Published in the IJCSI International Journal of Computer Science Issues, Vol. 9, Issue 1, No 1, January 2012,
www.IJCSI.org
ISSN (Online): 1694-0814, pp: 228-234
A Study on the Behavior of a Neural Network for Grouping 
the Data
Suneetha Chittineni 1 and Dr.Raveendra Babu Bhogapathi 2
1Department of Computer Applications,
R.V.R. & J.C. College of Engineering,
Guntur, India.
chittineni_es@yahoo.com
2Director-Operations
DELTA Technology & Management Services Pvt. Ltd.,
Hyderabad, India.
rbhogapathi@yahoo.com
Abstract
One of the frequently stated advantages of neural networks is 
that they can work effectively with non-normally distributed 
data. But optimal results are possible with normalized data.In 
this paper, how normality of the input affects the behaviour of a
K-means fast learning artificial neural network(KFLANN) for
grouping the data is presented. Basically, the grouping of high
dimensional input data is controlled by additional neural 
network input parameters namely vigilance and tolerance.
Neural networks learn faster and give better performance if the 
input variables are pre-processed before being fed to the input 
units of the neural network. A common way of dealing with 
data that is not normally distributed is to perform some form of 
mathematical transformation on the data that shifts it towards a 
normal distribution.In a neural network, data preprocessing 
transforms the data into a format that will be more easily and 
effectively processed for the purpose of the user. 
Among 
various methods, Normalization is one which organizes data for 
more efficient access. Experimental results on several artificial 
and synthetic data sets indicate that the groups formed in the 
data vary with non-normally distributed data and normalized
data and also depends on the normalization method used.
Keywords: Data Preprocessing, Normalization, Fast Learning                   
                    Artificial Neural Network.
1. Introduction
Data preprocessing describes any type of processing on 
atomic data that has not been processed further to
preparing it for another processing procedure. Different 
data preprocessing techniques like cleaning method, 
outlier detection, data integration and transformation can 
be carried out before clustering process to achieve 
successful analysis. Normalization
is an important 
preprocessing step in data mining to standardize the 
values of all variables from dynamic range into specific 
range.
             Typical 
objective 
functions 
in 
clustering 
formalize the goal of attaining high intra-cluster 
similarity (Patterns within a cluster are similar) and low 
inter-cluster similarity (Patterns from different clusters 
are dissimilar). This is an internal criterion for the quality 
of a clustering.
In unsupervised learning, an output unit is 
trained to respond to clusters of pattern within the input. 
In this paradigm, the system is supposed to discover 
statistically salient features of the input population. 
Unlike the supervised learning paradigm, there is no a 
priori set of categories into which the patterns are to be 
classified; rather, the system must develop its own 
representation of the input stimuli.
            Supervised networks like Simple Perceptrons,
Back Propagation (BP), and Radial Basis Function 
(RBF) networks need a teacher to tell the network what 
the desired output should be. Unsupervised nets include 
Kohonen Self Organizing maps (SOM), Adaptive
Resonance theory (ART) etc. The major applications of 
unsupervised nets include clustering data, reducing the 
dimensionality of the data. In data clustering, exactly one 
of small number of output units comes on in response to 
an input. In dimension reduction, large number of input 
units is compressed into a small number of output units.
            Kohonen 
clustering 
algorithm 
takes 
high-
dimensional input,
clusters it,
and retaining some 
topological ordering of the output [7].  Adaptive 
Resonance Theory (ART) was initially introduced by 
Grossberg (1976) as a theory of human information
processing [3]. ART neural networks are extensively 
used for supervised, unsupervised classification tasks and 
functional approximation. There exist many different 
variations of ART networks today (Carpenter and 
Grossberg, 1998). 
ART1 performs unsupervised 
learning for binary input patterns, ART2 is modified to 
handle both analog and binary input patterns, and ART3 
performs parallel searches of distributed recognition 
codes in a multilevel network hierarchy. Fuzzy 
ARTMAP represents a synthesis of elements from neural 
networks, expert systems, and fuzzy logic.
                   Many variations of fast learning artificial 
neural network algorithms have been proposed. A fast 
learning artificial neural network (FLANN) models was 
first developed by Tay and Evans [17] to solve a set of 
problems in the area of pattern classification. FLANN [3] 
[4] was designed with concepts found in ART but 
imposed the Winner Take All (WTA) property within the 
algorithm. Further improvement was done to take in 
numerical continuous value in FLANN II [11]. The 
original FLANN II was restricted by its sensitivity to the 
pattern sequence. This was later overcome by the 
inclusion of k-means calculations, which served to 
remove inconsistent cluster formations [13].
The 
KFLANN utilizes the Leader-type algorithm first 
addressed by Hartigan [9] and also draws some parallel 
similarities established in the Adaptive Resonance 
Theories developed by Grossberg [7] and later ART 
algorithms by Carpenter et al [2].The later improvement 
on KFLANN [15] includes data point reshuffling which 
resolves the data sequence sensitivity that creates stable 
clusters. Clusters are said to be stable if the cluster 
formation is complete after some iterations and the 
cluster centers remain consistent.
The organization of this paper is as follows. In section II, 
an overview of the data normalization methods are
described. Section III gives the details of neural network 
input parameters. Section IV presents various formulas 
for computing tolerance values of the attributes. In 
Section V the K-means Fast Learning Artificial Neural 
Network algorithm is presented. Section VI presents the 
experimental analysis of the results and conclusions 
follow in section VII.
2. Data normalization
1) Z-score normalization
              The Z-score is called as standardized unit. It 
indicates how far and in what direction a variable 
deviates from its distribution’s mean, expressed in units 
of its distribution’s standard deviation. The Z-scores are 
especially informative when the distribution to which 
they refer is normal. If the value of Z is positive, it means 
the variable X is above its mean and if Z is negative, then 
X is below its mean (Cryer & Miller, 1994). It can also
measure the outliers of a dataset. If the value of a Z-score 
is greater than 3, it indicates that the data distribution has
outliers (Tamhane & Dunlop, 2000). It can be
defined as follows:
    



