Journal of Robotics, Networking and Artificial Life, Vol. 2, No. 2 (September 2015), 94-99

Deep Feedback GMDH-Type Neural Network Using Principal Component-Regression
Analysis and Its Application to Medical Image Recognition of Abdominal Multi-Organs

Tadashi Kondo†
Graduate School of Health Sciences, Tokushima University
3-18-15 Kuramoto-cho Tokushima 770-8509 Japan
Email: †kondo@medsci.tokushima-u.ac.jp
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 proposed and applied to themedical image recognition of abdominal organs such as the liver and spleen. In this algorithm, the principal
component-regression analysis is used for the learning calculation of the neural network, and the accurate andstable predicted values are obtained. The neural network architecture is automatically organized so as to fit thecomplexity of the medical images using the prediction error criterion defined as Akaike’s Information Criterion(AIC) or Prediction Sum of Squares (PSS). The recognition results show that the deep feedback GMDH-type neuralnetwork algorithm is useful for the medical image recognition of abdominal organs.
Keywords: Deep neural networks, GMDH, Medical image recognition, Evolutionary computation

1. Introduction
The deep GMDH-type neural network algorithms
were proposed in our early works1 and can
automatically organize the neural network architecturesby using heuristic self-organization method2 which is a
type of the evolutionary computation. In this study, deepfeedback GMDH-type neural network algorithm isapplied to the medical image recognition of theabdominal organs such as the liver and spleen. The
learning calculations of the weights is the principal
component-regression analysis and the accurate andstable predicted values are obtained. The deep feedback
GMDH-type neural network algorithm is applied to the
medical image recognition of the abdominal organs andthe recognition results are compared with those obtainedusing the conventional neural networks trained using theback propagation algorithm.

2. Deep feedback GMDH-type neural network
The architecture of the deep feedback GMDH-type
neural network developed 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.

Published by Atlantis Press
Copyright: the authors94Σ fx1

Σf

x2x3.
.
.

xP

Σ f.
.
.

Σ fΣ

φ.
.

Σf
Σ fΣf

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
AIC3 or PSS4 value, are selected for each type of neuron
architectures.
(1) Sigmoid function neural network
1) The first type neuron
Σ: (Nonlinear function)(2)
zk=w1ui +w2uj+w3ui uj+w4ui2+w5uj2 - w0θ1f : (Nonlinear function)
1yk =
(3)
1 + e( − z )2) The second type neuron
Σ: (Linear function)zk= w1u1+w2u2+w3u3+ ··· +wrur - w0θ1 ( r<p ) (4)f : (Nonlinear function)
1
yk =
(5)
1 + e( − z )(2) Radial basis function neural network
1) The first type neuron
Σ: (Nonlinear function)(6)
zk=w1ui +w2uj+w3ui uj+w4ui2+w5uj2- w0θ1
f : (Nonlinear function)2(7)
y k = e ( − zk )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 networkkk1) The first type neuron
Σ: (Nonlinear function)(10)
zk=w1ui +w2uj+w3ui uj+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− φ'b) 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.
[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)
Here, v=(v1,v2,…,v5) , u=(ui, uj, uiuj, ui2, uj2)
v is orthonormal vectors and C is orthonormal matrix. C
is 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 multi-

Published by Atlantis Press
Copyright: the authors95

colinearity. In (19), useful orthogonal variables
νi (i=1,2,…,5) are selected using AIC3 or PSS4 criterion.
L neurons having the smallest AIC or PSS values
are selected for three types of neuron architectures. The
output 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 input
variables and yk is the intermediate variables. Eq. (20) is
calculated for three types of neural networkarchitectures. The neural network architecture which
has smallest AIC or PSS value is selected. Then, theestimated output values φ* which is calculated 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.

