Journal of Robotics, Networking and Artificial Life, Vol. 2, No. 4 (March 2016), 252-257

Medical Image Diagnosis of Lung Cancer by Deep Feedback GMDH-Type Neural Network

Tadashi Kondo†
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 Japan
Email: †kondomedsci@gmail.com
Junji Ueno
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 Japan
Shoichiro Takao
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 JapanAbstract
The deep feedback Group Method of Data Handling (GMDH)-type neural network is applied to the medical image
diagnosis of lung cancer. The deep feedback GMDH-type neural network can identified very complex nonlinear
systems using heuristic self-organization method which is a type of evolutionary computation. The deep neuralnetwork architectures are organized so as to minimize the prediction error criterion defined as Akaike’s Information
Criterion (AIC) or Prediction Sum of Squares (PSS). In this algorithm, the principal component-regression analysis
is used for the learning calculation of the neural network. It is shown that the deep feedback GMDH-type neuralnetwork algorithm is useful for the medical image diagnosis of lung cancer because deep neural networkarchitectures are automatically organized using only input and output data.
Keywords: Deep neural networks, GMDH, Medical image diagnosis, Evolutionary computation, lung cancer

1. Introduction
The deep GMDH-type neural network algorithms
were proposed in our early works1~4 and can
automatically organize the neural network architecturesusing heuristic self-organization method5,6 which is a
type of the evolutionary computation. In this study, deep
feedback GMDH-type neural network algorithm1 isapplied to the medical image diagnosis of lung cancer.
The learning calculations of the weights is the principal
component-regression analysis. In previous our work3,
we applied the logistic GMDH-type neural network to
the medical image diagnosis of lung cancer. First, thelung regions were recognized by the logistic GMDHtype neural network and these lung regions wereextracted and then the lung cancer regions wereextracted using the image post processing of theextracted lung regions. In another previous our work4,
we applied the hybrid feedback GMDH-type neuralnetwork to medical image diagnosis of liver cancer. The
liver cancer regions were recognized and extractedusing the same image processing using the hybrid
feedback GMDH-type neural network.
In this paper, we apply the deep feedback GMDHtype neural network and the lung cancer regions arerecognized directly using the deep feedback GMDHtype neural network and the lung cancer regions areextracted accurately. The recognition results shows thatthe deep feedback GMDH-type neural network canrecognize the lung cancer regions directly and extract
accurately.

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Tadashi Kondo, Junji Ueno. Shoichiro Takao

2. Deep feedback GMDH-type neural network1
The architecture of the deep feedback GMDH-type
neural network used in this paper has a feedback loop as
shown in Fig.1.
2.1 First loop calculation
First, all data are set to the training data. Then thearchitecture of the input layer is organized.
2.1.1 Input layer(1)
uj=xj (j=1,2,…,p)where xj (j=1,2,…,p) are the input variables of thesystem, and p is the number of input variables.
Σ fX1

Σf

X2X3.
.
.
XP

Σ f.
.
.

Σ f

Σ

φ.
.

Σf
Σ f
Σf

Fig.1 Architecture of the deep feedback GMDH-type neuralnetwork

2.1.2 Hidden layer
All combinations of the r input variables aregenerated. For each combination, three types of neuron
architectures which are the sigmoid function neuron, theredial basis function (RBF) neuron and the polynomial
neuron, are generated and L neurons which minimize
AIC7 and PSS8 value are selected for each type ofneuron architectures.
(1) Sigmoid function neural network
1) The first type neuron
Σ: (Nonlinear function)(2)
zk=w1ui+w2uj+w3uiuj+w4ui2+w5uj2 - w0θ1
f : (Nonlinear function)
1
yk =
(3)
1 + e( − z )2) The second type neuron
Σ: (Linear function)zk= w1u1+w2u2+w3u3+ ··· +wrur - w0θ1 ( r<p ) (4)kf : (Nonlinear function)yk =1
1 + e ( − zk )(2) Radial basis function neural network
1) The first type neuron
Σ: (Nonlinear function)zk=w1ui+w2uj+w3uiuj+w4ui2+w5uj2- w0θ1
f : (Nonlinear function)(5)(6)

2y k = e ( − zk )(7)2) The second type neuron
Σ: (Linear function)zk= w1u1+w2u2+w3u3+ ··· +wrur - w0θ1 ( r<p ) (8)f : (Nonlinear function)2(9)y k = e ( − zk )(3) Polynomial neural network
1) The first type neuron
Σ: (Nonlinear function)(10)
zk=w1ui+w2uj+w3uiuj+w4ui2+w5uj2 - w0θ1
f : (Linear function)(11)
yk= zk2) The second type neuron
Σ: (Linear function)zk= w1u1+w2u2+w3u3+ ··· +wrur - w0θ1 ( r<p) (12)f : (Linear function)(13)
yk= zkHere, θ1 =1 and wi (i=0,1,2,…,5) and wi (i=0,1,2,…,r)
are weights between the input and hidden layer. Weights
wi (i=0,1,2,…) in each neural network architecture are
estimated by the principal component-regression
analysis.
[Estimation procedure of weight wi ]First, values of zk** are calculated for each neuralnetwork architecture as follows.
a) Sigmoid function neural networkφ'(14)**)
zk = loge ('1−φb) RBF neural network**(15)
z k = − log e φ 'c) Polynomial neural network(16)
zk**=φwhere φ is an output variable and φ’ is the normalized
output variable whose values are between 0 and 1.