x
x
score
z



                   (1)
2) Min-Max normalization
Min-max normalization performs a linear transformation 
on the original data. Suppose that mina and maxa are the 
minimum and the maximum values for attribute A. Min-
max normalization maps a value v of A to v’ in the range
[new-mina,new-maxa]   by  computing
a
new
a
a
a
v
a
new
a
new
v
min
_
min
max
min
*
min
_
max
_
'





























            (2)
3. Neural Network Input Parameters
KFLANN is an atomic module, suitable for creating 
scalable networks which performs similar processing 
evident within biological neural systems. The original 
FLANN and KFLANN share the exact same network 
parameters. Both algorithms require an initialization of 
two network parameters, namely the Vigilance factor (ρ)
and the Tolerance setting (δ). These network parameters 
are the key to obtain an optimal clustering outcome.
3.1 Vigilance
The Vigilance (ρ) is a parameter that originated from [2]. 
It was designed as a means to influence the matching 
degree between the current exemplar and long term 
memory trace. The higher the ρ value, the stricter the 
match, while for a smaller ρ value, a more relaxed
matching criteria is set .The ρ value in the KFLANN is 
similar and it is used to determine the number of the 
attributes in the current exemplar that is similar to the 
selected output node. For example, if a pattern consists 
of 12 attributes and a clustering criteria was set such that 
a similarity of 4 attributes was needed for consideration 
into the same cluster, then the ρ should be held at 3.The 
Vigilance formulation is given by equation (3)
total
f
match
f


