Cancer Diagnosis Using Modified Fuzzy Network

Abstract

In this study, a modified fuzzy c-means radial basis functions network is proposed. The main purposes of the suggested model are to diagnose the cancer diseases by using fuzzy rules with relatively small number of linguistic labels, reduce the similarity of the membership functions and preserve the meaning of the linguistic labels. The modified model is implemented and compared with adaptive neuro-fuzzy inference system (ANFIS). The both models are applied on "Wisconsin Breast Cancer" data set. Three rules are needed to obtain the classification rate 97% by using the modified model (3 out of 114 is classified wrongly). On the contrary, more rules are needed to get the same accuracy by using ANFIS. Moreover, the results indicate that the new model is more accurate than the state-of-art prediction methods. The suggested neuro-fuzzy inference system can be re-applied to many applications such as data approximation, human behavior representation, forecasting urban water demand and identifying DNA splice sites.

Full text

Universal Journal of Computer Science and Engineering Technology
1 (2), 73-78, Nov. 2010.
© 2010 UniCSE, ISSN: 2219-2158
73
Corresponding Author: Essam Al-Daoud, Computer Science Department, Zarka University, Jordan.
Cancer Diagnosis Using Modified Fuzzy Network
Essam Al-Daoud
Faculty of Science and Information Technology
Computer Science Department, Zarka University
13110 Zarka, Jordan
essamdz@zpu.edu.jo
Abstract— in this study, a modified fuzzy c-means radial basis
functions network is proposed. The main purposes of the
suggested model are to diagnose the cancer diseases by using fuzzy
rules with relatively small number of linguistic labels, reduce the
similarity of the membership functions and preserve the meaning
of the linguistic labels. The modified model is implemented and
compared with adaptive neuro-fuzzy inference system (ANFIS).
The both models are applied on "Wisconsin Breast Cancer" data
set. Three rules are needed to obtain the classification rate 97% by
using the modified model (3 out of 114 is classified wrongly). On
the contrary, more rules are needed to get the same accuracy by
using ANFIS. Moreover, the results indicate that the new model is
more accurate than the state-of-art prediction methods. The
suggested neuro-fuzzy inference system can be re-applied to many
applications such as data approximation, human behavior
representation, forecasting urban water demand and identifying
DNA splice sites.
Keywords- fuzzy c-means, radial basis functions, fuzzy-
neuro, rules, cancer diagnosis
I. INTRODUCTION
The subjectivity of the specialist is an important problem of
diagnosing a new patient. It can be noted that the decision of
the professionals is related to the last diagnostic. Therefore, to
enhance the diagnostic and to interpret the patients signal
accurately, the huge volume of the empirical input- output data
must be automated and used effectively. Cancer diagnosis can
be seen as a matching procedure whose objective is to match
each set of the symptoms (feature space) to a specific case.
Many studies have been introduced to develop cancer diagnosis
systems by using intelligent computation see for example [1-2].
Kiyan and Yildirim applied general regression neural network,
multilayer perceptrons (MLP), and probabilistic neural network
on Wisconsin breast cancer dataset. They show that the general
regression neural network is the most accurate model for breast
cancer classification [3]. Zhou et al. introduced a new system
based on neural network ensemble [4]. They named it Neural
Ensemble Based Detection (NED) and used it to identify the
images of the cancer cells. Radial Basis Functions (RBF)
represents alternative approach to MLP’s in universal function
approximation [5]. It outperforms MLP due to the convergence
speed and the capability in handling the non-stationary
datasets.
Fuzzy-Neuro system uses a learning procedure to find a set
of fuzzy membership functions which can be expressed in form
if-then rules. Fuzzy-Neuro has many advantages: Firstly it
allows incorporating our experience and the previous
knowledge into the classifier. Secondly it provides an
understanding about the characteristic of the dataset. Thirdly it
helps to find the dependencies in the datasets. Fourthly it gives
an explanation which allows us to test the internal logic [6-8].
In this paper, a new intelligent decision support system for
cancer diagnosis is constructed and tested. The suggested
system is based on a modified version of fuzzy c-means
method and radial basis functions neural network. It can be
trained to establish a quality prediction system for a cancer
disease with different parameters. Moreover the suggested
neuro-fuzzy inference system can be applied to many
applications such as data approximation, dynamic system
processing, urban water demand forecasting, identifying DNA
splice sites and image compression. In general the suggested
model can be applied to any data needs classification,
interpretation, adaptation or rules' extraction. For example the
human behavioral representation in synthetic forces consists
from several fuzzy parameters; e.g., interactions, responses,
biomechanical, physical, psychophysical and psychological
parameters. Such this data are very suitable to be modeled by
using the suggested neuro-fuzzy inference system due to the
fact that human behavior represents highly complex nonlinear
and adaptable systems.
II. FUZZY-NEURO SYSTEMS
Fuzzy-Neuro system can be designed by using various
architectures. To improve the performance of the system, three
matters must be handled: finding the optimal number of the
rules, discovering the appropriate membership functions, and
tuning of both. The following is a short overview of the major
works in this area [9-12]:
 Fuzzy Adaptive Learning Control Network
(FALCON): FALCON consists from five layers. Tow
nodes for input data, one for the desired output and the
rest is for the actual output. The supervised learning is
implemented by using backpropagation algorithm .
 Generalized Approximate Reasoning Based
Intelligent Control (GARIC): Several specialized
feedforward network are used to implement GARIC. The

