of this step is assumed as the final per-
formance of the algorithm.
The details of these steps are as follows:
4.1 Feature generation
Feature extraction plays an important role in recognition systems, in this paper fea-
tures are generated from wavelet coefficients. In the first step, 3 levels "Haar" wavelet
packet applied on input signals, airflow, abdominal and thoracic movements. Then
several statistical measures are computed by attention to the coefficients related to
each apnea events, and considered as features of that event. These features represent
the inputs of proposed PSO-SVM algorithm in the next step. Full list of proposed
features are included in Table I.
29
Table I: List of statistical features, x is coefficients of wavelet.
( ( )) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( )
4.2 Particle representation
In this study, each particle consists of two arrays; the length of the first array is
equal to the number of features. Each cell can get a real number between 0 and 1 as
importance of the relevant feature. Features, which their corresponding cells have val-
ues higher than 0.5, are selected for classification. The second array is related to the
gamma and cost as parameters of the SVM, which can get a value between to .
5 Results and discussion
Experimental data consist of 20 samples which events of them are annotated by an
expert were provided by the Concord hospital in Sydney. We run the algorithm 5
different times; in each run 10 samples are chosen as the training, 5 samples as valida-
tion and 5 samples as the test set. RBF kernel is selected for the both of the Self-
advising and traditional SVM. In the constriction coefficient PSO structure, consid-
ered as 0.8 and and swarm contain 20 particles
Table 2 tabulates the number of central, obstructive and mixed events in each of
the validation set, train and test for these 5 runs.
Accuracy and also f-score of the self-advising and traditional SVM in classification
of these apnea events are as Table 3.
30
Table 2. Number of obstructive, central and mixed apnea in 5 different runs
Obstructive central Mixed
#1 931 375 312
#2 879 463 276
#3 913 478 227
#4 870 494 254
#5 894 453 271
Table 3. Accuracies and f-score of self-advising and traditional SVM in classifica-
tion of apnea events
SVM Self-Advising SVM
Accuracy f-score Accuracy f-score
#1 85.02 0.79 87.32 0.84
#2 86.31 0.83 86.81 0.84
#3 78.44 0.74 83.28 0.81
#4 77.45 0.79 79.95 0.80
#5 76.44 0.77 82.29 0.84
Total 80.732 0.784 83.93 0.826
The average accuracies for these two methods are as respective-
ly. Also, for more reliable evaluation between results of these two methods pair t-test
is used. The p value of t-test is as 0.028. These statistical tests show that the results
obtained by the self-advising SVM are significantly better than the results of tradi-
tional SVM.
Also, we consider the f-score as another performance measure to compare these
methods. Table 3, tabulated the f-scores for these two methods. The average f-score
for traditional SVM and self-advisable SVM are repectively. Also
paired t-test shows that self-advisable is significantly better than traditional SVM by
considering the f-score. The p value of t-test is as for the f-score is as 0.036.
6 Conclusion
In this study we proposed a new version of SVM named self-advising SVM for
classification of sleep apnea events into obstructive, central or mixed. This study
shows that self-advising SVM has advantage over traditional SVM in apnea classifi-
cation problem. More investigation of the proposed SVM algorithm in apnea detec-
tion or other classification problems must be study in future works.
31
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