neural networks were organized when the values of N
were from 3 to 10. When N was equal to 6, the neuralnetwork architecture had the smallest recognition error.
Fig.3 shows PSS values in the first feedback loop. PSS
value of the sigmoid neuron was smallest in the three
types of neurons. Fig.4 shows the variation of PSS value
in each layer. The PSS values were decreased gradually
through the feedback loops and small PSS value wasobtained in the fifth feedback loop. The deep feedback
GMDH-type neural network output the liver image(Fig.5) and the first post-processing analysis of theoutput liver image was carried out. Fig.6 shows theoutput image after the first post-processing. The output
image after the first post-processing was overlapped tothe original image (Fig.2) as shown in Fig.7. The
recognized liver region are very accurate. The liver
region was extracted from the original image as shownin Fig.8. A conventional neural network trained using
the back propagation algorithm was applied to the same
recognition problem. The output images, when thenumbers of neurons in the hidden layer (m) are 5, 7 and
9, are shown in Fig.9. These images contain moreregions which are not part of the liver.

3. Application to the medical image recognitionof abdominal multi-organs
In this study, the regions of the liver and spleen in
the abdominal regions were recognized and extracted
automatically. Multi-detector row CT (MDCT) imagesof the abdominal regions are used in this study.
3.1 Extraction of the liver regions
An abdominal MDCT image shown in Fig.2 wasused for organizing the deep feedback GMDH-typeneural network. The statistics of the image densities andx and y coordinates in the neighboring regions, the N×N
pixel regions, were used as the image features. The

Published by Atlantis Press
Copyright: the authors
96

Fig. 2 Original image

87PSS
6°°°
Fig. 6 Output image after the first post processing

50Polynomial RBF Sigmoid
Fig. 3 PSS values of three types of neurons (1)Fig.7 Overlapped image (1)Fig. 4Variation of PSS (1)Fig.8 Extracted image (1)(a)m=5Fig. 5 Output image(1)Published by Atlantis Press
Copyright: the authors
97

54PSS°°°3(b) m=720

Polynomial RBF SigmoidFig. 10 PSS values of three types of neurons (2)(c)m=9Fig.9 Output images of the conventional neural network (1)3.2 Extraction of the spleen regions
The deep feedback GMDH-type neural network wasapplied to the recognition of the spleen region using thesame MDCT image shown in Fig.2. Fig.10 shows thePSS values of three type neurons. The RBF neuralnetwork architecture was selected. Fig.11 shows thevariation of PSS values. Small PSS value was obtainedin the ninth feedback loop. The deep feedback GMDHtype neural network output the spleen image as shownin Fig.12. The output image after the second postprocessing was overlapped as shown in Fig.13. The
recognized spleen region was very accurate. The spleen
region was extracted from the original image as shownin Fig.14. A conventional neural network trained using
the back propagation algorithm was applied and theoutput images, when the numbers of neurons in thehidden layer (m) are 5, 7 and 9, are shown in Fig.15.

Fig. 11 Variation of PSS (2)

Fig.12 Output image (2)Published by Atlantis Press
Copyright: the authors
98Fig.13 Overlapped image (2)(c) m=9
Fig.15 Output images of the conventional neural network (2)4. Conclusions

Fig.14 Extracted image (2)In this paper, the deep feedback GMDH-type neuralnetwork algorithm using principal componentregression analysis was applied to the medical image
recognition of the abdominal multi-organs, and theseresults were compared with those of the conventionalsigmoid function neural network trained using the backpropagation algorithm.
Acknowledgment
This work was supported by (JSPS) KAKENHI
15K06145.
References
1. T. Kondo, J. Ueno and S. Takao, Medical image diagnosisof liver cancer by hybrid feedback GMDH-type neuralnetwork using principal component-regression analysis,
Proceedings of the nineteenth international symposium on(a)m=5artificial life and robotics (2014) pp.339-342.
2.

S. J. Farlow ed., Self-organizing methods in modeling,
GMDH-type algorithm, New York: Marcel Dekker Inc.,(1984).

3.

H. Akaike, A new look at the statistical model
identification, IEEE Trans. Automatic Control, AC-19,(6) (1974) 716-723.

4.

H. Tamura, T. Kondo, Heuristics free group method ofdata handling algorithm of generating optimum partial(b) m=7

polynomials with application to air pollution prediction,
Int. J. System Sci. 11 (9) (1980) 1095-1111.

Published by Atlantis Press
Copyright: the authors
99