GRAPHICAL MODEL AND CLUSTERINGREGRESSION BASED METHODS FOR CAUSAL INTERACTIONS: BREAST CANCER CASE STUDY

International Journal of Artificial Intelligence and Applications (IJAIA), Vol.11, No.3, May 2020
DOI: 10.5121/ijaia.2020.11302 11
GRAPHICAL MODEL AND CLUSTERING-
REGRESSION BASED METHODS FOR CAUSAL
INTERACTIONS: BREAST CANCER CASE STUDY
Suhilah Alkhalifah and Adel Aloraini
Computer Science Department College of Computer, Qassim University, Saudi Arabia
ABSTRACT
The early detection of Breast Cancer, the deadly disease that mostly affects women is extremely complex
because it requires various features of the cell type. Therefore, the efficient approach to diagnosing Breast
Cancer at the early stage was to apply artificial intelligence where machines are simulated with
intelligence and programmed to think and act like a human. This allows machines to passively learn and
find a pattern, which can be used later to detect any new changes that may occur. In general, machine
learning is quite useful particularly in the medical field, which depends on complex genomic
measurements such as microarray technique and would increase the accuracy and precision of results.
With this technology, doctors can easily diagnose patients with cancer quickly and apply the proper
treatment in a timely manner. Therefore, the goal of this paper is to address and propose a robust Breast
Cancer diagnostic system using complex genomic analysis via microarray technology. The system will
combine two machine learning methods, K-means cluster, and linear regression.
KEYWORDS
Microarray, K-means cluster, and linear regression.
1. INTRODUCTION
During the last decades, cancer has been one of the main focus and concern fields for scientists.
Cancer starts in cells which are the basic structural unit in the body. Cells of the cancer patient
are multiplying in a way that is difficult to control, those cells cause a tumor which can be benign
or premalignant. Benign tumors are usually not harmful and do not spread to other parts of the
body, which is the opposite of cancer lumps. Breast Cancer is one of the most types of cancers
which infects women, that is because of changes in lifestyle, increased age, and hormonal
disorders [1]. To study every gene in a cell, scientists spend a lot of time when they use manual
tools to monitor gene's behavior.
Alternatively, they use gene expression microarray technology to study complex relations
between various genes in genomics, thousands of genes or even every gene in an organism all at
once, [2]. The microarray technology has been widely applied to the range of machine learning
methods mainly to understand how data are obtained and analyzed [3]. Machine learning is a
branch of artificial intelligence and is an effective technique to classify data, it mostly used in
medical fields to diagnosis and treatment [4]. Moreover, Machine learning can help doctors take
accurate decisions when they discover the relationship between datasets from prior cases [5].

