AN ANALYSIS OF GENE EXPRESSION DATA USING PENALIZED
FUZZY C-MEANS APPROACH
P.K. Nizar Banu1 H. Hannah Inbarani2
1
Department of Computer Applications, B. S. Abdur Rahman University, Chennai, Tamilnadu,
India
Email: nizarbanu@gmail.com
2
Department of Computer Science, Periyar University, Salem, Tamilnadu, India
Email: hhinba@gmail.com

ABSTRACT
With the rapid advances of microarray technologies, large amounts of high-dimensional gene
expression data are being generated, which poses significant computational challenges. A first
step towards addressing this challenge is the use of clustering techniques, which is essential in
the data mining process to reveal natural structures and identify interesting patterns in the
underlying data. A robust gene expression clustering approach to minimize undesirable
clustering is proposed. In this paper, Penalized Fuzzy C-Means (PFCM) Clustering algorithm is
described and compared with the most representative off-line clustering techniques:
K-Means Clustering, Rough K-Means Clustering and Fuzzy C-Means clustering. These
techniques are implemented and tested for a Brain Tumor gene expression Dataset. Analysis of
the performance of the proposed approach is presented through qualitative validation
experiments. From experimental results, it can be observed that Penalized Fuzzy C-Means
algorithm shows a much higher usability than the other projected clustering algorithms used in
our comparison study. Significant and promising clustering results are presented using Brain
Tumor Gene expression dataset. Thus patterns seen in genome-wide expression experiments can
be interpreted as indications of the status of cellular processes. In these clustering results, we find
that Penalized Fuzzy C-Means algorithm provides useful information as an aid to diagnosis in oncology.

Keywords: Clustering, Microarray, Gene Expression, Brain Tumor, Fuzzy Clustering, FCM,
PFCM
produced. Searching for meaningful
information patterns and dependencies
among genes, in order to provide a basis for
hypothesis testing, typically includes the
initial step of a natural basis for organizing
gene expression data to group genes together
with similar patterns of expression. The field
of gene expression data analysis has grown
in the past few years from being purely datacentric
to
integrative,
aiming
at
complementing microarray analysis with
data and knowledge from diverse available
sources.
Advances
in
microarray
technologies have made it possible to
measure the expression profiles of thousands

1.INTRODUCTION
Gene expression is the fundamental
link between genotype and phenotype in a
species, with microarray technologies
facilitating the measurement of thousands of
Gene expression values under tightly
controlled conditions, e.g. (i) from a
particular point in the cell cycle, (ii) after an
interval response to some environmental
change, (iii) from RNA, isolated from a
tissue
exhibiting
certain
phenotypic
characteristics and so on (Kerr, et. al., 2008).
A problem inherent in the use of microarray
technologies is the huge amount of data
1

of genes in parallel under varying
experimental conditions. Due to the large
number of genes and complex gene
regulation networks, clustering is a useful
exploratory technique for analyzing these
data. It divides data of interest into a small
number of relatively homogeneous groups
or clusters. Clustering is a popular data
mining technique for various applications.
One of the reasons for its popularity is the
ability to work on datasets with minimum or
on a priori knowledge. This makes
clustering practical for real world
applications. We can view the expression
levels of different genes as attributes of the
samples, or the samples as the attributes of
different genes. Clustering can be performed
on genes or samples (Michael et. al. 1998).
This paper introduces the application of
Penalized Fuzzy C-Means algorithm to
cluster Brain Tumor genes.

expression
profiles
are
hierarchical
clustering algorithms (Michael et. al. 1998),
self-organizing maps (Paul, 1999) and
K-Means clustering algorithms (Tavazoie,
et. al., 1999). Hierarchical algorithms merge
genes with the most similar expression
profiles iteratively in a bottom-up manner.
Self-organizing
maps
and
K-means
algorithms partition genes into userspecified k optimal clusters. Other full space
clustering algorithms applied on gene
expression data include Bayesian network
(Friedman et. al. 2000) and neural network.
A robust image segmentation method that
combines the watershed segmentation and
penalized fuzzy Hopfield neural network
algorithms to minimize over-segmentation is
described in (Kuo et. al. 2006). (Brehelin et.
al., 2008) evaluates the stability of clusters
derived from hierarchical clustering by
taking repeated measurements. A wide
variety of clustering algorithms are available
for clustering gene expression data (Bezdek,
1981). They are mainly classified as
Partitioning methods, hierarchical methods,
Density based methods, Model based
methods, Graph Theoretic methods, soft
computing methods etc.

