Improving the performance of k nearest neighbor algorithm for the classification of diabetes dataset with missing values

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International Journal of Computer
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ISSN 0976 – 6375(Online)
Volume 3, Issue 3, October - December (2012), pp. 155-167
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IMPROVING THE PERFORMANCE OF K-NEAREST NEIGHBOR
ALGORITHM FOR THE CLASSIFICATION OF DIABETES DATASET
WITH MISSING VALUES
Y. Angeline Christobel1, P. Sivaprakasam2,
1
Research Scholar, Department of Computer Science, Karpagam University,
Coimbatore, India
2
Professor, Department of Computer Science, Sri Vasavi College, Erode, India

ABSTRACT
In today’s world, people get affected by many diseases which cannot be completely cured.
Diabetes is one such disease and is now a big growing health problem. It leads to the risk of heart
attack, kidney failure and renal disease. The techniques of data mining have been widely applied
to extract knowledge from medical databases. In this paper, we evaluated the performance of k-
nearest neighbor(kNN) algorithm for classification of Diabetes data. We considered the data
imputation, scaling and normalization techniques to improve the accuracy of the classifier while
using diabetes data, which may contain lot of missing values. We selected to explore KNN
because, it is very simple and faster than most of the complex classification algorithms. To
measure the performance, we used Accuracy and Error rate as the metrics. We found that data
imputation method will not lead to higher accuracy; instead it will give correct accuracy for
missing values and imputation along with a suitable data preprocessing method increases the
accuracy.

Keywords: Data Mining, Classification, kNN, Data Imputation Methods, Data
Normalization and Scaling

1. INTRODUCTION
Hospitals and medical institutions are finding difficult to extract useful information for decision
support due to the increase of medical data. So the methods for efficient computer based analysis
are essential. It has been proven that the benefits of introducing machine learning into medical
analysis are to increase diagnostic accuracy, to reduce costs and to reduce human resources.
Earlier detection of disease will aid in increased exposure to required patient care and improved
cure rates [17]. Diabetes is one of the most deadly diseases observed in many of the nations.
According to the World Health Organization (WHO) [18] there are approximately millions of
155

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976 – 6367(Print), ISSN
0976 – 6375(Online) Volume 3, Issue 3, October-December (2012), © IAEME

