INTEGRATING NAIVE BAYES AND K-MEANS CLUSTERING WITH DIFFERENT INITIAL CENTROID SELECTION METHODS IN THE DIAGNOSIS OF HEART DISEASE PATIENTS

Sundarapandian et al. (Eds): ICAITA, SAI, SEAS, CDKP, CMCA, CS & IT 08,
pp. 125–137, 2012. © CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2511
INTEGRATING NAIVE BAYES AND K-MEANS
CLUSTERING WITH DIFFERENT INITIAL CENTROID
SELECTION METHODS IN THE DIAGNOSIS OF
HEART DISEASE PATIENTS
Mai Shouman1
, Tim Turner2
, Rob Stocker3
School of Engineering and Information Technology
University of New South Wales at the Australian Defence Force Academy
Northcott Drive, Canberra ACT 2600
1
mai_shouman@yahoo.com
2
t.turner@adfa.edu.au
3
r.stocker@adfa.edu.au
ABSTRACT
Heart disease is the leading cause of death in the world over the past 10 years. Researchers
have been using several data mining techniques to help health care professionals in the
diagnosis of heart disease. Naïve Bayes is one of the data mining techniques used in the
diagnosis of heart disease showing considerable success. K-means clustering is one of the most
popular clustering techniques; however initial centroid selection strongly affects its results.
This paper demonstrates the effectiveness of an unsupervised learning technique which is k-
means clustering in improving supervised learning technique which is naïve bayes. It
investigates integrating K-means clustering with Naïve Bayes in the diagnosis of heart disease
patients. It also investigates different methods of initial centroid selection of the K-means
clustering such as range, inlier, outlier, random attribute values, and random row methods in
the diagnosis of heart disease patients. The results show that integrating k-means clustering
with naïve bayes with different initial centroid selection could enhance the naïve bayes
accuracy in diagnosing heart disease patients. It also showed that the two clusters random row
initial centroid selection method could achieve higher accuracy than other initial centroid
selection methods in the diagnosis of heart disease patients showing accuracy of 84.5%.
KEYWORDS
Data Mining, Naïve Bayes, K-Means Clustering, Initial Centroid Selection Methods, Heart
Disease Diagnosis.
1. INTRODUCTION
The World Health Organization reported that heart disease is the first leading cause of death in
high and low income countries [1]. The European Public Health Alliance reported that heart
attacks and other circulatory diseases account for 41% of all deaths [2]. The Economical and
Social Commission of Asia and the Pacific reported that in one fifth of Asian countries, most
lives are lost to non-communicable diseases such as cardiovascular, cancers, and diabetes
diseases [3]. Statistics of South Africa reported that heart and circulatory system diseases are the
third leading cause of death in Africa [4]. The Australian Bureau of Statistics reported that heart
and circulatory system diseases are the first leading cause of death in Australia, causing 33.7% all
deaths [5].