This paper is organized as follows.
In Section 2, Research background for
clustering Gene Expression patterns is
discussed. In Section 3, Methodology for
preparing Gene Expression patterns is
presented. Section 4 presents a method for
extracting highly suppressed and expressed
genes based on Penalized Fuzzy C-Means
algorithm. The Experimental results are
discussed in Section 5. Finally, section 6
concludes this paper by enumerating the
merits of the proposed approaches.

Multiple expression measurements
are commonly recorded as a real-valued
matrix, with row objects corresponding to
gene expression measurements over a
number of experiments and columns
corresponding to the pattern of expression of
all genes for a given microarray experiment.
Each entry xij, is the measured expression of
gene i in experiment j. Dimensionality of a
gene refers to the number of expression
values recorded for it. A gene/gene-profile x
is a single data item (row) consisting of d
measurements, x = (x1, x2, . . . , xd). An
experiment/sample y is a single microarray
experiment corresponding to a single
column in the gene expression matrix,
y = (x1, x2, …, xn)T where n is the number of

2. RESEARCH BACKGROUND
2.1. Clustering
Clustering genes, groups similar
genes into the same cluster based on a
proximity measure. Genes in the same
cluster have similar expression patterns. One
of the characteristics of gene expression data
is that it is meaningful to cluster both genes
and samples. The most commonly applied
full space clustering algorithms on gene
2

genes in the dataset. Clustering is considered
an interesting approach for finding
similarities in data and putting similar data
into groups. Initial step in the analysis of
gene expression data is the detection of
groups of genes that exhibit similar
expression patterns. In gene expression,
elements are usually genes and the vector of
each gene is its expression pattern. Patterns
that are similar are allocated in the same
cluster, while the patterns that differ
significantly are put in different clusters.
Gene expression data are usually of high
dimensions and relatively small samples,
which results in the main difficulty for the
application of clustering algorithms.
Clustering the microarray matrix can be
achieved in two ways:
(i) Genes can form a group which
show similar expression across
conditions,
(ii) Samples can form a group which
shows similar gene expression
across all genes.
This gives rise to global clustering, where a
gene or sample is grouped across all
dimensions. Additionally, the clustering can
be complete or partial. A complete
clustering assigns each gene to a cluster,
whereas a partial clustering does not. Partial
clustering tends to be more suited to gene
expression, as the dataset often contains
irrelevant genes or samples. Clearly this
allows:
(i) Noisy genes to be left out, with
correspondingly less impact on the
outcome and
(ii) Genes belonging to no cluster omitting a large number of
irrelevant contributions.
Microarrays measure expression for the
entire genome in one experiment, but genes
may change expression, independent of the
experimental condition. Forced inclusion in
well-defined but inappropriate groups may
impact the final structures found for the

data. Partial clustering avoids the situation
where an interesting sub-group in a cluster is
hidden through forcing membership of
unrelated genes (Kerr, et. al., 2008).
2.2. Categories of Gene Expression data
clustering
Methods of clustering can be
categorized as Hard Clustering or Soft
Clustering. Hard Clustering requires each
gene to belong to a single cluster, whereas
Soft
Clustering
permit
genes
to
simultaneously be members of numerous
clusters. Hard Clustering tells whether a
gene belongs to a cluster or not. Whereas in
Soft Clustering, with membership values,
every gene belongs to each cluster with a
membership weight between 0 (doesn’t
belong) and 1 (belongs). Clustering
algorithms which permit genes to belong to
more than one cluster are more applicable to
Gene expression. Gene expression data has
certain special characteristics and is a
challenging research problem
A modern working definition of a
gene is "a locatable region of genomic
sequence, corresponding to a unit of
inheritance, which is associated with
regulatory regions, transcribed regions, and
or other functional sequence regions".
Currently, a typical microarray experiment
contains 103 to 104 genes, and this number is
expected to reach to the order of 106.
However, the number of samples involved
in a microarray experiment is generally less
than 100. One of the characteristics of gene
expression data is that it is meaningful to
cluster both genes and samples. On one
hand, co-expressed genes can be grouped
into clusters based on their expression
patterns (Ben-Dor, et. al., 1999&Michael et.
al. 1998). In such gene-based clustering, the
genes are treated as the objects, while the
samples are the features. On the other hand,
the samples can be partitioned into
homogeneous groups. Each group may
3