UniCSE 1 (2), 73 -78, 2010
74
main disadvantage of GARIC is the complexity of the
learning algorithm.
 Neuro-Fuzzy Controller (NEFCON): NEFCON
Consists from two phases. The first is used to embed the
rules and the second modifies and shifts the fuzzy sets.
The main disadvantage of NEFCON is that it needs a
previously defined rule base.
 Adaptive Network Based Fuzzy Inference System
(ANFIS): ANFIS works with different activation
functions and uses un-weighted connections in each
layer. ANFIS consists from five layers and can be
adapted by a supervised learning algorithm.
 Neuro-Fuzzy Classification (NEFCLASS) NEFCLASS
can be created from scratch by learning or it can be
refined by using partial knowledge about patterns.
 Fuzzy Learning Vector Quantization (FLVQ): FLVQ
is based on the fuzzification of LVQ and it is similar to
Adaptive Resonance Theory (ART). The main
disadvantage of FLVQ is not tested widely [13].
 Evolutionary Fuzzy Neural Network (EFNN): EFNN
uses evolutionary algorithms to train the fuzzy neural
network, Aliev et. At. Train the recurrent fuzzy neural
networks by using an effective differential evolution
optimization (DEO) [14].
The proposed method will be compared with ANFIS for
two reasons: firstly ANFIS has been written in many
programming languages including Matlab fuzzy logic toolbox.
Secondly ANFIS is widely tested in various applications such
as noise cancellation, system identification, time series
prediction, medical diagnosis systems, and control [15]. Fig. 1
illustrates the architecture of ANFIS. For simplicity, we assume
that ANFIS has two inputs x and y and one output z, suppose
that the rule base contains two fuzzy if-then rules of Takagi and
Sugeno’s type [16]:
Rule 1: If x is A1 and y is B1, then f1 = p1x + q1y + r1
Rule 2: If x is A2 and y is B2, then f2 = p2x + q2y + r2
Figure 1. ANFIS architecture
Let Oj,i represents the output of the ith node in the layer j, the
ANFIS output is calculated by using the following steps [16]:
1-
)(
,1 xO i
Ai


i =1 ,2
2-
)(
2
,1 xO i
Bi 


i=3,4
3-
2,1,1,2 
 iii OOO
i=1,2
4-
2,21,2
,2
,3 OO
O
Oi
i

i=1,2
5-
)(
,3,3,4 iiiiiii rxqxpOfOO 
i=1,2
6-

i
OO ,41,5
The membership function for A (or B) can be any
parameterized membership function such as:
2
1
1