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In our study, we use a combination of two machine learning methods, linear regression, and k-
means. K-means is mainly used to find groups based on similarity and dissimilarity in the data
while the main purpose of using linear regression is to predict the amount of relationship between
variables obtained from the set of data [6]. In addition to its simplicity and capacity to interpret
the coefficients as interactions in the underlying network [7]. This study will be as a contribution
to what exists in the literature for feature selection research, as well.
The rest of the paper is organized as follows: Section 2 presents an overview of DNA-Microarray
and reviewed several previous studies that use machine learning to microarray data analysis.
Section 3 provides a description of the methods and software utilized in this study. Section 4
shows the different results found. For each result, we provide scientific reasons from our
perspectives on whether we accept the result or not. Section 5 concludes the paper.
2. RELATED WORK
Microarray technology has rapidly established a critical site in cancer research since 1996 [8].
The capacity of microarrays becomes the main attraction for molecular biologists. By
observation of the expressional behavior of the genes under various experiments [9]. In addition,
a microarray can be applied in a variety of fields such as drug discovery, genetics, and
microbiology [10]. The purpose of using a microarray differs from one researcher to another. For
example, the researcher may interest in finding the small change in gene expression that affects
phenotype. Another researcher may interest in understanding the architecture of genetic from the
whole gene expression that describes the mechanisms of transcription control in a cell [11]. The
accurate result depends on the careful design of the experiment and the appropriate selection for
the machine learning methods to extract the relationships between genes [12].
Through machine learning methods, it is possible to obtain an early diagnosis of cancer disease
from data that is collected by microarray gene expression technology [13]. Machine learning
methods can help doctors to make the correct decisions from discovering the relationship
between cases and predict the disease results using similar previous cases [5]. There are many
types of machine learning methods that can be applied to analyzing big data. For example, in
[14], the authors review two types of machine learning methods, which are Decision Trees and
Artificial Neural Networks. Using these methods can explore microarray data in a quick way.
The result was Decision Trees outperformed Artificial Neural Networks, because of Decision
Trees can inspect the result by humans directly. In a study [15], compared the performance of
several classification methods on different microarray datasets. Classification methods include
Support Vector Machine, Decision Tree, Radial basis function Neural Nets, Bayesian, Multi-
layer perceptron Neural Nets, and Random Forrest. The results reported the importance of
accurate classification was related to feature selection and the number of genes and samples. As
well in [16], the authors compared different classification methods which are Support Vector
Machine, Structure Adaptive Self-organizing map, K-Nearest Neighbor, and Multi-Layer
Perceptron. The results indicate a link between classifiers and features, which act as a guide to
choosing the best method for bioinformatics problems.
In our study, we focused on researches that used linear regression and K-means methods to
analyze microarray data. We have obtained a set of research that used one of these methods
without combined them for example, in [17], the authors obtain prior knowledge of genes from
the Gene Ontology database to improve the regression model. This model assumes the similarity
of weights between genes to reduce the errors of regression that arise from the spread data. [2] is
another study about microarray data analysis, where the authors improve a new method called
linear regression-based feature selection to obtain for accurate classification of a dataset by using
fewer features. In [18], using K-means clustering to compare various types of initialization value

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and distance to classify the patients depend on the attributes of breast cancer. There is another
study in [19], the authors evaluated different types of clustering algorithms to help scientists to
get the best group of a gene. The best algorithm was Diana that gave the best number of clusters.
In [20], applied K-means and K-nearest-neighbor on data of gene expression to predicting breast
cancer survival. The fitting calibration slope gave the best outcome. In a study [21], the authors
presented a new method to avoid the error in a number of clusters. This method applied to yeast
data and it gave a great result.
There are two important objectives for gene expression data which are the identification of
differentially expressed genes and clustering of genes. With linear regression, we can predict the
relationship between gene expression data [22], and with the clustering method we can find out
biological meaningful groups. Such groups are helpful for further studies including gene function
and regulation [9]. However, there are only limited related studies have been combined between
linear regression and K-means clustering. To the best of our knowledge, there are only two
studies [23], [24]. Those studies used the same method, clustering of the regression model, with a
different dataset. This method applies regression on gene expression then assumes gene clusters
depending on regression coefficients similarity. It can apply in a complex experiment and it will
provide an accurate cluster. However, K-means is more useful to examine the data that do not
have prior knowledge in correlations between genes such as in our case.
3. METHODOLOGY
A. K-means Clustering
K-means clustering is an unsupervised learning algorithm mostly used with unlabeled data to
solve clustering problems. It can be defined as the task of finding subgroups in datasets that are
very similar while data in other clusters are very different.
K-means clustering follows a simple procedure to classify any dataset into a number of clusters
by initially selecting the number of clusters and based on this the centroids are randomly set.
Each data point is assigned to the nearest centroid. The centroid is updated based on the data
points in the cluster until it reaches a limit when there is no change in the cluster's data [25]. In
the following, we provide details on how the k-means algorithm works.