correspond to some particular macroscopic
phenotype, such as clinical syndromes or
cancer types (Golub et. al., 1999). Such
sample-based clustering considers the
samples as the objects and the genes as the
features. The distinction of gene-based
clustering and sample-based clustering is
based on different characteristics of
clustering tasks for gene expression data.
Some clustering algorithms, such as KMeans and hierarchical approaches, can be
used both to group genes and to partition
samples.
Hard clustering algorithms like
K-Means and k-medoid place a restriction
that a data object can belong precisely to
only one cluster during clustering process.
This can be too restrictive while clustering
high dimensional data like Gene Expression
data because genes have a property of
getting expressed in multiple conditions.
Fuzzy set clustering like Fuzzy C-Means,
Penalized Fuzzy C-Means allows data
objects to belong to multiple clusters based
on the degree of membership.

to remember that when a gene expression
profile is analyzed in a given sample, it is
just a snapshot in time and space.
2.4 Clustering Techniques
K-Means Algorithm
The K-means method aims to minimize
the sum of squared distances between all
points and the cluster centre. This procedure
includes the steps, as described by Tou and
Gonzalez (Tou et. al. 1974).
Rough Set Theory
Rough set theory introduced by
Pawlak (Pawlak, 1982) deals with
uncertainty and vagueness. Rough set theory
became popular among scientists around the
world due to its fundamental importance in
the field of artificial intelligence and
cognitive sciences. Similar to fuzzy set
theory it is not an alternative to classical set
theory but it is embedded in it. Rough set
theory can be viewed as a specific
implementation of Frege’s idea of
vagueness, i.e., imprecision in this approach
is expressed by a boundary region of a set,
and not by a partial membership, like in
fuzzy set.

2.3. Analysis of Gene Expression data
Gene expression data is usually
represented by a matrix, with rows
corresponding to genes, and columns
corresponding to conditions, experiments or
time points. The content of the matrix is the
expression levels of each gene under each
condition. Those levels may be absolute,
relative or otherwise normalized. Each
column contains the results obtained from a
single array in a particular condition, and is
called the profile of that condition. Each row
vector is the expression pattern of a
particular gene across all the conditions.
Analyzing gene expression data is a
process by which a gene's information is
converted into the structures and functions
of a cell. Thousands of different mRNAs are
present in a given cell; together they make
up the transcriptional profile. It is important

Rough Clustering
A rough cluster is defined in a
similar manner to a rough set that is with
lower and upper approximation. The lower
approximation of a rough cluster contains
genes that only belong to that cluster. The
upper approximation of a rough cluster
contains genes in the cluster which are also
members of other clusters (SushmitaMitra,
2004 & SushmitaMitra, 2006). To use the
theory of rough sets in clustering, the value
set (Va) need to be ordered. This allows a
measure of the distance between each object
to be defined. Distance is a form of
similarity, which is a relaxing of the strict
4

requirement of indiscernibility outlined in
canonical rough sets theory, and allows the
inclusion of genes that are similar rather
than identical. Clusters of genes are then
formed on the basis of their distance from
each other. An important distinction
between rough clustering and traditional
clustering approaches is that, with rough
clustering, an object can belong to more than
one cluster.

