necessary for a human expert to observe images of the
collected data.
Next, labeled training samples are randomly selected
and manually labeled with an index of the anomaly
pattern. These are denoted as (s
(p)
, l
(p)
), where s
(p)
is the
pth data piece, and l
(p)
is the corresponding anomaly
pattern index. Generally, a training ration of 1%–5%
is sufficient to cover all the representative data anomaly
patterns. In this article, a single-label classification
method is employed, that is, when an image shows mul-
tiple anomalous features, the label is determined by the
major intrinsic feature for all data in that image.
Construction and training of DNNs. The process of image
acquisition is different between human vision and com-
puter vision. In a three-dimensional (3D) space,
humans watch images in full view at once, whereas
computers ‘‘see’’ an image by scanning its pixel col-
umns serially. Hence, to show images to a computer,
the 1003100 image pixel array is transformed into an
1000031 image vector by sequentially stacking the
pixel columns.
To imitate the human decision-making process for a
deep understanding of the characteristics of anomalies,
the fast and effective stacked autoencoder DNN is
employed.
35
DNN is a type of artificial neural network
(ANN) with more than one hidden layer, which allows
them to learn high-level abstractions of the input. In
the late 1990s, DNNs were largely discarded by the
machine learning community because of their signifi-
cantly long training time. In 2006, a breakthrough was
achieved by introducing an unsupervised layer-wise
pre-training procedure, which made it possible to train
a deep architecture in a short time with unlabeled
data.
36
The stacking of pre-trained layers overcomes
the disappearing gradient of the weights tuning.
35,37
A two-hidden-layer stacked autoencoder neural net-
work is constructed to demonstrate the two-stage train-
ing procedure (Figure 2). Let s
(p)
denote the pth piece
of source data out of a total of P data pieces, f
s
denote
the sampling frequency, and T
d
denote the duration of
data in each plot. Therefore, the sample point number
of each s
(p)
is f
s
3T
d
. If the dimension of an image pixel
array is n3n, the dimension of the corresponding image
vector x
(p)
is n
2
31, as shown in Figure 3.
Generally, in a neural network, each unit has an acti-
vation value, defined as
a
(l + 1)
i
= f (z
(l + 1)
i
) ð1Þ
Figure 2. Construction of a two-hidden-layer neural network: in each autoencoder, the weights between the input layer and
hidden layer are extracted, and the node values of the hidden layer of each training sample are fed into the subsequent autoencoder
or softmax classifier.
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