Aşırı Öğrenme Makineleri ile biyolojik sinyallerin gizli kaynaklarına ayrıştırılması
Öz
Artan teknoloji, düşen maliyetler ve küçülen donanım boyutları nedeniyle işaret işleme yöntemleri birçok
alanda sıklıkla kullanılmaya başlanmıştır. Algılanan bazı sinyaller tek bir kaynaktan değil de birçok
kaynaktan oluşan sinyallerin karışımı olabilmektedir. Bu tip durumlarda işaret işleme teknikleriyle elde
edilebilecek başarı oranı düşüktür. Aynı zamanda sistemin içyapısının anlaşılması zordur. Bu tip
durumlarda gizli kaynak ayrıştırma işlemi ile ölçülen sinyaller gizli kaynaklarına ayrıştırılabilmektedir. Bu
amaçla yaygın olarak kullanılan temel kaynak ayrıştırma (PCA) ve bağımsız kaynak ayrıştırma (ICA)
istatiksel yöntemlerinde sinyallerin ayrıştırılabileceği gizli kaynak sayısı ölçülen sinyal sayısı ile sınırlıdır.
Bu sebeple karmaşık sinyallerde gizli kaynaklara ulaşmak bu yöntemlerle zordur.
Bu yöntemlere alternatif olarak yapay sinir ağları (YSA) da gizli kaynak ayrıştırma amacıyla başarıyla
kullanılmıştır. Bu çalışmada ise tek gizli katmanlı ileri beslemeli yapay sinir ağlarını eğitmek için kullanılan
aşırı öğrenme makineleri (ELM) yöntemi klasik YSA ile gizli kaynak ayrıştırma yöntemlerinden farklı bit
yaklaşım ile kullanılarak tek bir sinyal birden fazla birbirinden bağımsız gizli kaynağa ayrıştırılmıştır. Bu
amaçla EEG, EMG, ECG sinyalleri ile ivmeölçer, magnetometre ve jiroskop algılayıcılarından alınan zaman
sinyalleri gizli kaynaklarına ayrıştırılmıştır.
Önerilen metodun başarısını eğitim başarısını gösteren ortalama hataların karekökü (RMSE) ve gizli
kaynakların bağımsızlığını gösteren kovaryans kullanılmıştır. Test sinyallerinde 10-4
-64x10-4 aralığında
RMSE ve 0.2x10-4
-38.3x10-4 aralığında kovaryans değerleri elde edilmiştir. Elde edilen RMSE değerleri
YSA’nın başarılı olarak eğitildiğini, elde edilen kovaryans değerleri ise ayrıştırılmış sinyallerin birbirinden
bağımsız olduğunu göstermiştir. Ayrıca 2 adet epileptik ve 2 adet normal EEG sinyali 16 ayrı gizli kaynağa
kadar ayrıştırılmıştır. Dört örnekte de elde edilen başarı oranları önerilen metodun gizli kaynak
ayrıştırmada başarıyla kullanılabileceğini göstermiştir.
Anahtar Kelimeler
Blind Signal Separation by Extreme Learning Machines
Abstract
Improvements in the technology cause not only
decrease in the sensor costs but also, reduce the
dimensions of the sensors. Based on these facts the
importance of signal processing methods increases
day by day. But, in most applications sensors pick up
a collection or mixture of signals from many sources
instead of only one sensor. In this case, it is hard to
understand or manipulate the system. For example,
recorded EEG signals are mixtures of action
potentials of many neurons, therefore, the reasons or
mechanisms behind epilepsy are still since unknown.
For such situations, blind signal separation methods
have been employed. Generally, used blind signal
separation methods are principal component
analysis (PCA) and independent component analysis
(ICA) methods. Although many successful results of
PCA and ICA have been reported in the literature,
they suffer from a major drawback; the number of
sources that will be separated must be equal or less
than the number of sensors. Therefore, it is hard to
obtain the true sources of complex signals by these
methods. As an alternative, the method of delay was
proposed to separate a signal into two independent
sources, but its performance is highly dependent on
the delay value.
Addition to these methods, artificial neural network
(ANN) was also employed for the purpose of blind
signal separation. By ANN, better blind signal
separation results with compared to PCA and ICA
were reported in the literature. In this study, extreme
learning machine, which is a novel learning scheme
of single hidden layer feed-forward artificial neural
network, was employed. In ELM, the weights and
biases in the hidden layer are assigned arbitrary
and the weights in the output layer are calculated
analytically. Therefore, ELM showed faster training
stage and higher generalization capability with
compare to back-propagation trained ANN.
The proposed approach has three main
contributions, which are: (1) proposed approach
can be employed to separate a signal into a desired
number of sources without the limitation of PCA and
ICA, which is the number of sources that the signals
can be separated, must be equal to or less than the
observations, (2) unlike the classical ANN
approaches, in the proposed approach, an
orthogonal transfer function was used in the output
of each neuron in the hidden layer, and (3) the
proposed approach is extremely fast because of the
training scheme of ELM.
To evaluate and validate the proposed approach,
biological signals, which are the EEG, ECG, EMG,
accelerometer, gyroscope, and magnetometer
signals, were utilized. Achieved RMSE in the
training stage were in the range of 10-4
-64x10-4 and
the duration of training for different lengths of data
were in the range of 0.37-2.33 sec, for separating a
signal into 2 and 10 sources, respectively, while the
length of the dataset is 106
. Additionally, obtained
covariance of the separated signals were in the
range of 0.2x10-4
-38.3x10-4
.
Obtained RMSE values and fast training stage
showed that the proposed approach has high
accuracy in the separation of a signal and also it
has an extremely fast learning stage. These
advantages are because of the training scheme of
ELM. Moreover, obtained covariance values showed
that the separated signals are highly independent. In
order to investigate the reason of obtained low
covariance, a traditional transfer function was
employed and not only higher covariance but also
higher RMSEs were obtained. These results showed
that using orthogonal transfer functions (such as
sine and cosine, Bessel functions, etc.) after each
neuron in the hidden layer increases the dependency
of the separated signals. Furthermore, two normal
EEG and two epileptic EEG signals were separated
into 1-16 independent sources. Achieved results
showed that there is not any relation between the
numbers of separated sources with obtained the
independency of sources of sources and also
training accuracy.
As a summary, in this study a novel approach, which
is based on ELM, was proposed in order to separate
a signal into a desired number of independent
sources. Achieved results showed that the proposed
approach is fast and can successfully separate a
signal into independent sources.
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