people in this world are suffering from diabetes. Data classification is an important problem in
engineering and scientific disciplines such as biology, psychology, medicines, marketing,
computer vision, and artificial intelligence. The goal of the data classification is to classify
objects into a number of categories or classes.
A lot of research work has been done on Pima Indian diabetes dataset. In [8],
Jayalakshmi and Santhakumaran used the ANN method for diagnosing diabetes, using the Pima
Indian diabetes dataset without missing data and obtained 68.56% classification accuracy.
Manaswini Pradhan et al.[12] suggested an Artificial Neural Network (ANN) based
classification model for classifying diabetic patients. Best accuracy being 72% with average
accuracy of 72.2%.
Umar Sathic Ali, Dr.C.Jothi Ventakeswaran[13] proposed an improved evidence
theoretic KNN algorithm which combines Dempster Shafer theory of evidence and K nearest
neighbouring rule with distance metric based neighborhood with the average accuracy of 73.57%.
Pengyi Yang, LiangXu,Bing B Zhou, Zili Zhang,and Albert Y Zomaya [14] proposed a
particle swarm based hybrid system for remedying the class imbalance problem in medical and
biological data mining. To guide the sampling process, multiple classification algorithms are
used. The classification algorithms used in the hybrid system composition includes Decision
Tree (J48), k-Nearest Neighbor (kNN), Naive Bayes (NB), Random Forest (RF) and Logistic
Regression (LOG). Four medical datasets such as blood, survival, breast cancer and Pima Indian
Diabetes from UCI Machine Learning Repository and a genome wide association study (GWAS)
dataset from the genotyping of Single Nucleotide Polymorphisms (SNPs) of Age-related
Macular Degeneration (AMD) are used. The different methods of the study includes PSO
(Particle Swam based Hybrid System), RO(Rndom OverSampling), RU (Random
UnderSampling) and Clustering. The metrics used are AU(Area under ROC curve), F-measure
and Geometric mean.Particle Swam based Hybrid System (PSO) gives an average accuracy of
71.6%, RU 67.3%, RO 65.8% and cluster 64.9% with KNN Classifier for Pima Indian Diabetes.
Also with other classifiers and dataset, the study shows that PSO gives better accuracy.
In[15], Biswadip Ghosh applies FCP (Fuzzy Composite Programming) to build a
diabetes classifier using the PIMA diabetes dataset. He evaluated the performance of the Fuzzy
classifier using Receiver Operating Characteristic (ROC) Curves and compared the performance
of the Fuzzy classifier against a Logistic Regression classifier. The results show that FCP
classifier is better when the calculated AUC values are compared. The classifier based on
logistic regression has an AUC of 64.8%, while the classifier based on FCP has an AUC of
72.2%. He proved that the performance of the fuzzy classier was found to be better than a
logistic regression classifier. Quinlan applied C4.5 and it was 71.1% accurate (Quinlan 1993).
In [3], Wahba's group at the University of Wisconsin applied penalized log likelihood
smoothing spline analysis of variance (PSA). They eliminated patients with glucose and BMIs of
zero leaving n=752. They used 500 for the training set, and the remaining 252 as the evaluation
set which showed an accuracy of 72% for the PSA model and 74% for a GLIM model (Wahba,
Gu et al. 1992).
Michie et al. used 22 algorithms with 12-fold cross validation reported the following
accuracy rates on the test set and: Discrim 77.5%, Quaddisc 73.8%, Logdisc 77.7%,
SMART 76.8%, ALLOC80 69.9%, k-NN 67.6%, CASTLE 74.2%, CART 74.5%, IndCART
72.9%, NewID 71.1%, AC2 72.4%, Baytree 72.9%, NaiveBay 73.8%, CN2 71.1%, C4.5 73%,
Itrule 75.5%, Cal5 75%, Kohonen 72.7%, DIPOL92 77.6%, Backprop 75.2%, RBF 75.7%, and
LVQ 72.8% (Michie, Spiegelhalter et al. 1994, p. 158)

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J. Oates (1994) used Multi-Stream Dependency Detection (MSDD) algorithm on two-
thirds of the dataset for training. Accuracy on the one-third of evaluation was 71.33%.
Although the cited articles use different techniques, the average accuracy is 70.64% for
Pima Indian Diabetes dataset.
The representation of lot of missing values by zeros itself forms a characteristic and hence
affects the accuracy of the classifier. The main objective of this paper is to explore the ways to
improve the classification accuracy of a classification algorithm using suitable techniques such
as data imputation, scaling and normalization for the classification of diabetes data which may
contain lot of missing values.

2. DATA PREPROCESSING
Data in the real world is incomplete, noisy, inconsistent and redundant. The knowledge
discovery during the training phase is difficult if there is much irrelevant and redundant
information. Data preprocessing is important to produce quality mining results. The main tasks
in data preprocessing are data cleaning, data integration, data transformation, data reduction and
data discretization. The final dataset used will be the product of data preprocessing.

2.1. Missing Values and Imputation of Missing Values
Many existing, industrial and research datasets contain missing values. They are introduced due
to reasons, such as manual data entry procedures, equipment errors and incorrect measurements.
The most important task in data cleaning is processing missing values. Many methods have been
proposed in the literature to treat missing data [21,22]. Missing data should be carefully handled;
otherwise bias might be introduced into the knowledge induced and affect the quality of the
supervised learning process or the performance of classification algorithms [3, 4]. Missing
values imputation is a challenging issue in machine learning and data mining [2]. Due to the
difficulty with missing values, most of the learning algorithms are not well adapted to some
application domains (for example Web Applications) because the existed algorithms are
designed with the assumption that there are no missing values in datasets. This shows the
necessity for dealing with missing values. The satisfactory solution to missing data is good
database design but good analysis can help to reduce the problems [1]. Many techniques can be
used to deal missing data. Depending on the problem domain and the goal for the data mining
process, the right technique should be selected.