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Medical image diagnosis of[Principal component-regression analysis]
Multi-colinearity is generated in the function Σ ofthe neurons. In this study, the function Σ is calculatedusing the principal component-regression analysis.
In the case of Eq.(2), orthogonal vector v is calculated .
v=C⋅u(17)22Here, v=(v1,v2,…,v5) , u=(ui uj, uiuj, ui , uj )v is orthonormal vectors and C is orthonormal matrix. Cis calculated using the following eigenvalue equation.
R・C＝C・Λ
(18)
Here, R is a correlation matrix. Then, variable zk iscalculated using orthogonal regression analysis.
zk = wT⋅ v=w1v1+w2v2+…+w5v5(19)
Using the principal component-regression analysis,
variable zk in the function Σ is calculated without multicolinearity. In (19), useful orthogonal variables
νi(i=1,2,…,5) are selected by stepwise regression
analysis9 using AIC7 or PSS8 criterion.
L neurons having the smallest AIC or PSS values
are selected for three types of neuron architectures. Theoutput variables yk of L selected neurons for three typesof neuron architectures are set to the input variables of
the neurons in the output layer.
2.1.3 Output layer
For three types of neural network, the outputs yk of
the neurons in the hidden layer are combined by thefollowing linear function.
(20)
Here, L is the number of combinations of the inputvariables and yk is the intermediate variables. The
optimal intermediate variables yk are selected by
stepwise regression analysis9 using AIC7 or PSS8criterion. Eq. (20) is calculated for three types of neuralnetwork architectures. The neural network architecture
which has smallest AIC or PSS value is selected. Then,the estimated output values φ* which is selected in theoutput layer is used as the feedback value.
2.2 Second and subsequent loop calculationsFirst, the estimated output value φ* is combined with
the input variables x and all combinations between theestimated output value φ* and the input variables x aregenerated. The same calculation as the first feedback
loop is iterated. When AIC or PSS value of the linear
function in (20) is not decreased, the loop calculation is
terminated and the complete neural network architectureis organized by the L selected neurons in each feedbackloop.
3. Application to the medical image diagnosis oflung cancer
In this study, the lung cancer regions wereautomatically recognized using the deep feedback
GMDH-type neural network and these regions wereextracted. Multi-detector row CT (MDCT) images ofthe lung were used in this study.
3.1 Results of the medical image recognition by thedeep feedback GMDH-type neural network
The MDCT image shown in Fig.3 which wasextracted from the MDCT image in Fig.2, was used fororganizing the neural network. x and y coordinates andthe statistics of the image densities in the neighboring
regions of the N×N pixels at the positions of the learning
points are used as the input variables of the neuralnetwork. Only five input variables which are the mean,
the standard deviation, the variance and x and ycoordinates were automatically selected as useful input
variables. The output value of the neural network is zeroor one. When N×N pixel region is contained in the lungcancer and blood vessel regions, the neural network set
the pixel value at the center of the N×N pixel region to
one and this pixel is shown as the white point. The
neural networks were organized when the values of N
were from 3 to 10. It was determined that when N was
equal to 3, the neural network architecture had thesmallest recognition error. Five useful neurons wereselected in each hidden layer. Fig.4 shows the PSS
values of the three types of neurons in the second layer.
The RBF neural network architecture was selected by
the deep GMDH-type neural network algorithm. Fig.5
shows the variation of PSS values in each layer. PSS
values decreased gradually and very small PSS value
was obtained at the seventh feedback loop calculation.
The lung cancer and blood vessel regions wererecognized by using the organized neural network andPublished by Atlantis Press
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Tadashi Kondo, Junji Ueno. Shoichiro Takao

was extracted automatically. Fig.6 shows the output
image of the deep feedback GMDH-type neural network.
This output image was processed by the post-processing
analysis. In the post-processing, the small isolated
regions were eliminated and the outlines of the lungcancer regions were expanded outside by N/2 pixels.
Fig.7 shows the output image after this processing. Inorder to check the matching between the original image
and the output image of the neural network, the output
image was overlapped on the original image in Fig.3.
The overlapped image is shown in Fig.8. From Fig.8,
we can see that the output image was very accurate.
Fig.9 shows the extracted gray scale lung cancer image.
These image processing were carried out for all slices
by the organized deep feedback GMDH-type neuralnetwork and the 3-dimensional lung cancer image wasgenerated as shown in Fig.10.

Fig. 4 PSS values of three types of neurons

PSS

Number of feedback loops
Fig.2 Original image

Fig. 5 Variation of PSS value in each feedback loop

Fig. 6 Output image

Fig.3 Original image extracted from Fig.2

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Medical image diagnosis of

Fig.7 Output image after the post processing

Fig.10 The 3-dimensional image of lung cancer

3.2 Extraction by the conventional neural network
using sigmoid function.
A conventional neural network trained using theback propagation algorithm was applied to the same
recognition problem. The learning calculations of theweights were iterated changing structural parameterssuch as the number of neurons in the hidden layer andthe initial values of the weights. The output images,
when the numbers of neurons in the hidden layer (m) are5, 7 and 9, are shown in Fig.11. These images containmore regions which are not part of the lung cancer andblood vessel regions, and the outlines of the lung cancer
are not extracted with required clarity compared withthe output images obtained using the deep feedback
GMDH-type neural network algorithm, which areshown in Fig.6.

Fig. 8 Overlapped image

Fig. 9 Extracted gray scale image of lung cancer(a) m=5

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Tadashi Kondo, Junji Ueno. Shoichiro Takao

Acknowledgment
This work was supported by (JSPS) KAKENHI
26420421.
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In this paper, the deep feedback GMDH-type neuralnetwork algorithm was applied to the medical image
recognition of lung cancer regions and the results werecompared with those of the conventional sigmoid
function neural network trained using the backpropagation algorithm. It was shown that the deep
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