Breast Tumor Classification Diagnosis Based on LS-SVM
Chao Liu
1,2
，
3
, Bo Zhou
1
, Qingzhu Li
4
, Yu Chen
1
,Guowei Qin
1
and Guangkuo Hu
2
，
3
1
Kunming University of Science and Technology;
2
The First People’s Hospital of Yunnan Province;
3
Affiliated Hospital of Kunming University of Science and Technology;
4
Yan’ An Hospital of Kunming
Keywords: Breast tumor; LS-SVM; Neural network; Support vector machine; clinical diagnostic value.
Abstract: To accurately predict breast cancer, breast cancer prediction method based on least squares support vector
(LS-SVM) proposed. Patients with breast cancer through the data on the basis of 469 cases, including 400
cases of data relevance vector machine training, and the remaining 69 cases data sample tests, and finally
through with neural networks, support vector machines comparison, breast cancer diagnosis model based on
LS-SVM prediction accuracy is higher than the neural network and support vector machine. Has good
diagnostic value of breast cancer diagnosis based on LS-SVM model, which provides a new method for
breast cancer diagnosis.
1 INTRODUCTION
Cancer(LU Xin-guo,2010)is called malignant tumor
in field of medicine. It is a kind of cells cancerous
result at partial tissue caused by action of carious
factors such as the chemical, physical, microbe and
its metabolic product. It is often shown as: partial
tissue abnormal cellular proliferation and form of
partial lump. Cancer is a kind of disease caused by
multiple causes, stages and mutations of normal
cells in the body. Cancer is characterized by: ability
to infinite proliferation and loss of contact inhibition
phenomena at the same time, the cancer cells
between viscosity reduced, easy to be lectin
agglutination, this will consume a lot of nutrients of
cancer patients(LIN Xiao-gang,2009);Cancer cells
release a variety of toxins, causing the human body
to produce a series of symptoms; cancer cells can
also be spread through blood, lymphatic or direct
methods such as transferred to the whole body,
leading to a large amount of nutrients in the body is
consumed, and viscera function is damaged. Benign
tumor is easy to clean, and generally, no transfer, no
recurrence, only extrusion of organs, tissues and
blocking effect. Malignant tumor leads to tumor
metastasis and malignant tumor destroys the normal
structure and function of tissues and organs, cause
necrosis bleeding merge infection, the patient
eventually died due to organ failure.
Medical studies have found that the nuclear
micrograph of breast tumor lesion tissue is different
from that of normal tissue, but it is difficult to
distinguish it by general image processing method.
Therefore, it is particularly important to use
scientific methods to diagnose benign or malignant
breast tumors according to the nuclear microscopic
images of breast tumor foci(XU Wei-yun,2003).
Based on this, this paper proposes to use LS-
SVM to conduct classified diagnosis of breast
tumors, and to prove its effectiveness and accuracy
by comparison.
2 PRINCIPLE OF LEAST
SQUARES SUPPORT VECTOR
MACHINE ALGORITHM
In 1995, Corinna Cortes and Vapnik initially put
forward support vector machine (SVM) which show
unique advantages in solving nonlinear, high
dimension, small sample, and can be applied to the
function fitting other machine learning problems
(WANG Yu-hong,2004).It can be expressed as
follows:

For training data set,
),(
ii
yx
，linear function
is used to fit sample,
φ
represents a mapping from
the input space
x
to the feature space,
w
is the
weight and
b
is the deviation.
bxwxy
T
+= )()( φ
(1)
Equation (1) is optimized as follows:
∑
=
+=
n
i
i
ewewK
1
22
2
1
||||
2
1
),(min
γ
(2)
ii
t
i
ebxwyts =−−..
(3)
Equation(2)
γ
is called regularization
parameter.
n
is the number of training samples;
e
is
the training error, and finally the LSSVM model can
be obtained as follows:
bxxaLy
n
i
i
i
+=
∑
=1
^
),(
(4)
In Equation(4),
a
is called as Lagrange
multiplier, and
L
is the kernel function. The radial
quantity machine (RBF) is used as the kernel
function,
}
2
||||
{
2
2
),(
σ
i
xx
i
exxL
−
−
=
(5)
In Equation(5),
σ
is the kernel function width.
3 LS-SVM MODEL OF BREAST
TUMOR
The data of 469 cases of breast tumors (including
325 cases of benign and 144 cases of malignant) in a
hospital in Yunnan province were taken as an
example. Database contains 10 characteristics, the
nucleus radius, texture, perimeter, area, smoothness,
compactness, sag degrees, symmetry degree and
fracture degree, each feature and means value,
standard deviation and the worst value, namely, a
total of 30 sets of data, a diagnosis of benign or
malignant.
Fig 1 Parameter roughly selection.
From figure 1, c can be narrowed down to 2 ^ (-7)
~2 ^ (8), g can be narrowed down to 2 ^ (-6) ~ 2 ^
(6), it based on a rough parameter selection for
parameter selection. Take c values change for: 2 ^ (-
7), 2 ^ (-6.5)... 2 ^ (8).G change values for: 2 ^ (-6),
2 ^ (5.5)... 2 ^ (6).In order to see the change of
accuracy more clearly, the actual change interval of
the accuracy of the final parameter selection result
graph was set to 0.9.
The result of fine parameter selection is shown in
figure 2.As can be seen from the figure, the most
parameter c is 8, g is 0.17678, and the cross
validation accuracy is 97.8 %.As can be seen from
figure 3, only the 69th value is different, and the rest
are the same, that means the classification accuracy
is 68/69=98.55%, proving that a better classification
accuracy can be achieved by using the least squares
support vector machine.