      
(3)
If the vigilance value is high more number of clusters 
were formed than when it was set lower.
3.2 Tolerance
          Tolerance parameter provides the localized 
control, affects individual input features where as   the 
Global variation in the input features is governed by
vigilance parameter.   Tolerance setting, δ, is the 
measurement of a particular feature consistency that 
measures the maximum range that the specified feature is 
allowed to fluctuate. The tolerance setting can be 
performed 
through 
various
methodologies. 
Three 
methods are described in the sections that follow. The 
tolerance setting of the exemplar attributes is the   
measurement   of   attributes   dispersion,   and   thus 
computation is performed for every feature of the 
training exemplar at the initial stage.
1.
The presence of Domain knowledge is 
perhaps the most helpful form of tolerance 
setting.  With the existence of knowledge 
from the domain expert, the tolerance of 
pattern attributes may be determined. This
approach is able to produce an acceptable 
clustering result since the domain knowledge 
is 
usually 
superior.
However, 
domain 
knowledge is not always available. Two other 
approaches have been included to harness the 
clustering capabilities of K-FLANN even in 
the absence of domain knowledge.
2.
In the mathematical context, Standard
3.
deviation is the measurement of dispersion 
of a particular variable from the mean value 
[1]. Standard deviation method used as the 
tolerance   setting   of   each   feature.   The   
tolerance computation formula is given in 
equation (4). From the equation, it indicates 
that it is susceptible to outlier’s values, which 
may increase the δ value.  This method  is  
appropriate  only  if  the  variation  of  each 
feature  in  exemplar  is  uniform.  There 
should be a minimal presence of the extreme
points lying in the outer regions of the main 
cluster body. However
in most pattern 
classification problems, the data sets are 
usually attach with the outliers points.
1.
1.
p


n
n
k
x
d
d
d
dk






1
2


               (4)
Where xdk is the dth feature of the kth pattern and μd is the 
respective mean value of the attribute.
3. This method uses of the equation shown in Eq. (5)
(Max-Min method)
2
min
max
diff
diff

                        (5)
4. KFLANN Algorithm
4.1 KFLANN Architecture
The basic architecture of KFLANN is delineated in 
Figure 1. It consists of two layers, similar to the basic 
Kohonen network model [2] and the ART1 model 
[4].Connecting the output layer and the input layer is a 
set of weight vectors. Each output node has weights 
connected to each element of the input vector. The 
weight assignment system is unlike that of the Kohonen 
network or ART1. If a novel pattern is to be stored, it 
performs a direct copy of the input vector into the weight 
vector. No other forms of equation are needed for 
evaluating the weight vectors. The output layer can be 
viewed as a single dimensional layer which grows 
dynamically as more novel patterns are encountered. As 
these novel patterns are encountered, the output system 
will allocate memory space for the pattern. This implies 
that the design stages of the network would not require a 
detailed plan of the output layer, but only a correct 
configuration of the input layer. The output layer will 
determine its own size, as the system is trained. 
Classification results are eventually obtained directly 
from the winning output node.
Fig 1 KFLANN Architecture
4.2 Algorithm
Step 1 
Initialize the network parameters.
Step 2 
Present the pattern to the input layer. If there is 
no output node, GOTO step 6
Step 3 
Determine all possible matches output node 
using Eq (6).




n
x
w
n
i
i
ij
i



0
2
2

          ≥        ρ  
(6)
Step 4 
Determine the winner from all matches output 
             nodes using Eq.(7)
          