3. METHODOLOGY
Cluster analysis, is an important tool in gene
expression
data
analysis.
For
experimentation, we used a set of gene
expression data that contains a series of gene
expression measurements of the transcript
(mRNA) levels of brain tumor gene. In
clustering gene expression data, the genes
are treated as objects and the samples are
treated as attributes. Gene pattern extraction
consists of 4 steps.
i)
Data Preparation
ii)
Data Normalization
iii)
Clustering
iv)
Pattern analysis

Fuzzy Clustering
Cluster analysis is a method of
grouping data with similar characteristics
into larger units of analysis. First in (Zadeh,
1965) fuzzy set theory that gave rise to the
concept of partial membership, based on a
membership function, fuzziness was
articulated and has received increasing
attention. Fuzzy clustering which produces
overlapping cluster partitions has been
widely studied and applied in various areas.
In fuzzy clustering, the Fuzzy C-Means
(FCM) clustering algorithm is the best
known and most powerful methods used in
cluster analysis (Bezdek, 1981). In (Yu et.
al., 2007), a general theoretical method to
evaluate the performance of fuzzy clustering
algorithm is proposed. The Fuzzy integrated
model is accurate than rough integrated
model and conventional integrated model
(Banu et. al., 2011). Fuzzy clustering
approach captures the uncertainty that
prevails in gene expression and becomes
more suitable for tumor prediction. One of
the important parameters in the FCM is the
weighting exponent m. When m is close to
one, the FCM approaches the hard C-Means
algorithm. When m approaches infinity, the
only solution of the FCM will be the mass
center of the data set. Therefore, the
weighting exponent m plays an important
role in the FCM algorithm.

3.1. Data Preparation
We represent the gene expression
ˆ {m |i 1,2,...,n , j 1,2,...,n},
data as ng by ns matrix: M
i, j
g
s
There are ns columns, one for each sample
and ng rows, one for each gene. One row of
genes is also called a gene vector, denoted

. Thus a gene
as g i  m , m ,..., m
vector contains the values of a particular
attribute for all samples.
i ,1

i,2

i ,n

s

3.2. Data Normalization
Data sometimes need to be
transformed before being used. For example;
attributes may be measured using different
scales, such as centimeters and kilograms. In
instances where the range of values differ
widely from attribute to attribute, these
differing attribute scales can dominate the
results of the cluster analysis. It is therefore
common to normalize the data so that all
attributes are on the same scale. The
following are two common approaches for
data normalization of each gene vector:

m i, j 

m i, j  m i

m i, j 

5

,
mi
m i, j  m i

i

or

,

where
mi 



ns
j 1

ns

m i, j

 m
ns

, i 

j 1

The membership weighting system reduces
noise effects, as a low membership grade is
less important in centroid calculation.
PFCM algorithm helps in identifying
hidden pattern and providing enhanced
understanding of the functional genomics in
a better way.

 mi 

2

i, j

ns  1

m i, j denotes the normalized value

and
for gene vector i of sample j, mi,j represents
the original value for gene i of sample j, ns is
the number of samples, m i is the mean of
the values for gene vector i over all samples,
and  i is the standard deviation of the ith
gene vector.

Fuzzy Clustering permit genes to
belong to more than one cluster, is more
applicable to Gene Expression. Noisy genes
are unlikely to be members of several
clusters and genes with similar change in
expression for a set of samples are involved
in several biological functions and groups
should not be co-active under all conditions.
This gives rise to high inconsistency in the
gene groups and some overlap between
them. The boundary of a cluster is usually
fuzzy for three reasons:

The Brain Tumor gene expression
data is used for our experiments. This data
set is publically available in Broad Institute
web site. The various cluster validation
techniques namely Root Mean Square Error
(RMSE), Mean Absolute Error (MAE) and
Xie-Beni (XB) validity index are used to
validate the clusters obtained after applying
the clustering algorithms.

i.
4. PROPOSED PPROACH:
PENALIZED FUZZY C-MEANS

ii.