In literature, the different approaches to handle missing values in dataset are given as:
1. Ignore the tuple
2. Fill in the missing values manually
3. Use a global constant to fill in the missing values
4. Use attribute mean to fill in the missing values
5.Use the attribute mean for all samples belonging to the same class as the given tuple

2.2. Mean substitution
The popular imputation method to fill in the missing data values is to use a variable’s mean or
median. This method is suitable only if the data are MCAR(Missing Completely At Random).
This method creates a spiked distribution at the mean in frequency distributions. It lowers the
correlations between the imputed variables and the other variables and underestimates variance.

157


The Simple Data Scaling Algorithm
The following algorithm explains the data scaling method.
Let
D = { A1, A2, A3, ….. An }
Where
D is the set of unnormalized data
Ai – is the ith attribute column of values of
m- is the member of rows (records)
n - is the number of attributes.
Function Normalize(D)
Begin
For i=1 to n {
Maxi ←max(Ai)
Mini←min(Ai)
For r =1 to m {
Air ← Air-Mini
Air ← Air/ Maxi
Where
Air is the element of Ai at row r
}
}
Finally we will have the scaled data set.
End
The Mean Substitution Algorithm
The following algorithm explains the very commonly used form of mean substitution method [9]
Let
D = { A1, A2, A3, ….. An }
Where
D is the set of data with missing values
Ai – is the ith attribute column of values of D with missing values in some or all columns
n - is the number of attributes.
Function MeanSubstitution(D)
Begin
For i=1 to n {
ai ← Ai ∩ mi
where
ai is the column of attributes without missing values
mi is the set of missing values in Ai (missing values denoted by a symbol)
Let µi be the mean of ai
Replace all the missing elements of Ai with µi
}
Finally we will have the imputed data set.
End

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2.3. k-Nearest Neighbor(knn) Classification Algorithm
KNN classification classifies instances based on their similarity. It is one of the most popular
algorithms for pattern recognition. It is a type of Lazy learning where the function is only
approximated locally and all computation is deferred until classification. An object is classified
by a majority of its neighbors. K is always a positive integer. The neighbors are selected from a
set of objects for which the correct classification is known.

The kNN algorithm is as follows:
1. Determine k i.e., the number of nearest neighbors
2. Using the distance measure, calculate the distance between the query instance and all the
training samples.
3. The distance of all the training samples are sorted and nearest neighbor based on the k
minimum distance is determined.
4. Since the kNN is supervised learning, get all the categories of the training data for the
sorted value which fall under k.
5. The prediction value is measured by using the majority of nearest neighbors.

The Pseudo Code of kNN Algorithm
Function kNN(train_patterns , train_targets, test_patterns )
Uc - a set of unique labels of train_targets;
N - size of test_patterns
for i = 1:N,
dist:=EuclideanDistance(train_patterns, test_patterns(i))
idxs := sort(dist)
topkClasses := train_targets(idxs(1:Knn))
c := DominatingClass (topkClasses)
test_targets(i) := c
end

2.4. Validating the Performance of the Classification Algorithm
Classifier performance depends on the characteristics of the data to be classified. Performance of
the selected algorithm is measured for Accuracy and Error rate. Various empirical tests can be
performed to compare the classifier like holdout, random sub-sampling, k-fold cross validation
and bootstrap method. In this study, we have selected k-fold cross validation for evaluating the
classifiers. In k-fold cross validation, the initial data are randomly partitioned into k mutually
exclusive subset or folds d1,d2,…,dk, each approximately equal in size. The training and testing
is performed k times. In the first iteration, subsets d2, …, dk collectively serve as the training set
in order to obtain a first model, which is tested on d1; the second iteration is trained in subsets d1,
d3,…, dk and tested on d2; and so no[19]. The accuracy of the classifier refers to the ability of a
given classifier to correctly predict the class label of new or previously unseen data [19].