Winner    =








n
i
i
ij
x
w
0
2
min
           
(7)                     
Step 5
Match node is found. Assign the pattern to the 
match output node. GOTO Step 2
Step 6 
Create new output node. Perform direct 
mapping of the   input vector into weight 
vectors.
Step 7 
If complete a single epoch compute clusters 
centroid. If centroid points of all clusters unchanged 
Terminate
Else 
GO TO Step 2.
Step 8
Find closest pattern to the centroid and re-
shuffle it to the top of the dataset list, GOTO
Step 2.
Note:    ρ   is the Vigilance Value,   δi      is the 
tolerance for  ith    feature of the input space , W 
ij   used to denote  the weight connection of  jth
output to the  ith input,   Xi   represent the  ith  
feature.
4.3 Tolerance Tuning
Using the domain knowledge it is possible to know 
number
of clusters in the given data set.
After 
completing a single epoch, if desired number of clusters 
are not formed then KFLANN requires tolerance tuning 
.It is given as follows:
i.
Initialize 
δi = ( δimax + δimin )/2
(8)
ii.
While number of clusters formed is not appropriate
iii.
run  KFLANN algorithm without step 7 based on 
current δ, values
iv.
if number of clusters is less than expected
δi = (δi + δimin) / 2
(9)
v.
else if number of clusters is more than expected
δi = (δi + δimax) / 2
(10)
vi.
end while
δi - Tolerance value for attribute i. δimin - Minimum 
difference in attribute values for attribute i. This is the 
difference between the smallest and the second smallest 
values of the attribute. δimax - Maximum difference in 
attribute values for attribute i. This is the difference 
between the smallest and largest values of the attribute.
5. Experimental Results
5.1 Data Sets
5.1.1 Artificial Data Sets Used
The data sets that are used to test the KFLANN 
algorithm 
are 
obtained 
from 
the 
site
http://kdd.ics.uci.edu/)
Table 1: Description of Artificial Data Sets
Data Set
# of 
patterns
# of 
features
# of clusters
Iris 
150
4
3(class 1-50,class 2-50,class 3-
50)
Wine
178
13
3(class 1-59,class 2-70,class 3-
49)
Glass
214
9
7(class 1-70,class 2-76,class 3-
17,class 4-0,class 5-13,class 6-
9,class 7-29)
Haberman
306
3
2(class 1-227,class 2-79)
New Thyroid
215
5
3(class 1-150,class 2-35,class 3-
30)
Image 
Segmentation
210
19
7(30 per class)
Pima-Indian 
diabetes
768
8
2(class 1-500,class 2-268)
Ionosphere
351
34
2(class 1-225,class 2-126)
5.1.2 Synthetic Data Sets Used
Table 2: Description of Synthetic Data Sets
Data Set
# 
of 
patter
ns
#of 
features
# of clusters
Synthetic Data Set 
1(Well separated)
1000
2
2(class 1-500,class 2-
500)
Synthetic Data Set 
2(Half separated)
1000
2
2(class 1-500,class 2-
500)
Synthetic Data Set 
3(Not separated)
1000
2
2(class 1-500,class 2-
500)
Synthetic Data Set 4
500
8
3(class 1-250,class 2-
150,class 3-100 )
Synthetic Data Set 5
400
8
3(class 1-150,class 2-
150,class 3-100 )
Synthetic Data Set 6
350
8
3(class 1-100,class 2-
150,class 3-100 )
5.2 Setting the Vigilance Parameter (ρ) and 
Tolerance Parameter (δ) is fixed for each 
attribute.
                     The following plots shows the number of 
clusters formed with the given vigilance value. The 
groups formed in the data grow with the increase in the 
vigilance value.  
      Fig. 1 Plots of Rho Vs Vigilance
          