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As we see the steps to implement the algorithm are:
1. The number of clustering is given (k).
2. Initialization step:
i) Randomly select the cluster center (vj)
3. Iteration step:
i) Calculate the distance between the centers and each point using Euclidean distance.
Where ||xi - vj|| is the Euclidean distance between xi (the set of data points) and vj (the set
of centers), ci is the number of data points in ith cluster, c is the number of cluster centers.
ii) Assign the data point to the nearest cluster center.
iii) Recalculate the new cluster center using vj.
iv) Repeat until no data point was reassigned.
B. Linear Regression
Linear Regression is a method for predicting the relationship between variables. The value of
the dependent variable is based on the given independent variable. It is relatively considered a
simple and most useful algorithm. There are different types of linear regressions, simple linear
regression and multiple linear regression are some of them. Throughout this study, we focus on
multiple linear regression. The equation of multiple linear regression is: Y=β0+β1x1+ β2x2+ε
[26].
In this study:
 Y represents the effect variable.
 Xs represents the causal variables.
 β represents the coefficient value. The coefficient value represents the amount of the
correlation e.g. if the coefficient value is high that means there is a high correlation
between these two genes and vice versa.
 The sign represents the type of correlation. e.g. if the sign is positive that means there is
a positive correlation between those two genes, in another word, if the value of one gene
is increased the value of another gene will be increased as well and conversely in the
inverse correlation, if the value of one gene is increased the value of another gene will be
decreased.
C. WEKA Software
WEKA stands for Waikato Environment for Knowledge Analysis, and it was developed at
Waikato University in New Zealand. It is open-source software written in Java and used for data
mining tasks. WEKA includes a library of the machine learning algorithm, such as clustering,
regression, and classiﬁcation [27]. The main advantages of using WEKA in this research is that it
is freely available, easy to use by providing a user-friendly GUI, and has a large collection of
data preprocessing and modeling methods [28]. The WEKA version used in this study is version
3.8.2 installed on Windows 7.
D. Dataset
The dataset, that contains 209 Breast Cancer samples were obtained from [29] via microarray
technology. Due to the limitation of our hardware, especially in WEKA memory. We just
included 30 samples. Fig. 1 shows our dataset, in which the first column represents the name of
genes, and the rest of the columns represent gene expressions.

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Fig.1 Dataset
4. RESULT
A. K-means Experiments
Initially, we applied K-means algorithm to find groups based on similarity and dissimilarity in
the dataset. To do this work we applied some experiments until we got a satisfactory result.
First, we start with the all gene in the dataset (30 genes) and we use two clusters to found the
largest number of associated genes. The result was: (MAPK3- DUSP1-MAPK11 - RELA -
PDGFA - RPS6KA1 - MAP2K1 - MAP2K2 - MAPT - MAPK9 - MKNK2 - FGFR4 - DUSP2 -
MAP3K3 - CDC25B - IL1R1 - NFKB1) in cluster one, and (IL1A - BDNF - FGFR2 - MOS -
TRAF6 - PRKCB - NF1 - PAK2 - TGFB2 - MAP3K13 - MAP3K5 - NTRK2 - FGF7) in cluster
two. We remove MAPK3 and IL1A, which represents a class of gene name in WEKA, because
we have identified the genes associated with them. Then we repeat the same operation for all
remained genes.
Second, we applied the same previous experiment with a minor change, in which we removed
one gene at a time from the most numerous clusters. This is the most efficient approach, to get an
accurate result from the previously discussed results, because we give more chance for each
gene.
From the first and second experiments, gene RPS6KA1 for example associated with (MAP2K1 -
MAP2K2 - MAPK9 - MKNK2 - FGFR4 - MAP3K3 - CDC25B - IL1R1 - NFKB1) in the first
experiment, while the same gene associated with (MAP2K1 - MAP2K2 - MAPT - MAPK9 -
MKNK2 - FGFR4 - DUSP2 - MAP3K3 - CDC25B - IL1R1 - NFKB1) in the second experiment.
We observed a difference in the genes associated with it, such as there is an association with
MAPT and DUSP2 in the second experiment but it is not shown in the first experiment. Another
example is NF1 associated with (PAK2 - TGFB2 - MAP3K13 - MAP3K5 - NTRK2 - FGF7) in
the first experiment, while the same gene associated with (PAK2 - TGFB2 - MKNK2 -
MAP3K13 - FGFR4 - DUSP2 - MAP3K5 - MAP3K3 - NTRK2 - FGF7) in the second
experiment. There is an association with MKNK2, FGFR4, DUSP2 and MAP3K3 in the second
experiment but it is not existing in the first experiment. When we realized different results, we
decided to try an alternative operation due to the following reasons:

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 When we remove one or two genes from the dataset, the number of associations for the
remaining genes is reduced.
 In each step, we set two clusters. However, this does not mean that the two clusters are
an optimal number of clusters. This obviously happens due to a weakness in the K-means
method.
In the following, we started from the largest number of clusters, i.e. 29 clusters to the least
number of clusters, i.e. 2 clusters and we do not remove any gene from the dataset. In each step,
we extracted the genes that have more associated with each other. For example, when we
specified the number of clusters to 29, we observed MOS and NF1 belong to the same cluster
(which is cluster number 12) and each other gene in a separate cluster, as shown in Fig. 2.
Fig.2 A Result of Cluster Number 29
We Applied The Same Operation For All Possible Number Of Clusters And We Get The Result
Shown In Table 2.
Table 2. A Result Of The Third Experiment Using K-Means
Cluster Number Cluster Result Associations
29 Cluster 1 MOS - NF1
Cluster 2 TRAF6 - MAP3K5
Cluster 3 MAPT - DUSP2
Cluster 4 RELA - MAP2K1
Cluster 5 MAPK3 - CDC25B

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Cluster 6 IL1A – BDNF
Cluster 2 TRAF6 - MAP3K5 - PAK2
22 Cluster 1 MOS - NF1 - NTRK2
Cluster 7 FGFR4 - MAP3K3
Cluster 7 FGFR4 - MAP3K3 - MKNK2
Cluster 8 MAPK11 – PDGFA
Cluster 9 MAP3K13 - FGF7
17 Cluster 1 MOS - NF1 - NTRK2 - TGFB2

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Cluster 4 RELA - MAP2K1 - MAP2K2
Cluster 5 MAPK3 - CDC25B - RPS6KA1
Cluster 2 TRAF6 - MAP3K5 - PAK2 - FGFR2
Cluster 7 FGFR4 - MAP3K3 - DUSP1
Cluster 8 MAPK11 – PDGFA - MKNK2 (changing cluster)
12 Cluster 1 MOS - NF1 - NTRK2 - TGFB2 – PRKCB
Cluster 8 MAPK11 – PDGFA - MKNK2
11 Cluster 1 MOS - NF1 - NTRK2 - TGFB2 - PRKCB - MAP3K13
(changing cluster)

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Cluster 9 FGF7
10 Cluster 1 MOS - NF1 - NTRK2 - TGFB2 - PRKCB - MAP3K13 -
IL1A - BDNF (changing cluster)- FGF7 (changing
cluster)
IL1A - BDNF - FGF7
Cluster 3 MAPT - DUSP2 - FGFR4 - MAP3K3 - DUSP1 (changing
cluster)
IL1A - BDNF - FGF7
Cluster 3 MAPT - DUSP2 - FGFR4 - MAP3K3 - DUSP1 - MKNK2
(changing cluster)
Cluster 4 RELA - MAP2K1 - MAP2K2 - MAPK11 - PDGFA
(changing cluster)
IL1A - BDNF - FGF7
Cluster 5 MAPK3 - CDC25B - RPS6KA1 - NFKB1
IL1A - BDNF - FGF7 - TRAF6 - MAP3K5 - PAK2 -
FGFR2 (changing cluster)
FGFR2
Cluster 3 RELA - MAP2K1 - MAP2K2 - MAPK11 - PDGFA -
MAPK9
FGFR2
Cluster 2 MAPT - DUSP2 - FGFR4 - MAP3K3 - DUSP1 - MKNK2 -
RELA - MAP2K1 - MAP2K2 - MAPK11 - PDGFA -
MAPK9 (changing cluster)
FGFR2