126 Computer Science & Information Technology (CS & IT)
Motivated by the world-wide increasing mortality of heart disease patients each year, researchers
have been using data mining techniques to help health care professionals in the diagnosis of heart
disease [6-7]. Data mining is an essential step in knowledge discovery. It is the exploration of
large datasets to extract hidden and previously unknown patterns, relationships and knowledge
that are difficult to be detected with traditional statistical methods [8-12]. The application of data
mining is rapidly spreading in a wide range of sectors such as analysis of organic compounds,
financial forecasting, weather forecasting and healthcare [13].
Data mining in healthcare is an emerging field of high importance for providing prognosis and a
deeper understanding of medical data. Healthcare data mining attempts to solve real world health
problems in diagnosis and treatment of diseases [14]. Researchers are using data mining
techniques in the medical diagnosis of several diseases such as diabetes [15], stroke [16], cancer
[17], and heart disease [18]. Several data mining techniques are used in the diagnosis of heart
disease such as Naïve Bayes, Decision Tree, neural network, kernel density, bagging algorithm,
and support vector machine showing different levels of accuracies [18-24].
Naïve Bayes is one of the successful data mining techniques used in the diagnosis of heart disease
patients [22-23]. Although researchers are investigating enhancing naïve bayes performance in
classification problems [25], less research is done on enhancing naïve bayes performance in
disease diagnosis. This research investigates enhancing naïve bayes performance in the diagnosis
of heart disease patients through integrating clustering as a pre-processing step to naïve bayes
classification.
K-means clustering is one of the most popular and well know clustering techniques. Its simplicity
and good behaviour made it popular in many applications [26]. Initial centroid selection is a
critical issue in k-means clustering and strongly affects its results [27]. This paper investigates
integrating k-means clustering using different initial centroid selection methods with naïve bayes
in the diagnosis of heart disease patients. The rest of the paper is divided as follows: the
background section investigates applying data mining techniques in the diagnosis of heart
disease; the methodology section explains k-means clustering, different initial centroid selection
methods; and naïve bayes used in the diagnosis of heart disease patients; the heart disease data
section explains the data used, the results section presents the results of integrating k-means
clustering and naïve bayes; followed by the summary section.
2. BACKGROUND
Researchers have been investigating the use of statistical analysis and data mining techniques to
help healthcare professionals in the diagnosis of heart disease. Statistical analysis has identified
the risk factors associated with heart disease to be age, blood pressure, smoking [28], cholesterol
[29], diabetes [30], hypertension, family history of heart disease [31], obesity, and lack of
physical activity [32]. Knowledge of the risk factors associated with heart disease helps health
care professionals to identify patients at high risk of having heart disease.
Researchers have been applying different data mining techniques over different heart disease
datasets to help health care professionals in the diagnosis of heart disease [18-19, 22-24, 33]. The
results of the different data mining research cannot be compared because they have used different
datasets. However, over time a benchmark data set has arisen in the literature: the Cleveland
Heart Disease Dataset (CHDD).1
Naïve bayes is one of the data mining techniques showing considerable success compared to
other data mining techniques over different heart disease datasets [19, 21-23, 34]. Palaniappan
1
http://archive.ics.uci.edu/ml/datasets/Heart+Disease.

Computer Science & Information Technology (CS & IT) 127
and Awang investigated comparing different data mining techniques in the diagnosis of heart
disease patients. These techniques involved naïve bayes, decision tree, and neural network. The
results showed that the naïve bayes could achieve the best accuracy in the diagnosis of heart
disease patients [34]. Rajkumar and Reena investigated comparing naïve bayes, k-nearest
neighbour, and decision list in the diagnosis of heart disease patients. The results showed that the
naïve bayes could achieve the best accuracy in the diagnosis of heart disease patients [21].
Applying naïve bayes in diagnosing heart disease patients showed different accuracies on
different datasets that ranged between 62% and 95% [22, 34]. Cheung applied naive bayes
classifier on the Cleveland heart disease dataset showing accuracy of 81.48% [35].
Researchers are investigating enhancing naïve bayes performance in classification problems.
Ratanamahatana and Gunopulos described a selective bayesian classifier that uses only the
features that C4.5 would use in its decision tree showing that selective bayesian classifier
performs reliably better than naïve bayes on the ten tested datasets [36]. Ramana, Babu et al.
investigated integrating the naïve bayes classification technique with bagging and boosting in the
diagnosis of Liver diseases to enhance the performance of the naïve bayes classifier [25].
Although researchers are investigating enhancing naïve bayes performance, less research is done
on enhancing naïve bayes performance in the diagnosis of heart disease patients. This paper
demonstrates the effectiveness of unsupervised learning such as k-means clustering in improving
supervised learning which is naïve bayes in the diagnosis of heart disease patients.
K-means clustering is one of the most popular clustering techniques; however initial centroid
selection is a critical issue that strongly affects its results. This paper investigates applying
different methods of initial centroid selection such as range, inlier, outlier, random attribute
values, and random row methods for k-means clustering technique in the diagnosis of heart
disease patients. This paper investigates if integrating k-means clustering with naïve bayes can
enhance the classifier’s performance in diagnosing heart disease patients. Importantly, the
research involves a systematic investigation of which initial centroid selection method can
provide better performance in diagnosing heart disease patients. It also investigates if applying
different numbers of clusters can provide different performance in diagnosing heart disease
patients and which number of clusters will provide the better performance.
3. METHODOLOGY
The methodology section discusses k-means clustering with five initial centroid selection methods.
It also discusses the naïve bayes classifier used in the diagnosis of heart disease patients (Figure 1).
Naïve bayes cannot deal with continuous attributes so they need to be converted into discrete
ones, a process called discretization. Dougherty et al. carried out a comparative study between
two unsupervised and two supervised discretization methods using 16 data sets showing that
differences between the classification accuracies achieved by different discretization methods are
not statistically significant [37]. Equal frequency discretization is a popular and successful
unsupervised discretization method [38]. Previous related research has shown that this
discretization method provides marginally better accuracy when applied on the CHHD. So it is
used as a pre-processing step to convert the continuous heart disease attributes to discrete ones.
3.1 K-Means Clustering
K-means clustering is one of the most popular and well know clustering techniques because of its
simplicity and good behaviour in many applications [26, 38]. The steps used in k-means
clustering are shown in Figure 1.