Fig. 2 Plots of Synthetic Data Sets
5.3 Non-normalized data 
           The Experiments are conducted with non-
normalized input data with the given neural network 
input parameters namely vigilance and tolerance. The 
following table shows the misclassification rate when
Eq. (5) 
was used for computing tolerance setting for 
each attribute.
Table 3: Results with non-normalized data and tolerance 
with Eq.5
data set
Vigilance 
(ρ)
#of clusters          
With Eq. 
(5) Error 
Rate (%)
Iris
1
3
7.3333
New 
Thyroid
1
4(3 is the actual value, 
(tolerance tuning is 
required))
20.4651
New 
Thyroid
0.8
2(3 is the actual value, 
(tolerance tuning is 
required))
24.6512
Ionosphere
0.5294
2
29.6296
Pima 
Indian 
diabetes
0.6250
2
33.4635
Wine
0.7692
3
35.3933
Glass
0.8889
7
54.6729
Haberman
0.3333
6(2 is the actual value, 
tolerance tuning is 
required)
70.2614
Image 
Segmentati
on
0.8947,0.9
474
4,8(7 is the actual value, 
tolerance tuning is 
required)
79.0476,
64.4286
The following table shows the misclassification rate 
when (standard deviation i.e. Eq. (4) was used for 
computing tolerance setting for each attribute.
Table 4: Results with non-normalized data and tolerance
With Eq.4
data set
Vigilance 
(ρ) 
#of clusters          
With Eq. 
(4) Error
Rate (%)
Iris
0.5
3
10
New Thyroid
0.4
2(3 is the actual 
value, 
tolerance 
tuning is required)
30.2326
Ionosphere
0.2647
2
31.3390
Pima Indian 
diabetes
0.2500
2
34.2448
wine
0.3077
3
38.2022
New Thyroid
0.6
4(3 is the actual 
value
,tolerance 
tuning is required)
45.5814
Haberman
0.3333
2
48.6928
Image 
Segmentation
0.6842,0.7
368
7
64.2857,64.
7619
Glass
0.4444
7
67.2897
The above results show that the error rate was low when 
Eq. (5) was used for computing tolerance than Eq. (4) 
was used .KFLANN performs well only for iris data. For 
New Thyroid data set and Image Segmentation, actual
number of clusters are not formed with the given 
vigilance value, so tolerance tuning was required. So 
Normalization was required in order to classify samples 
with lower misclassification. 
5.4 Normalized data
5.4.1 Z-score normalization
Table 5: Results with Z-Score and tolerance with Eq.5
Data Set
Vigilance 
(ρ) 
#of Clusters          
With Eq. 
(5) Error 
Rate (%)
Iris
0.75
3
5.3333
New Thyroid
0.8
4(actual 
value is 3)
16.7442
Haberman
0.6667
2
25.4092
wine
0.9231
3
32.5843
Ionosphere
0.8235
2
42.4501
Pima Indian diabetes
0.75
2
48.4375
Glass
0.8889
7
52.8037
Image Segmentation
0.9,1
6 ,10(actual 
value is 7)
80.25,
82.30
Table 6: Results with Z-Score and tolerance with Eq.4
data set
Vigilance 
(ρ) 
#of clusters          
With Eq. 
(4) Error 
Rate (%)
Iris
0.5
3
5.3333
New Thyroid
0.2
3
13.4884
Ionosphere
0.3235
2
40.1709
wine
0.4615
3
43.2584
Pima Indian 
diabetes
0.1250
2
48.3073
Haberman
0.3333
2
53.2680
Glass
0.4444
7
56.0748
Image 
Segmentation
0.6842
6 (actual value is 
7,tolerance tuning 
is required)
87.6190
5.4.2 Max-Min Normalization
Table 7: Results with Max-Min and tolerance with Eq.5
Data Set
  
Vigilance 
(ρ) 
#of clusters          
With 
Eq.(5)Error 
Rate (%)
Pima Indian 
diabetes
0.6250
2
0
Iris
1
3
10
wine
0.7692
3
14.6067
New Thyroid
0.8,1
2,4(actual value is 
3,tolerance tuning is 
required)
21.8605,12.
5581
Ionosphere
0.5294
2
29.6296
Glass
0.8889
7
49.5327
Image 
Segmentation
0.9474
8 (tolerance tuning 
is required)
59.5238
Haberman
0.6667,1
3,6(actual value is 
2,tolerance tuning is 
required)
60.7843,80.
7190
Table 8: Results with Max-Min and tolerance with Eq.4
data set
  