i
i
A
a
cx

or (1)
)exp(
2









i
i
Aa
cx

(2)
Network can be trained by finding suitable parameters for
layer 1 and 4. Gradient decent are typically used for non linear
parameters of layer 1 while batch or recursive least squares are
used for linear parameters of layer 4 or even combination of
both.
III. THE PROPOSED MODEL
The main purposes of the suggested model are to diagnose
the cancer diseases by using fuzzy rules with relatively small
number of linguistic labels, reduce the similarity of the
membership functions and preserve the meaning of the
linguistic labels. The learning algorithm of the proposed model
consists of three phases:
Phase 1: Modified fuzzy c-means algorithm (MFCM). The
standard fuzzy c-means has various well-known problems,
namely the number of the clusters must be specified in
advanced, the output membership functions have high
similarity, and FCM is unsupervised method and cannot
preserve the meaning of the linguistic labels. On the contrary,
the grid partitions method solves some of the previous matters,
but it has very high number of the output clusters. The basic
idea of the suggested MFCM algorithm is to combine the
advantages of the two methods, such that, if more than one
cluster's center exist in one partition then merge them and
calculate the membership values again, but if there is no
cluster's center in a partition then delete it and redefined the
other clusters. Algorithm 1 illustrates the modified fuzzy c-
means algorithm
Algorithm 1. Modified fuzzy c-means algorithm
Input: Pattern vector, target vector, K the number of the
patterns and the partitions intervals of each attribute
k
ik
P,
Output: Centers, membership values and the new projected
partitions.

UniCSE 1 (2), 73 -78, 2010
75
1- Delete all the attributes that have low correlation
with the target
2- For each class in the target vector apply the
following steps on the corresponding patterns.
3- Choose c=K/2 seeds (first c patterns are selected as
seeds).
4- Compute the membership values M using













c
j
q
jk
ik
ik
cu
cu
m
1
)1/(2
||||
||||
1
, k=1,2,…K and q>1.
(3)
5- Calculate c cluster centers using:




K
k
q
ik
K
kk
q
ik
i
m
um
c
1
1
(4)
6- Compute the objective function.
  
 c
i
K
kik
q
ik
c
iic cumJcccMJ
1 1
2
1
21 ||||),...,,,(
(5)
7- If either J is less than a certain threshold level or the
improvement in the previous iteration is less than a
certain tolerance then go to step 8, else go to step 4.
8- If there are centers that exist in one partition=


K
kik k
P
1,
then merge it
n
c
c
n
vv
new


1
, c=c-v+1
(6)
9- If all partitions that are related to a projected
partition =

h
ik
P,

K
hkk ik k
P
,1 ,
do not contain a
center then delete the projected partition
h
ik
P,
and
redefined the attribute h partitions.
10- If step 8 or 9 is true then go to step 4.
Phase 2: Sort the initial fuzzy rules (centers) for each target
class, the weight of rule x with regard to class y is calculated
as following:


 z
yii iy
y
xNPNPRW
,1
)(
, (7)
Where NP is the number of patterns that have high participate
in the antecedents and the consequences of the rule x (the high
participate means that the membership is not less than T for
each attribute. In this paper T=0.5).
Phase 3: Modified RBF learning algorithm (MRBF). Fig. 2
shows the architecture of the MRBF, the hidden layers consist
from n layer, where n is the number of the target classes. Each
hidden layer growths iteratively, one node (Rule) per iteration
until accurate solution is found. The output layer consists from
n nodes, one node for each class. The MRBF is trained by
solving the system of equations using pseudo-inverse.
Figure 2. MRBF architecture
Algorithm 2. Modified RBF learning algorithm.
Input: Pattern vector, target vector, K the number of the
patterns
Output: The weight of the hidden-output layer, the
representative rules
1- Pick up the next highest weight of the rules (centers)
for class i and represent it as new node in the hidden
layer i.
2- Calculate the new outputs of all the hidden layers and
all the patterns. Where the output of the node j and
the pattern k is
kj