Several researchers have identified that age, blood pressure and cholesterol are critical risk factors
associated with heart disease [28, 31-32] . In identifying the attributes that will be used in the
clustering, these attributes are obvious clustering attributes for heart disease patients. The number
of clusters used in the k- means in this investigation ranged between two and five clusters. The
difference between the initial centroid methods is discussed in the following section.
Figure 1: Integrating K-means Clustering and Naïve Bayes
3.2 Initial Centroid Selection
Initial centroid selection is an important matter in k-means clustering and strongly affects its
results [27]. This section discusses the generation of initial centroids based on actual sample data
points using inlier method, outlier method, range method, random attribute method, and random
row method [39]
3.2.1 Inlier Method
In generating the initial K centroids using inlier method the following equations are used:
Ci = Min (X) – i where 0≤ i ≤ k (1)
Cj = Min (Y) – j where 0≤ j ≤ k (2)
Where the initial centroid is C (ci, cj) and min (X) and min (Y) are the minimum value of attribute
X, and attribute Y respectively. K represents the number of clusters.
3.2.2 Outlier Method
In generating the initial K centroids using outlier method the following equations are used:
Ci = Max (X) – i where 0≤ i ≤ k (3)
Cj = Max (Y) – j where 0≤ j ≤ k (4)

Where the initial centroid is C (ci, cj) and max (X) and max (Y) are the maximum value of attribute
X, and attribute Y respectively.
3.2.3 Range Method
In generating the initial K centroids using range method the following equations are used:
Ci = ((Max (X) –Min (X)) / K) * n where 0≤ i ≤ k (5)
Cj = ((Max (Y) –Min (Y)) / K) * n where 0≤ j ≤ k (6)
The initial centroid is C (ci, cj). Where max (X) and min (X) are maximum and minimum values of
attribute X, max (Y) and min (Y) are maximum and minimum values of attribute Y respectively.
3.2.4 Random Attribute Method
In generating the initial K centroids using random attribute method the following equations are
used:
Ci = random(X) where 1≤ i ≤ k (7)
Cj = random(Y) where 1≤ j ≤ k (8)
The initial centroid is C (ci, cj). The values of ‘i’, and ‘j’ vary from 1 to ‘k’.
3.2.5 Random Row Method
In generating the initial K centroids using random row method the following equations are used:
I = random (V) where 1≤ V ≤ N (9)
Ci = X (I) (10)
Cj = Y (I) (11)
The initial centroid is C (ci, cj). N is the no of instances in the training dataset. X (I) and Y(I) are
the values of the attributes X and Y respectively for the instance I.
3.3 Naïve Bayes
Naïve bayes is one of the data mining techniques that show considerable success in classification
problems and specially in diagnosing heart disease patients [19, 22]. Naïve bayes is based on
probability theory to find the most likely possible classifications [26]. It is based on prior
probability of the target attribute and the conditional probability of the remaining attributes. For
the training data the prior and conditional probability are calculated for each cluster. For each
testing instance in the testing dataset, the probability is calculated with each of the target attribute
values and the target attribute value with the largest probability is then selected. The probability of
the testing instance for the target attribute value is calculated using the following formula:
P (v=ci) = P(ci) × (12)
Where v is the testing instance, ci is the target attribute value, aj is a data attribute and vj is its
value [38].
3.4 10 Fold Cross Validation
To measure the stability of the performance of the proposed model the data is divided into training
and testing data with 10-fold cross validation. The sensitivity, specificity, and accuracy are
calculated. The sensitivity is the proportion of positive instances that are correctly classified as
positive (e.g. the proportion of sick people that are classified as sick). The specificity is the
proportion of negative instances that are correctly classified as negative (e.g. the proportion of