The Accuracy and Error rate can be defined as follows:
Accuracy = (TP+TN) / (TP + FP + TN + FN)
Error rate = (FP+FN) / (TP + FP + TN + FN)
Where

159


TP is the number of True Positives
TN is the number of True Negatives
FP is the number of False Positives
FN is the number of False Negatives

3. EXPERIMENTAL RESULTS
3.1. Pima Indians Diabetes Dataset
The Pima (or Akimel O'odham) are a group of American Indians living in southern Arizona. The
name, "Akimel O'odham", means "river people". The short name, "Pima" is believed to have
come from the phrase pi 'añi mac or pi mac, meaning "I don't know," used repeatedly in their
initial meeting with Europeans [25]. According to World Health Organization (WHO) [18 ], a
population of women who were at least 21 years old of Pima Indian Heritage was tested for
diabetes. The data were collected by the US National Institute of Diabetes and Digestive and
Kidney Diseases.
Number of Instances: 768
Number of Attributes: 8 (Attributes) plus 1 (class label)
All the attributes are numeric-valued

Sl
Attribute Explanation
No
1 Pregnant Number of times pregnant
Plasma glucose concentration
2 Glucose
(glucose tolerance test)
Diastolic blood pressure (mm
3 Pressure
Hg)
4 Triceps Triceps skin fold thickness (mm)
5 Insulin 2-Hour serum insulin (mu U/ml)
Body mass index (weight in
6 Mass
kg/(height in m)^2)
7 Pedigree Diabetes pedigree function
8 Age Age (years)
9 Diabetes Class variable (test for diabetes)

Class Distribution: Class value 1 is interpreted as "tested positive for diabetes"
Class Value : 0 - Number of instances - 500
Class Value : 1 - Number of instances – 268

While the UCI repository index claims that there are no missing values, closer inspection of the
data shows several physical impossibilities, e.g., blood pressure or body mass index of 0.They
should be treated as missing values to achieve better classification accuracy.

The following 3D plot clearly shows the complex distribution of the positive and negative
records in the original Pima Indians Diabetes Database which will complicate the classification
task.

160


Fig 1. The 3D plot of original Pima Indians Diabetes Database

3.2. Results of the 10 Fold Validation
The following table shows the results in terms of accuracy, error and run time in the case of 10
fold validation

Table 1. 10 Fold Validation Results
Performanc
After
e with Actual After
Imputation
different Data Imputation
and Scaling
Metrics
Accuracy 71.71 71.32 71.84
Error 28.29 28.68 28.16
Time 0.2 0.28 0.23

As shown in the following graphs, the performance was considerably improved while using
imputed and scaled data. The performance after imputation is almost equal or little bit lower
than using normal data. The reason is, the original data contains lot of missing values and the
missing values represented by 0 are treated as a significant feature by the classifier. Even though
the performance of original data is higher than that of imputed data, we should not consider
because it will not be accurate. If we train the system with original data which has lot of missing
values and use it for classifying real world data which may not contain any missing value, then
the system will not classify the ideal data correctly.

161


Performance in terms of Accuracy

71.9

Accuracy(%)
71.8
71.7
71.6
71.5
71.4
71.3
71.2
71.1
71
Actual Data After After
Imputation Imputation
and Scaling

Fig 2. Comparison of Accuracy –10 Fold Valuation

The accuracy of classification has been significantly improved after imputation and scaling.
Performance in terms of Error

28.8
28.7
28.6
Error(%)

28.5
28.4
28.3
28.2
28.1
28
27.9
and Scaling

Fig 3. Comparison of Error –10 Fold Valuation

The classification error has been significantly reduced after imputation and scaling.

3.3. Results of the Average of 2 to 10 Fold Validation
The following table shows the average of results in terms of accuracy, error and run time in the
case of 2 to 10 fold validation

Table 2. Average of 2 to 10 Fold Validation Results
Performanc
After
e with Actual After
Imputation
different Data Imputation
and Scaling
Metrics
Accuracy 71.94 71.26 73.38
Error 28.06 28.74 26.62
Time 0.19 0.19 0.19

162


Performance in terms of Accuracy

74
73.5

Accuracy(%)
73
72.5
72
71.5
71
70.5
70
and Scaling

Fig 4. Comparison of Accuracy Avg. of 2-10 Fold Valuations

The accuracy of classification has been significantly improved after imputation and scaling. The
average of 2 to 10 fold validations clearly shows the difference in accuracy.