= φ (
jjk tx

|||| 
) =
2
2
|||| jjk tx
e


(8)
tj is the current center(rule) and  is the width.
3- Find the new weights of the hidden-output layer for
each class by solving the following system:
   
T
z
T
ztttwww ...... 2121 


(9)
Where z is the number of the processed centers (rules)
and


is the pseudo-inverse of the matrix














kzkk
z
z




...
............
...
...
21
22221
11211
(10)
4- If the error is less than a threshold then stop, else go
to step 1

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76
IV. EXPERIMENTAL RESULTS
In this section we will apply ANFIS and the modified
Fuzzy RBF (MFRBF) on "Wisconsin Breast Cancer" data set.
This data set contains 569 instances (patterns) distributed into
two classes (357 benign and 212 malignant). Features are
computed from a digitized image of a fine needle aspirate
(FNA) of a breast mass [17]. The number of the attributes that
are used in this paper is 11 (10 real-valued input features and
diagnosis). The features are summarized in Table 1.
TABLE I. DIAGNOSTIC BREAST CANCER FEATURES
Feature
Max
value
Min
Value
Correlation
Radius
28.1
6.981
0.7300
Texture
39.3
9.710
0.4152
Perimeter
188.5
43.790
0.7426
Area
2501
143.50
0.7090
Smoothness
0.2
0.0526
0.3586
Compactness
0.3
0.0194
0.5965
Concavity
0.4
0
0.6964
Concave points
0.2
0
0.7766
Symmetry
0.3
0.106
0.3305
Fractal dimension
0.1
0.05
-0.0128
Matlab 7.0 is used to implement the both algorithms, the
data is normalized by using the Matlab function premnmx()
and then the correlation between each feature and the target is
calculated and listed in Table 1. It can be observed that the
symmetry feature and fractal dimension feature have the lowest
correlation, thus they are deleted and the other 8 features are
used. Fig. 3 shows the first feature (Radius) distribution. A k-
folding scheme with k=5 is applied. The training procedure is
repeated 5 times, each time with 80% (455 patterns) of the
patterns as training and 20% (114) for testing. All the reported
results are obtained by averaging the outcomes of the five
separate tests.
Figure 3. The first feature (Radius) distribution
The initial shadow partitions for each feature in Algorithm
1 is chosen to be (small, Medium, Large) corresponding to ([-1,
-3.3), [-3.3,3.3), [3.3,1]). The number of the initial centers
(rules) is K/2=227. After running Algorithm 1 for 7 epochs
many centers are merged and the final number of the centers is
23. On the other hand, the projected partitions are redefined as
shown in Table 2. The deleted partitions can be substituted by
its neighborhood partition; for example, if the large partition is
deleted then the medium partition means (medium or large).
The projected partitions in Table 2 indicate that the fifth feature
(smoothness) can be ignored.
TABLE II. THE OUTPUT PROJECTED PARTITIONS
Feature
Max
value
Min
Value
Correlation
Radius
28.1
6.981
0.7300
Texture
39.3
9.710
0.4152
Perimeter
188.5
43.790
0.7426
Area
2501
143.50
0.7090
Smoothness
0.2
0.0526
0.3586
Compactness
0.3
0.0194
0.5965
Concavity
0.4
0
0.6964
Concave points
0.2
0
0.7766
Symmetry
0.3
0.106
0.3305
Fractal dimension
0.1
0.05
-0.0128
In phase 2, the rules are sorted according to its weights, the
highest weight rule is:
If (radius is small and texture is small and perimeter is
small and area is small and compactness is small and concavity
is small and concave point is small)
Then Benign
For simplicity, the above rule will be written as following:
if (s, s, s, s, s, s, s) then Benign
The number of the layers are needed in phase 3 is two
hidden layers, and one output layer, after two nodes (rules) are
added to the hidden layers (one for each), the classification
rate becomes 96% (4 out of 114 is classified wrongly). If
another node is added to the first layer then the classification
rate becomes 97% (3 out of 114 is classified wrongly). Table 3
compares the number of rules and the accuracy that are
generated by ANFIS and MFRBF.
TABLE III. COMPARISON BETWEEN ANFIS AND MFRBF
Method
Rules
Number
classification
rate
ANFIS
2,  =0.8
0.9474
MFRBF
2
0.9649
ANFIS
2, =0.5
0.9386
MFRBF
2
0.9649
ANFIS
3, =0.4
0.9474
MFRBF
3
0.9737
ANFIS
7, =0.3
0.9737
MFRBF
7
0.9737
ANFIS
19, =0.2
0.9649
MFRBF
19
0.9821
Table 3 indicates that by using MFRBF we can get high
accuracy with fewer rules. On the contrary, by using ANFIS