Vigilance 
(ρ) 
#of clusters          With Eq.(4)
   Error Rate (%)
Pima Indian diabetes
0.2500
2
0.1302
Iris
0.5
3
12
New Thyroid
0.4,1
2,4(tolerance 
tuning is 
required)
30.2326,12.5581
Ionosphere
0.2647
2
31.3390
Haberman
0.3333
2
54.5752
Image Segmentation
0.7368
7
57.1429
Wine
0.3077
3
64.6067
Glass
0.4444
7
65.8879
With the above results, it was observed that accuracy is 
high with normalized data. KFLANN performs well for 
Pima Indian Diabetes data set where the error rate is 
zero. Using Z-score normalization for the Iris data set the 
error rate was same when either of the method (stated 
above) was used for computing tolerance. It was found 
that Z-score Normalization was well suited for 
Haberman survival data and Max-Min normalization was
well suited for Wine, Ionosphere and Glass (tolerance 
setting with Max-Min) data sets as the error rate was low 
when compared with Z-Score Normalization.
5.5 Why tolerance tuning?
                From the above results, it was found that 
desired number of clusters is not formed with maximum 
vigilance value (1) and also with the next maximum 
value. So there is no chance of getting stated number of 
clusters because if the vigilance value is reduced number 
of clusters formed is less than the previous value. Getting 
number of clusters stated in the domain knowledge is 
possible only with tolerance tuning when max-min 
method was used for setting  tolerance parameter for the 
attributes. For some of the artificial data sets tolerance 
tuning is required as expected number of clusters is not 
formed. For example consider New Thyroid Data set 
.The number of clusters are 3.but with the given 
vigilance values 2 and 4 are formed.
5.5.1 Synthetic Data Sets
                     On all the Synthetic data sets, KFLANN 
requires tolerance tuning. The misclassification rate was 
as follows:
Table 9: Results with Synthetic Data sets
Data Set
Vigilance (ρ) 
#of 
clusters          
Eq. (4) or Eq. (5) 
Error Rate (%)
Synthetic  Data  
Set 1
1
2
0
Synthetic  Data  
Set 2
1
2
1.8
Synthetic  Data  
Set 3
1
2
29.2
Synthetic  Data  
Set 4
1
3
0
Synthetic  Data  
Set 5
1
3
0
Synthetic  Data  
Set 6
1
3
54.2857
6. Conclusions
                 This paper was intended to observe the 
behavior of a KFLANN algorithm used for unsupervised 
learning. The above results show that the performance of 
the algorithm and the quality of the clustering was based 
on the input data
presented
(normalized or non-
normalized). The result of the KFLANN was varied 
between non-normalized and normalized data and was
not same for all types of data normalization. For a given 
input data, one of the normalization method stated above 
was well suited for a given input because the efficiency 
of the KFLANN was improved. So normalization is one 
of the most important factors in clustering. The operation 
of the KFLANN also depends on above mentioned two
parameters namely vigilance and tolerance. It was 
observed that the misclassification rate is low when 
Max-Min formula was used for tolerance and also 
independent of normalization method. For all synthetic 
data sets the misclassification rate is same with the 
vigilance setting and with different formulas used for 
tolerance setting.A comparative analysis showed that the 
clustering results depended on the normalization method 
used and the noisiness of the data. In particular, the 
selection of the vigilance and tolerance setting values for 
the 
KFLANN 
algorithm 
was
sensitive 
to 
the 
normalization method used for datasets with large 
variations across samples. The fine behavior obtained 
with neural network for the clustering problems studied 
here can be used with other difficult optimization 
problems.
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1Suneetha Chittineni, Associate Professor in the 
department of Computer Applications, R.V.R.&                               
J.C  college of Engineering,Chowdavarm,Guntur. 
She has 12 years of teaching experience. Currently
she is pursuing Ph.D. from Acharya Nagarjuna 
University, Guntur. Her research interests include 
                          Artificial Intelligence, Machine learning, Pattern 
                          Recognition.
2Dr B. Raveendra Babu obtained his Masters in 
Computer Science and Engineering from Anna
University, Chennai. He received his Ph.D. in 
Applied Mathematics at S.V University, Tirupati. 
He is
currently leading a Team as Director 
(Operations), M/s. Delta Technologies (P) Ltd., 
             Madhapur, Hyderabad. He has 26 years of teaching   
           experience. He has more than 25 International &   
            National publications to his credit. His research 
            areas of interest include VLDB, Image Processing,   
           Pattern Analysis and Information Security.