Penalized Fuzzy C-Means (PFCM)
algorithm for clustering gene expression
data is introduced in this paper, which
modified Fuzzy C-Means (FCM) algorithm
to produce more meaningful fuzzy clusters.
Genes are assigned a membership degree to
a cluster indicating its percentage
association with that cluster. The two
algorithms differ in the weighting scheme
used for the contribution of a gene to the
mean of the cluster. FCM membership
values for a gene are divided among clusters
in proportion to similarity with that clusters
mean. The contribution of each gene to the
mean of a cluster is weighted, based on its
membership grade. Membership values are
adjusted iteratively until the variance of the
system falls below a threshold. These
calculations require the specification of a
degree of fuzziness parameter which is
problem specific (Dembele et. al., 2003).

iii.

The gene expression dataset might
be noisy and incomplete
The similarity measurement between
genes is continuous and there is no
clear cutoff value for group
membership
A gene might behave similarly to
gene1 under a set of samples and
behave similarly to another gene2
under another set of samples.
Therefore, there is a great need for a
fuzzy clustering method, which
produces clusters in which genes can
belong to a cluster partially and to
multiple clusters at the same time
with different membership degrees.

The main objective of using this method is
to minimize the objective function value so
that the highly suppressed genes and highly
expressed genes are clustered separately and
also it helps to diagnose at an early stage of
tumor formation.

6

Based on the numerical results PFCM is
more accurate than FCM.
The steps of the PFCM algorithm are given
as follows:
Step 1: Initialize the cluster centroids
wj (2  j  c),v(v  0),
fuzzification parameter,
m (1  m   ),
and the value   0. Gives a fuzzy
C-partition  ( 0 ) and t=1.

4.1. Penalized Fuzzy C-Means Algorithm
Another
strategy
for
fuzzy
clustering, called the penalized Fuzzy CMeans (PFCM) algorithm, with the addition
of a penalty term was proposed by Yang
(Yang, 1993 &Yang, 1994). Yang made the
fuzzy extension of the Classification
Maximum Likelihood (CML) procedure in
conjunction with fuzzy C-partitions and
called it a class of fuzzy CML procedures.
The idea of penalization is also important in
statistical learning. Combining the CML
procedure and penalty idea, Yang (Yang,
1993) added a penalty term to the FCM
objective function JFCM and then extended
the FCM to the so-called Penalized FCM
(PFCM) which produces more meaningful
and effective results than the FCM
algorithm. Thus, the PFCM objective
function is defined as follows:

Step 2: Calculate  (j t ) , w(jt ) with ( t 1) using
Eqs. (1) and (2).
Step 3: Calculate the membership matrix
 ( t )  [ui , j ]with  (jt ) , w(jt )

using Eq. (3)



c n
1c n m
2 1
JPFCM ui, j || xi wj ||  vuim, j lnj
2 j1 i1
2 j1 i1

1 c n m
 JFCM vui, j lnj
2 j1 i1

(
5. EXPERIMENTAL RESULTS

where  j is a proportional constant of
class j and v (≥ 0) is a constant. The penalty
term  1 v   u ln  is added to the
c

n

j1

i1

m
i, j

2

The effectiveness of the algorithms
based on cluster validity measure is
demonstrated in this section.

j

objective function, when v=0, JPFCM is equal
to JFCM.
αj, wj and
ui,j are defined as
n
u im, j

 j  c i 1 n
, j  1, 2,..., c
m
ui, j

(1)
j 1 i 1
wj 

n

1
n

 u 

 u 

m

i, j

xi

5.1. Data Source
A set of gene expression data that
contains a series of gene expression
measurements of the transcript (mRNA)
levels of brain Tumor gene is used in this
paper to analyze the efficiency of the
proposed approach.
The brain tumor dataset is taken
from
the
Broad-Institute
website
(http://www.broadinstitute.org/cgibin/cancer/datasets.cgi). The dataset is titled
as “Gene Expression-Based Classification
and Outcome Prediction of Central Nervous

(2)

m i 1

i, j

i 1

ui, j






Step 4: Compute   max |  (t 1)   ( t ) | .
If    , and , t  t  1 go to Step 2;
otherwise go to Step 5.
(
Step 5: Find the results1for the final class
centroids.
)

 c || x  w || 2 v ln 
i
j
j
 
 l 1 || x  w || 2 v ln 
i
l
l





1 /( m 1)