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MAPK9
Cluster 3 MAPK3 - CDC25B - RPS6KA1 - NFKB1 - IL1R1
FGFR2
MAPK9 - MAPK3 - CDC25B - RPS6KA1 - NFKB1 -
IL1R1 (changing cluster)
Now we define the associations of each gene from Table 2 according to genes that are frequently
associated together in the largest number of clusters.
First group: MOS - NF1 - NTRK2 - TGFB2 – PRKCB
The association between MOS and NF1 appeared at the beginning when we applied 29 clusters
until NTRK2 joined to them when the number of clusters became 22. In the cluster number 17,
TGFB2 joined. The last gene joined to the group was PRKCB at the cluster number 12.
Second group: TRAF6 - MAP3K5 - PAK2 - FGFR2
TRAF6 and MAP3K5 associate together in cluster number 28. Then PAK2 joined when
clustering number 23. The last gene joined to the group was FGFR2 at the cluster number 12.
This group is repeated until cluster number 6.
Third group: MAPT - DUSP2
MAPT and DUSP2 associated together from cluster number 27 until 10. Then, other genes joined
to them.
Fourth group: RELA - MAP2K1 - MAP2K2 - MAPK11 - PDGFA - MAPK9
The association between RELA and MAP2K1 appeared at cluster number 26. Then, MAP2K2
joined them in cluster number 16. This group is repeated until cluster number 8, then MAPK11
and PDGFA joined to them. The last gene joined to the group was MAPK9 at cluster number 5.
Fifth group: MAPK3 - CDC25B - RPS6KA1 - NFKB1 - IL1R1
MAPK3 and CDC25B associate together in cluster number 25. Then RPS6KA1 joined when
clustering number 15. In the cluster number 7, NFKB1 is joined. The last gene joined to the
group was IL1R1at the cluster number 3.
Sixth group: IL1A – BDNF
IL1A and BDNF associated together from cluster number 24 until 11. Then, they joined to other
genes.
Seventh group: FGFR4 - MAP3K3 - DUSP1 - MKNK2
The association between FGFR4 and MAP3K3 appeared at cluster number 21. Then, MKNK2
joined to them in cluster number 20, but in cluster number 13 MKNK2 change his group until
cluster number 9 then it returned to this group. MKNK2 belongs to this group because the
number of times it appears in this group is more than the other group (it appeared in this group 11
times while in another group just 4 times). The last gene joined to the group was DUSP1 at the
cluster number 13.
Eighth group: MAP3K13 - FGF7
The association between MAP3K13 and FGF7 appeared at cluster number 18 until 12. Then,
they joined to other genes.
B. Linear Regression Experiment
After we extracted the gene groups, we applied the linear regression method to interpret the
correlation coefficients. In WEKA, we adjusted some settings to know the correlation
coefficients among all genes in one group. When we selected the linear regression method, we
set the attribute selection method field to NO attribute. Table 2 shows the results:

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Table 2. A Result Of Experiment Using Linear Regression
Group Number Y Xs Correlation Value (β)
1 MOS PRKCB -0.25
NF1 +0.5545
TGFB2 -0.0233
NTRK2 +0.2113
PRKCB MOS -0.1207
NF1 +0.8328
TGFB2 +0.0741
NTRK2 +0.1635
NF1 MOS +0.2351
PRKCB +0.7315
TGFB2 +0.1283
NTRK2 -0.0953
TGFB2 MOS -0.0511
PRKCB +0.3363
NF1 +0.6625
NTRK2 +0.3698
NTRK2 MOS +0.3622
PRKCB +0.5807
NF1 -0.3851
TGFB2 +0.2895
2 TRAF6 PAK2 -0.0033
FGFR2 +0.2302
MAP3K5 +0.1608
PAK2 TRAF6 -0.035
FGFR2 -0.3851
MAP3K5 -0.1115
FGFR2 TRAF6 +0.7766
PAK2 -0.1234
MAP3K5 -0.3446
MAP3K5 TRAF6 +0.90
PAK2 -0.168
FGFR2 -0.90
3 DUSP2 MAPT +0.2872
MAPT DUSP2 +0.7159
4 MAPK11 RELA +0.0624
PDGFA +0.5131
MAP2K1 -0.1363
MAP2K2 -0.0606
MAPK9 -0.1693
RELA MAPK11 +0.175
PDGFA +0.0272
MAP2K1 -0.0059
MAP2K2 +0.3966
MAPK9 -0.0204
PDGFA MAPK11 +0.9894
RELA +0.0187
MAP2K1 -0.2666
MAP2K2 -0.2754
MAPK9 +0.0528
MAP2K1 MAPK11 -0.2148
RELA -0.0033