healthy people that are classified as healthy). The accuracy is the proportion of instances that are
correctly classified [38].
Sensitivity = True Positive / Positive (13)
Specificity = True Negative / Negative (14)
Accuracy = (True Positive + True Negative) / (Positive + Negative) (15)
4. HEART DISEASE DATA
The data used in this study is the Cleveland Clinic Foundation Heart disease data set available at
http://archive.ics.uci.edu/ml/datasets/Heart+Disease. The data set has 76 raw attributes.
However, all of the published experiments only refer to 13 of them. Consequently, to allow
comparison with the literature, we restricted testing to these same attributes (see Table 1). The
data set contains 303 rows of which 297 are complete. Six rows contain missing values and they
are removed from the experiment.
Table 1: Selected Cleveland Heart Disease Data Set Attributes
Name Type Description
Age Continuous Age in years
Sex Discrete
1 = male
0 = female
Cp Discrete
Chest pain type:
1 = typical angina
2 = atypical angina
3 = non-anginal pain
4 =asymptomatic
Trestbps Continuous Resting blood pressure (in mm Hg)
Chol Continuous Serum cholesterol in mg/dl
Fbs Discrete
Fasting blood sugar > 120 mg/dl:
1 = true
0 = false
Restecg Discrete
Resting electrocardiographic results:
0 = normal
1 = having ST-T wave abnormality
2 =showing probable or define left ventricular hypertrophy by
Estes’criteria
Thalach Continuous Maximum heart rate achieved
Exang Discrete
Exercise induced angina:
1 = yes
0 = no
Old peak ST Continuous Depression induced by exercise relative to rest
Slope Discrete
The slope of the peak exercise segment :
1 = up sloping
2 = flat
3= down sloping
Ca Discrete
Number of major vessels colored by fluoroscopy that ranged
between 0 and 3.
Thal Discrete
3 = normal
6= fixed defect
7= reversible defect
Diagnosis Discrete
Diagnosis classes:
0 = healthy
1= patient who is subject to possible heart disease

5. RESULTS
The results of sensitivity, specificity, and accuracy in the diagnosis of heart disease using k-means
clustering and naïve bayes with different initial centroids selection methods and different numbers
of clusters are shown in Table 2. For the random attribute and random row methods, ten runs are
executed and the average and best for each method are calculated and shown in Table 2.
Table 2: Integrating different initial centroid selection for k-means clustering with naïve bayes in
diagnosing heart disease patients
Noof
Clusters
Initial Centroid Selection Method Sensitivity Specificity Accuracy
Noofclusters=2
Inlier Method 74.1 79.9 83.2
Outlier Method 74.3 80.9 83
Range Method 74.3 80.9 83
Random Attribute Avg 74.01 79.82 82.56
Best 73.3 82.5 84.2
Random Row Avg 74.31 80.43 83.12
Best 75.7 81.9 84.5
Noofclusters=3
Outlier Method 74.9 81.1 83.8
Range Method 78.2 78.3 84.2
Best 74.7 81.2 83.4
Random Row Avg 74.36 79.41 82.48
Best 77.6 79.1 84
Noofclusters=4
Range Method 77.4 77.1 83.2
Best 77.8 76.5 82.6
Random Row Avg 73.84 77.07 81.11
Best 75.3 78.5 82.6
Noofclusters=5
Inlier Method 72 71.8 77.9
Range Method 72 71.8 77.9
Best 70.4 78.7 80.3
Random Row Avg 69.93 76.59 78.62
Best 72.5 77.8 79.9

Table 2 shows that there is no significant difference between the accuracy of two clusters of the
inlier, outlier, and range initial centroid selection methods in the diagnosis of heart disease
patients. It also shows that the random attribute and random row methods achieved higher
accuracy than inlier, outlier, and range methods with two clusters. The best accuracy achieved is
by two clusters random row initial centroid selection method showing accuracy of 84.5% as shown
in Table 2. The sensitivity, specificity, and accuracy achieved by increasing the number of clusters
of inlier, outlier, range, random attribute and random row initial centroid selection methods are
shown in Figure 2 to 6 respectively.
The number of clusters of the inlier, outlier, and range initial centroid selection methods could
enhance their accuracy in the diagnosis of heart disease patients showing the best accuracy with
the three clusters. However increasing the number of clusters more than three clusters decreases
their accuracy in the diagnosis of heart disease patients. Also the increase shown in the accuracy
with the three clusters of the inlier, outlier, and range initial centroid selection methods is still less
than that achieved by two clusters random row initial centroid selection as shown in Figure 7.
Increasing the number of clusters of the random attribute and random row initial centroid selection
methods did not show any enhancement in their accuracy in the diagnosis of heart disease patients
as shown in Figure 7.
Figure 2: Different Number of Clusters Performance for Inlier Method
Figure 3: Different Number of Clusters Performance for Outlier Method