Fig 2 Parameter fine selection.
Fig 3 Actual classification & Prediction classification.
4 DIFFERENTIAL DIAGNOSIS
AND COMPARISON OF
BREAST TUMORS
According to the established LS-SVM model, the
diagnostic accuracy and running time of diagnosis
were obtained by MATLAB programming, and then
the sensitivity and specificity of diagnosis were
obtained by the method of ten-fold cross validation
(HE Ya-peng, 2012) . .From table 1 LS-SVM
running time, accuracy, sensitivity and specificity
degree were higher than that of SVM and BP neural
network. It illustrates the breast tumor classification
diagnosis model based on the LS-SVM for breast
tumor.
Table 1 Comparison of diagnostic performance.
Method
Time
(t)
Accuracy
(%)
Sensitivity
(%)
Specificity
(%)
LS-SVM 3.242 97.80 94.45 95.58
SVM 3.363 94.35 93.63 94.32
BP
neural
networ
k
3.745 91.77 91.23 91.77
5 CONCLUSIONS
The benign tumor by treatment and reasonable diet
will gradually recover, but malignant tumors grow
quickly, growth often extends into the surrounding
tissue, few coated surface, often have systemic
symptom such as transfer, so difficult to cure. At
present, the highest incidence of breast cancer is
women's diseases; cancer has become the world's
highest incidence of female breast cancer, so
accurate and timely diagnosis for breast neoplasms
is particularly important.
This article used LS-SVM in breast cancer
diagnosis, by solving the linear equation to obtain
the optimal solution. Compared with the traditional
SVM (WANG Bo, 2012)and BP neural network (LI
Xiao-feng, 2008), it has huge advantages in terms of
calculation speed, cost of computing and high
accuracy. Therefore, the classification diagnosis
model based on LS-SVM is very suitable for breast
diagnosis, and the simulation results prove its
accuracy as well.
REFERENCES
1. Lu, X., Lin, Y., &Luo, J. 2010. Classification
Algorithm Combined GCM with CCM in Cancer
Recognition. Journal of SoftwarestSoftw, 21(11),
2838-2851.
2. Lin X. G. Pan, Y. J., Guo, Y. C. 2009. The study of
cervical cancer cells model based on UV absorption
spectrum. Spectroscopy and Spectral Analysis, 29(9),
2547-2550.
3. Xu, W. Y., Chen, L., He, S., Li, Y. C., Yang, Y. H.,
Wang, A. Q., &Xie, G. 2003. Quantitative pathologic
technique in prognostic identification of breast
carcinoma with negative lymph node. Chinese journal
of oncology, 25(5), 461-463.
4. Wang, Y. H., Huang, D. X., Gao, D. J., & Jin, Y. H.
2004. Nonlinear predictive control based on LS-SVM.
Control and Decision, 19, 383-387.

5. He, Y. P., Zhuang, S. N., Zhang, Y. H., & Zhu, X. H.
2012. Cross validation based robust-SL 0 algorithm
for target parameter extraction. Systems Engineering
and Electronics, 34(1), 64-68.
6. WANG, B., DU, X. X., & JIN, M. 2012. Application
of Breast Tumor Diagnosis Based on Learning Vector
Quantization Neural Network [J]. Computer
Simulation, 8, 042.
7. Li, X. F.,&Shen, Y. 2008. Support vector machines
based computer-aided diagnosis system of breast
tumor with ultrasound images. JOURNAL OF
OPTOELECTRONICS LASER, 19(1), 115-119.