Performance in terms of Error

29
28.5
28
Error(%)

27.5
27
26.5
26
25.5
and Scaling

Fig 5. Comparison of Error Avg. of 2-10 Fold Valuations

The classification error has been significantly reduced after imputation and scaling. The average
of 2 to 10 fold validations clearly shows the difference in classification Error.

The graphs above show that imputation alone does not give higher accuracy but imputation with
a data preprocessing technique can improve the accuracy of a dataset which has missing values.

We also compared our improved KNN with Weka’s Implementation of KNN. The results show
that improved kNN’s accuracy with imputation and scaling method is 3.2% higher than
the standard Weka's Implementation of kNN.

4. CONCLUSION AND SCOPE FOR FURTHER ENHANCEMENTS
The result shows that the characteristics and distribution of data and the quality of input data had
a significant impact on the performance classifier. Performance of the kNN classifier is measured
in terms of Accuracy, Error Rate and run time using 10-fold validation method and average of 2-
10 fold validation. The application of imputation method and data normalization had obvious
163


impact on classification performance and significantly improved the performance of kNN. The
performance after imputation is almost equal or little bit lower than using original data. The
reason is, the original data contains lot of missing values and the missing values represented by 0
are treated as a significant feature by the classifier. So the data imputation method not always
lead to so called “ good results” they only give “correct” results. It means imputation will not
always lead to higher accuracy for imputed missing values. But Imputation along with a suitable
data preprocessing method increases the accuracy. Our improved kNN’s accuracy with
imputation and scaling method is 3.2% higher than the standard Weka's Implementation of
kNN. To improve the overall accuracy, we have to improve the performance of the classifier or
use a good feature selection method. Future works may address hybrid classification model using
kNN with other techniques. Even though the achieved accuracy of kNN based method is little bit
lower than some of the previous methods, still there are scope for improving the kNN based
method. For example, we may use another distance metric function instead of the standard
Euclidean distance function in the distance calculation part of kNN for improving accuracy.
Even we may use any evolutionary computing technique such as GA or PSO for feature selection
or Feature weight selection for attaining maximum possible accuracy of classification with kNN.
So, future work may address the ways to incorporate these ideas along with the standard kNN.

ANNEXURE –RESULTS OF K-FOLD VALIDATION
The following table shows the k-fold validation results where k is changed from 2 to 10. We
used the average of this results as well as the results corresponding to k=10 for preparing graphs
in the previous section IV.
Table 3. Results With Actual Pima Indian Diabetes Dataset

k Accuracy Error Time
2 72.53 27.47 0.13
3 74.35 25.65 0.20
4 71.61 28.39 0.16
5 70.98 29.02 0.17
6 72.40 27.60 0.19
7 70.90 29.10 0.25
8 72.14 27.86 0.20
9 70.85 29.15 0.19
10 71.71 28.29 0.20
avg 71.94 28.06 0.19

164


Table 4. Results With Imputed Data

2 71.22 28.78 0.16
3 70.44 29.56 0.19
4 70.83 29.17 0.16
5 71.24 28.76 0.14
6 71.88 28.13 0.19
7 71.56 28.44 0.20
8 71.61 28.39 0.17
9 71.24 28.76 0.19
10 71.32 28.68 0.28
Avg 71.26 28.74 0.19

Table 5. Results With Imputed and Scaled/Normalized Data

2 74.74 25.26 0.22
3 74.09 25.91 0.13
4 71.88 28.13 0.16
5 73.59 26.41 0.17
6 72.92 27.08 0.17
7 74.31 25.69 0.16
8 74.09 25.91 0.22
9 72.94 27.06 0.22
10 71.84 28.16 0.23
Avg 73.38 26.62 0.19

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Improving the performance of k nearest neighbor algorithm for the classification of diabetes dataset with missing values