UniCSE 1 (2), 73 -78, 2010
77
more rules are needed to get the same accuracy. Moreover the
features projected partition in ANFIS is ambiguous and can
not preserve the meaning of the linguistic labels, see Fig. 4.
Figure 4. Ambiguous membership functions that are generated by ANFIS
The following is a sample rule produced by ANFIS:
If (in1 is in1mf1) and (in2 is in2mf1) and (in3 is in3mf1) and
(in4 is in4mf1) and (in5 is in5mf1) and (in6 is in6mf1) and
(in7 is in7mf1) and (in8 is in8mf1)
Then (out1 is out1mf1)
On the other Hand, the output rules in MFRDF are
unambiguous and do not need any farther processing. The best
number of the rules is trade-off between the accuracy and the
rules number, for example, the following three rules are
recommend, these rules are produced by MFRBF with
acceptable classification accuracy (97%):
If (s, s, s, s, s, s, s) then Benign
If (m or l, m or l, m or l, m or l, m or l, m or l, m or l)
Then Malignant
If (m or l, m or l, m or l, s, m or l, s , m or l) then Malignant
In Table 4, CLOP package are used to implement and to
compare the suggested model with the state-of-art prediction
methods (CLOP Package http://clopinet.com/CLOP/). Two
measurements are used: Balance Error Rate (BER) and Area
Under Carve (AUC). The results indicate that MFRBF is more
accurate than the other methods, where the balance error rate
is 2.2, while the balance error rate is 9.92 by using nonlinear
support vector machine (NonLinearSVM).
TABLE IV. COMPARISON BETWEEN THE STATE-OF-ART PREDICTION
METHODS
Method
Testing
BER
AUC
ANFIS
4.41
98.49
MFRBF
2.20
99.21
NeuralNet
6.15
97.81
LinearSVM
12.36
93.75
Kridge
8.53
96.22
NaiveBayes
10.4
95.21
NonLinearSVM
9.92
96.98
V. CONCLUSION
To produce unambiguous rules that are suitable for cancer
diagnosis, a modified fuzzy c-means radial basis functions
(MFRBF) is introduced. The experimental results show that:
we can use MFRBF to get high accuracy with fewer and
unambiguous rules. The classification rate is 97% (3 out of 114
is classified wrongly) by using only three rules. On the
contrary, more rules are needed to get the same accuracy by
using ANFIS. Moreover the features projected partition in
ANFIS is ambiguous and can not preserve the meaning of the
linguistic labels. The results indicate that MFRBF is superior to
state-of-art prediction methods, where the balance error rate is
2.2 by using MFRBF, while the balance error rate is 9.92 by
using nonlinear support vector machine.
ACKNOWLEDGMENT
This research is funded by the Deanship of Research and
Graduate Studies in Zarka University /Jordan
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