1 /( m 1)

1

 (3)



7

System Embryonal Tumors”. The Datasets
Consists of three types of Brain Tumors data
namely Medulloblastoma classic and
desmoplastic, Multiple Brain tumors,
Medulloblastoma treatment outcome. Each
dataset contains nearly 7000 genes with 42
samples.
In order to evaluate the proposed
algorithm, we applied it to the Brain Tumor
gene expression data taken from Broad
Institute by taking 7129, 5000, 3000, and
1000 genes for all samples with various
numbers of clusters.

above mentioned validity measures and the
effectiveness of the proposed algorithm is
well understood. We tested our method for
the Brain Tumour gene expression dataset to
cluster the highly suppressed and highly
expressed genes and are depicted for various
dataset sizes. It is observed that for each set
of genes taken, the value of validity
measures for the proposed algorithm is
lower than the value of validity measures for
other algorithms and it is graphically
illustrated from Figure 1 to Figure 12.
Among
these
clustering
algorithms
Penalized Fuzzy C-Means produces better
results in identification of differences
between data sets. This helps to correlate the
samples according to the level of gene
expression.

5.2. Comparative Analysis
A comparative study of the
performance of K-Means (Tou et. al. 1974),
Rough K-Means (Peters, 2006) and Fuzzy
C-Means (Peters, 2006) is made with
Penalized Fuzzy C-Means algorithm (Shen
et. al, 2006).

In terms of MAE, Penalized Fuzzy
C-Means shows superior performance and
K-Means and rough K-Means exhibits better
performance than Fuzzy C-Means.

Cluster Validation
In this paper, Root Mean Square
Error, Mean Absolute Error and Xie-Beni
validity index are used to validate the
clusters obtained after applying the
clustering algorithms. To assess the quality
of our method, we need an objective
external criterion. In order to validate our
clustering results, we employed Root Mean
Square Error (RMSE), Mean Absolute Error
(MAE) (Pablo de Castro et. al., 2007).
Xie-Beni validity index has also been
chosen as the cluster validity measure
because it has been shown to be able to
detect the correct number of clusters in
several experiments (Pal et. al. 1995).

Also, With respect to RMSE and
Xie-Beni Index Penalized Fuzzy C-Means
produces greater performance than the other
algorithms.
The comparative results based on
Root Mean Square Error, Mean Absolute
Error and Xie-Beni validity measure for all
the Gene expression data clustering
algorithms for various Brain Tumor data sets
taken with different number of clusters are
enumerated in Table 1.
Figure 1 to Figure 3 shows the
comparative analysis of various approaches
for 7129 genes taking K as 7, 5 and 3
respectively. It can be observed from the
figures,
Penalized
Fuzzy
C-Means
outperforms other approaches Fuzzy CMeans, Rough K-Means and K-Means.

K Means, Rough K-Means, Fuzzy C-Means
and Penalized Fuzzy C-Means clustering
algorithm are applied and analysed for Brain
Tumour genes.
Table.1 shows the experimental
results that are obtained by applying the
8