Figure 4: Different Number of Clusters Performance for Range Method
Figure 5: Different Number of Clusters Performance for Random Attribute Method
Figure 6: Different Number of Clusters Performance for Random Row Method

Figure 7: Different Number of Clusters Accuracy with Different Initial Centroid Selection
Methods
When comparing integrating k-means clustering and naïve bayes with traditional naïve bayes
applied previously on the same dataset, integrating k-means clustering with naïve bayes could
enhance the accuracy of naïve bayes in diagnosing heart disease patients as shown in Table 3.
Also integrating k-means clustering and naïve bayes could achieve higher accuracy than the
decision tree and bagging algorithm in the diagnosis of heart disease patients as shown in Table 3.
Table 3: Comparing integrating k-means clustering and naïve bayes with traditional naïve bayes
and other data mining techniques
Author/ Year Technique Accuracy
Cheung, N., 2001 Naïve Bayes 81.48%
Tu, et al., 2009
Decision tree 78.91%
Bagging Algorithm 81.41%
Our work
Two Clusters Random Row Initial Centroid
Selection K-Means Clustering with Naïve
Bayes
84.5%
Integrating k-means clustering with naïve bayes showed the best accuracy with the Random Row
two clusters k-means clustering naïve bayes. Why do two clusters show better performance than
other numbers of clusters in the diagnosis of heart disease patients? There is a need for an
explanation why the two clusters showed better performance than other numbers of clusters in the
diagnosis of heart disease patients. The number of instances is relatively small in the CHHD. A
larger dataset is needed to identify if two clusters will still provide the best accuracy results. Also,
the target attribute of the Cleveland heart disease dataset has two values which are health and
sick. Further investigation is also needed to identify if there is a relationship between the number
of clusters showing best accuracy results and the number of values of the target attribute.
Although a larger data set is needed to verify the results of integrating naïve bayes and k-means
clusters; however the Cleveland heart disease data is used as an initial step to be able to compare
its results with other data mining techniques results previously applied on the same data set. As a

future work investigating integrating naïve bayes and k-means clusters will be applied on a larger
data set obtained from heart disease hospital.
6. SUMMARY
Heart disease is the leading cause of death all over the world in the past ten years. Researchers
have been investigating applying different data mining techniques to help health care professionals
in the diagnosis of heart disease. Naïve bayes is one of the successful data mining techniques used
in the diagnosis of heart disease patients. This paper investigates integrating k-means clustering
with naïve bayes in the diagnosis of heart disease patients. Initial centroid selection is a critical
issue that strongly affects k-means clustering results. This paper systematically investigates
applying different methods of initial centroid selection such as range, inlier, outlier, random
attribute values, and random row methods for k-means clustering technique in the diagnosis of
heart disease patients. The results show that integrating k-means clustering and naïve bayes can
enhance naïve bayes accuracy in the diagnosis of heart disease patients. The results also show that
the random attribute and random row methods could achieve higher accuracy than inlier, outlier,
and range methods in the diagnosis of heart disease patients. The best accuracy achieved is by two
clusters random row initial centroid selection method showing accuracy of 84.5%. Finally, some
limitations on this work are noted as pointers for future research.
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Authors
1. Mrs Mai Mohammed Shouman: PhD Candidate Lecturer in School of
Engineering and Information Technology UNSW@CANBERRA
Email: mai.shouman@student.adfa.edu.au
2. Dr Tim Turner: Senior Lecturer in School of Engineering and
Information Technology UNSW@CANBERRA
Email: t.turner@adfa.edu.au
3. Dr Robert Stocker: Visiting Fellow in School of Engineering and
Information Technology UNSW@CANBERRA
Email : r.stocker@adfa.edu.au

INTEGRATING NAIVE BAYES AND K-MEANS CLUSTERING WITH DIFFERENT INITIAL CENTROID SELECTION METHODS IN THE DIAGNOSIS OF HEART DISEASE PATIENTS

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