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PDGFA -0.2179
MAP2K2 -0.322
MAPK9 -0.1184
MAP2K2 MAPK11 -0.058
RELA +0.1354
PDGFA -0.1368
MAP2K1 -0.1957
MAPK9 -0.2321
MAPK9 MAPK11 -0.9496
RELA -0.0408
PDGFA +0.1536
MAP2K1 -0.4216
MAP2K2 -0.90
5 MAPK3 RPS6KA1 +0.1622
CDC25B +0.1976
IL1R1 -0.0957
NFKB1 +0.1103
RPS6KA1 MAPK3 +0.1561
CDC25B +0.118
IL1R1 +0.0215
NFKB1 +0.0773
CDC25B MAPK3 +0.8836
RPS6KA1 +0.5479
IL1R1 +0.0616
NFKB1 +0.2324
IL1R1 MAPK3 -0.90
RPS6KA1 +0.2643
CDC25B +0.1634
NFKB1 -0.0921
NFKB1 MAPK3 +0.0909
RPS6KA1 +0.0662
CDC25B +0.0428
IL1R1 -0.0064
6 IL1A BDNF +0.7658
BDNF IL1A +0.7731
7 DUSP1 MKNK2 +0.1864
FGFR4 +0.1538
MAP3K3 +0.2045
MKNK2 DUSP1 +0.5298
MAP3K3 +0.4731
FGFR4 +0.2693
FGFR4 DUSP1 +0.0882
MKNK2 +0.0544
MAP3K3 +0.9066
MAP3K3 DUSP1 +0.0681
MKNK2 +0.0554
FGFR4 +0.5262
8 MAP3K13 FGF7 +0.7071
FGF7 MAP3K13 +0.5845
C. Graphical Representation for Genes Associations
After we applied the K-means method, we got the associations between genes in our dataset.
Then, in the linear regression method, we specified the amount of those associations. One of the

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most representative methods for gene associations is a graphical model representation. Based on
our results, we plotted Fig.3 which shows genes association produced from the K-means method.
The numerated arrows in this figure represent the amount of those associations produced from
the linear regression method.
Fig.3 Graphical Representation for Genes Associations
The most significant finding based on the results discussed above is the correlation between two
genes, similar in signals while the numbers are different in most cases. We explain those
correlations for each group in detail.
G1: MOS and NF1have a positive correlation and the effect of NF1 on MOS more because it has
the highest correlation's value. MOS and PRKCB have a negative correlation and a weak effect
on some of them because they have a low correlation value. MOS and TGFB2 have the same
correlation between MOS and PRKCB. MOS and NTRK2 have a positive correlation and a
weak effect on some of them because they have a low correlation value.
NF1 and TGFB2 have a positive correlation and the effect of NF1 on TGFB2 more because it has
the highest correlation's value. NF1 and NTRK2 have a negative correlation and a weak effect on
some of them because they have a low correlation value. NF1 and PRKCB have a positive
correlation and a strong effect on some of them because they have a high correlation value.
TGFB2 and NTRK2 have a positive correlation and a weak effect on some of them because they
have a low correlation value. TGFB2 and PRKCB have the same correlation between TGFB2
and NTRK2.
NTRK2 and PRKCB have a positive correlation and effect of PRKCB on NTRK2 more because
it has the highest correlation's value.