Data Set Size=7129
k=7

Value of Valididty Measures

Value of Valididty Measures

1.2
1
0.8
0.6
0.4
0.2
0

FCMeans
RKMeans
KMeans
MAE

RMSE

XB

PFCMeans

1.2
1
0.8
0.6
0.4
0.2
0

Value of Valididty Measures

Value of Valididty Measures

FCMeans
RKMeans
KMeans
XB

PFCMeans

1.2
1
0.8
0.6
0.4
0.2
0

FCMeans

0.4

RKMeans

Value of Valididty Measures

Value of Valididty Measures

0.6

KMeans
MAE

RMSE

XB

PFCMeans

FCMeans
RKMeans
KMeans
RMSE

XB

PFCMeans

Figure5: Validity Measure for Data set size = 5000, k=5

Data Set Size=7129
k=3

0.2
0

XB

Validity Measures

Figure 2: Validity Measure for Data set size =7129, k=5

0.8

RMSE

Data Set Size=5000
k=5

MAE

Validity Measures

1

KMeans

Figure4: Validity Measure for Data set size =5000, k=7

Data Set Size=7129
k=5

RMSE

RKMeans

Validity Measures

Figure 1: Validity Measure for Data set size = 7129, k=7

MAE

FCMeans

MAE

Validity Measures

1.2
1
0.8
0.6
0.4
0.2
0

Data Set Size=5000
k=7

PFCMeans

1
0.8

Data Set Size=5000
k=3

0.6
0.4

FCMeans

0.2

KMeans

RKMeans

0
MAE

RMSE

XB

PFCMeans

Validity Measures

Validity Measures
Figure 3: Validity Measure for Data set size = 7129, k=3

Figure6: Validity Measure for Data set size =5000, k=3

Figure 4 to Figure 6 shows the
comparative analysis of various approaches
for 5000 genes taking K as 7, 5 and 3
respectively. The experimental result shows
that the Penalized Fuzzy C-Means
outperforms other approaches Fuzzy CMeans, Rough K-Means and K-Means.

Figure 7 to Figure 9 shows the
comparative analysis of various approaches
for 3000 genes taking K as 7, 5 and 3
respectively. The experimental result shows
that the Penalized Fuzzy C-Means gives
better results than the other algorithms.

9

Data Set Size=3000
k=7

3

Value of Valididty
Measures

Value of Valididty Measures

4

FCMeans

2

RKMeans

1

KMeans

0
MAE

RMSE

XB

PFCMeans

3
2.5
2
1.5
1
0.5
0

Value of Valididty
Measures

Value of Valididty Measures

FCMeans
RKMeans

0.5

KMeans

0
MAE

RMSE

XB

PFCMeans

4
3

PFCMeans

Data Set Size=1000
k=5
FCMeans
RKMeans

1

KMeans

0
MAE

RMSE

XB

PFCMeans

Validity Measures

Figure8: Validity Measure for Data set size =3000, k=5

Figure 11: Validity Measure for Dataset Size =1000, k=5

Data Set Size=3000
k=3

Value of Valididty Measures

Value of Valididty
Measures

XB

2

Validity Measures

1.2
1
0.8
0.6
0.4
0.2
0

KMeans

Figure10: Validity Measure for Data set size =1000,
k=7

Data Set Size=3000
k=5

1

RKMeans

Validity Measures

Figure 7: Validity Measure for Data set size = 3000, k=7

1.5

FCMeans

MAE RMSE

Validity Measures

2

Data Set Size=1000
k=7

FCMeans
RKMeans
KMeans
PFCMeans
Validity Measures

1.5

Data Set Size=1000
k=3

1

FCMeans
RKMeans

0.5

KMeans
0
MAE

RMSE

XB

PFCMeans

Validity Measures
Figure12: Validity Measure for Data set size =1000, k=3

Figure 9: Validity Measure for Data set size = 3000, k=3

Figure 10 to Figure 12 shows the
comparative analysis of various approaches
for 1000 genes taking K as 7, 5 and 3
respectively. The experimental result shows
that the Penalized Fuzzy C-Means performs
better than the other algorithms

10

Table 1: Performance Analysis of K-Means, Rough K-Means, Fuzzy C-Means and Penalized Fuzzy C-Means