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G2: TRAF6 and PAK2 have a negative correlation and a weak effect on some of them because
they have a low correlation value. TRAF6 and FGFR2 have a positive correlation and the effect
of TRAF6 on FGFR2 more because it has the highest correlation's value. TRAF6 and MAP3K5
have a positive correlation and the effect of TRAF6 on MAP3K5 more because it has the highest
correlation's value.
PAK2 and MAP3K5 have a negative correlation and a weak effect on some of them because they
have a low correlation value. PAK2 and FGFR2 have the same correlation between PAK2 and
MAP3K5.
MAP3K5 and FGFR2 have a negative correlation and the effect of FGFR2 on MAP3K5 more
because it has the highest correlation's value.
G3: MAPT and DUSP2 have a positive correlation and the effect of DUSP2 on MAPT more
because it has the highest correlation's value.
G4: MAPK11 and RELA have a positive correlation and a weak effect on some of them because
they have a low correlation value. MAPK11 and PDGFA have a positive correlation and the
effect of MAPK11 on PDGFA more because it has the highest correlation's value. MAPK11 and
MAP2K1have a negative correlation and a weak effect on some of them because they have a low
correlation value. MAPK11 and MAP2K2 have a negative correlation and have the same effect
on some of them, this effect is weak because they have a low correlation value. MAPK11 and
MAPK9 have a negative correlation and the effect of MAPK11 on MAPK9 more because it has
the highest correlation's value.
RELA and MAP2K1 have a negative correlation and have the same effect on some of them, this
effect is weak because they have a low correlation. RELA and MAP2K2 have a positive
correlation and a weak effect on some of them because they have a low correlation value. RELA
and PDGFA have the same correlation between RELA and MAP2K2. RELA and MAPK9 have a
negative correlation and a weak effect on some of them because they have a low correlation
value.
MAP2K1 and MAP2K2 have a negative correlation and a weak effect on some of them because
they have a low correlation value. MAP2K1 and MAPK9 have the same correlation between
MAP2K1 and MAP2K2. MAP2K1 and PDGFA also have the same correlation between
MAP2K1 and MAP2K2.
MAP2K2 and MAPK9 have a negative correlation and the effect of MAP2K2 on MAPK9 more
because it has the highest correlation's value. MAP2K2 and PDGFA have a negative correlation
and a weak effect on some of them because they have a low correlation value.
MAPK9 and PDGFA have a positive correlation and a weak effect on some of them because they
have a low correlation value.
G5: MAPK3 and RPS6KA1 have a positive correlation and have the same effect on some of
them, this effect is weak because they have a low correlation. MAPK3 and CDC25B have a
positive correlation and the effect of MAPK3 on CDC25B more because it has the highest
correlation's value. MAPK3 and IL1R1 have a negative correlation and the effect of MAPK3 on
IL1R1 more because it has the highest correlation's value. MAPK3 and NFKB1 have a positive
correlation and a weak effect on some of them because they have a low correlation value.

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RPS6KA1 and IL1R1 have a positive correlation and a weak effect on some of them because
they have a low correlation value. RPS6KA1 and CDC25B have a positive correlation and the
effect of RPS6KA1 on CDC25B more because it has the highest correlation's value. RPS6KA1
and NFKB1 have a positive correlation and a weak effect on some of them because they have a
low correlation value. IL1R1 and CDC25B have a positive correlation and a weak effect on some
of them because they have a low correlation value. IL1R1 and NFKB1 have a negative
correlation and a weak effect on some of them because they have a low correlation value.
CDC25B and NFKB1 have a positive correlation and a weak effect on some of them because
they have a low correlation value.
G6: IL1A and BDNF have a positive correlation and have the same effect on some of them, this
effect is strong because they have a high correlation value.
G7: DUSP1 and FGFR4 have a positive correlation and a weak effect on some of them because
they have a low correlation value. DUSP1 and MAPK3K3 have the same correlation between
DUSP1 and FGFR4. DUSP1 and MKNK2 have a positive correlation and the effect of DUSP1
on MKNK2 more because it has the highest correlation's value.
FGFR4 and MAPK3K3 have a positive correlation and the effect of MAPK3K3 on FGFR4 more
because it has the highest correlation's value. FGFR4 and MKNK2 have a positive correlation
and a weak effect on some of them because they have a low correlation value.
MAPK3K3 and MKNK2 have a positive correlation and the effect of MAPK3K3 on MKNK2
more because it has the highest correlation's value.
G8: MAPK3K13 and FGF7 have a positive correlation and a strong effect on some of them
because they have a high correlation value.
5. CONCLUSION
Breast Cancer is a complex disease and early detection is essential for effective treatment. In our
paper we present the gene expression correlations in graphical model using the K-means
clustering and linear regression methods. The K-means clustering is used to find out the best
subset of genes then the linear regression method is applied to predict the amount of association
between those genes. With this approach, doctors can apply the target cancer treatment to the
infected area instead of applying the treatment to the whole body, which normally results in
effecting all cells even normal once. The work we have done in this project was based on 30
cancer samples. Our future goal is work with the biggest dataset. Another possible direction for
future work is concerned with a comparison between cancer and normal samples to find out
which gene works in a different way. For example, based on our results, MAPK3K13 and FGF7
have a positive correlation and a strong effect on some of them. We want to know how
MAPK3K13 and FGF7 work in normal samples.
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