No. of

No. of

Clusters

Genes

7

5

3

7

7129

5000

3000

1000

Root Mean

Mean

Square

Absolute

Error

Error

K-Means

0.0019

0.0044

0.2804

Rough K-Means

0.0511

0.0874

0.0020

Fuzzy C-Means

1.0438

0.8627

0.9548

Penalized Fuzzy C-Means

0.0043

0.0009

0.0001

K-Means

0.0034

0.0074

0.4798

Rough K-Means

0.0624

0.4654

0.0581

Fuzzy C-Means

1.0336

0.7504

0.0184

Penalized Fuzzy C-Means

0.0255

0.0015

0.0002

K-Means

0.0065

0.0150

0.1240

Rough K-Means

0.0336

0.0082

0.0203

Fuzzy C-Means

0.9925

0.6331

0.0624

Penalized Fuzzy C-Means

0.0079

0.0002

0.0001

K-Means

0.0225

0.0470

0.4994

Rough K-Means

0.1204

1.0548

0.1079

Fuzzy C-Means

1.8542

2.7108

0.1107

Penalized Fuzzy C-Means

0.0056

0.0015

0.0001

Clustering Algorithms

Xie-Beni
Index

Table .2 Parameter setting and other issues

Clustering
Algorithm

Cluster
Membership

Input

Proximity
Measure

K-Means

Binary

Starting Prototype,
Stopping Threshold, K

Pair wise
Distance

Rough K-Means

Rough
Membership

Starting Prototype,
Stopping Threshold, K

Pair wise
Distance

Fuzzy C-Means

Fuzzy
Membership

Degree of fuzziness,
Starting Prototypes,
Stopping Threshold, K

Pair wise
Distance

Penalized Fuzzy
C-Means

Improved Fuzzy
Membership

Fuzzification Parameter,
K

Pair wise
Distance

11

Other Issues
Very Sensitive to Input
parameters and order of
Input
Imprecision in Gene
Expression data can be
captured
Careful interpretations
of membership values.
Sensitive to Input
parameters and order of
Input
Quality of membership
is increased by
introducing Penalty
term

Pattern Analysis
The parameter setting and other
issues of the clustering approaches which
are discussed are given in Table.2.

For each gene, red indicates a high
level of expression (highly expressed Genes)
relative to the mean; green indicates a low
level of expression (highly suppressed
Genes) relative to the mean.

Transcriptional Initiation is the most
important mode for control of gene
expression
level.
Suppressed
gene
expression level may be stimulated by gene
therapy (i.e.) promoter insertion or up
regulation of suppressed gene and radiation
therapy (i.e.) more amount of radiation may
cause sudden mutation in gene, due to this
sudden change the gene expression may be
in high level. This helps to correlate the
samples according to the level of gene
expression. When precise functions for over
or under expressed genes are determined,
new avenues for intervention strategies may
emerge. These studies are in their infancy;
however,
the
improved
technology
employed here shows reasonable promise as
our understanding of these deadly tumours
increases. Therefore, future treatment
decisions based on the expression profile of
a primary tumour is a rational approach
towards preventing the outgrowth of
metastases.

6. CONCLUSION
Cluster
analysis
applied
to
microarray measurements aims to highlight
meaningful patterns for gene expression.
The goal of gene clustering is to identify the
important gene markers. Gene expression
data are the representation of nonlinear
interactions among genes and environmental
factors. Brain Tumor is so deadly because,
it is not usually diagnosed until it has
reached an advance stage. Early detection
can help prolong or save lives, but clinicians
currently have no specific and sensitive
method. Computing analysis of these data is
expected to gain knowledge of gene
functions and disease mechanisms. We used
a set of gene expression data that contains a
series of gene expression measurements of
the transcript (mRNA) levels of Brain
Tumor gene. Highly expressed genes and
suppressed genes are identified and
clustered
using
various
clustering
techniques. The following methods such as
Post-Translational Modification, Small
RNAs and Control of Transcript Levels,
Translational Initiation, Transcript Stability,
RNA Transport, Transcript Processing and
Modification, Epigenetic Control and
Transcriptional Initiation can be used to
reduce the tumor level.
The empirical results also reveal the
importance of using Penalized Fuzzy CMeans (PFCM) clustering methods for
clustering
more
meaningful
highly
suppressed and highly expressed genes from
the gene expression data set. Meanwhile,
evaluation metrics Root Mean Square Error,

Figure 13: Clusters of Brain Tumor Genes

Figure.13 represents the Clusters of tumor
genes by Penalized Fuzzy C-Means using all
genes exhibiting variation across the data
set.
12

Mean Absolute Error and Xie-Beni Index is
adopted to assess the quality of clusters, and
the experimental results have shown that the
proposed approach is capable of effectively
discovering gene expression patterns and
revealing the underlying relationships
among genes as well. This clustering
approach can be applied for any gene
expression dataset and tumor growth can be
predicted easily.

[8]

[9]

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