INTRODUCTION
Parkinson’s Disease (PD) is an important nervous system disorder, which
affects nervous system in a division of the brain that controls muscle movements.
Symptoms of Parkinson's disease, slowness and poverty of movement, resting tremor,
rigidity, bradykinesia, etc., are commonly diagnosed in patients (Singh
et al., 2007), which generally affects people over the age of 60
and it is more common in men than in women. PD is an irreversible brain lesion.
If this kind of disease can be diagnosed and treated earlier, drug treatments
would mitigate or relieve the effects of the symptoms.
Up to now, the causes of Parkinson disease are not so clear. There is a lack
of clear laboratory tests that can help to confirm the diagnosis sporadic PD.
Particularly in early stages, the disease can be difficult to diagnose accurately.
Scientists and researchers are doing a lot of researches to investigate the
causes of this disease. They are trying to study many possible causes, including
aging and environmental poisons. One of the researchers, was performed and developed
a method to identify different voice patterns through the use of voice disorders
to diagnose Parkinson's disease (Little et al., 2007).
Related studies indicate that sound distortion occurs on 90% of patients with
Parkinson's disease (Ho et al., 1998). Subsequently,
Little et al. (2009) used a different approach,
Support Vector Machine (SVM), got overall classification accuracy reaches 91.4%.
The researcher concludes that combined specific algorithms with harmonic noise
ratio would be the best way to classify the healthy from PD subjects (Little
et al., 2009).
Later on some researchers used the dataset from Little et
al. (2007). The work done by Resul (2010) emphasize
on comparing the accuracy of different types of classification methods for effective
evaluate and diagnosis of Parkinson's. Various classifiers, Regression, DMNeural,
Neural Network and Decision Tree, have been used to identify the Parkinson's
disease. As a result, the neural network obtains the optimal classification
accuracy of 92.9%. On the basis of accuracy, KNN classifier shows the best to
distinguish between Parkinson's disease and those who do not have it. The KNearest
Neighbor (KNN) classifier is one of the most heavily usage and benchmark in
classification. Even comparing the most advanced machine learning approaches,
this simple and easytouse algorithm still can produce superior results. However,
there are several critical issues affecting the performance of KNN, mainly including
the choice of k, the new class label of the data prediction, the selection the
distance metric and its data preprocessing method.
Many scholars in the past mostly used arbitrarily chosen k values to be calculated
and tried, such as preselected k = 3 (Yang et al.,
2012), k = 1, 2, …, 10 (Sierra et al.,
2011), k = 1, 2, …, 50 (Wang et al., 2007)
or k = square (number of samples) (Mitra et al.,
2002; Bhattacharya et al., 2012). But there
isn't clear enough to provide the necessary guideline for determining the kvalue.
Generally, Larger values of k presents less sensitive to noise and makes smoother
between the boundaries of classes. As a result, choosing the same (optimal)
k becomes almost impossible for different applications. Historically, the optimal
k for most of the datasets is always located between 3 and 10. However, this
is not absolutely certain criteria. Determining the value of k is actually supposed
to be discussed further.
In addition, using different distance metrics to calculate the accuracy of
classification may produce different results. Many scholars have been promoted
to develop a variety of distance metrics for enhancing the accuracy of KNN algorithm
(Wang et al., 2007; Bhattacharya
et al., 2012; Yang et al., 2012).
Furthermore, database preprocessing and model’s validation methods also
have an impact on the accuracy of classification. In statistical external validation,
the whole dataset splits into training and testing sets randomly, using this
skill to check the quality of the classifier. Here, how to determine the split
ratio of the dataset and compare the possible similarities and differences in
each execution, this will be another issue to be explored. Throughout the above
description of k neighboring points, distance function and data pattern, PD
has been classified using KNN classifier, the parameters impact on the best
classification accuracy has been discussed either. The aim of this article is
twofold.
The first one is to determine the value of k, that is, what is the optimal value for the neighboring constant ‘k’, and how should it be obtained? Exhaustive search is used to calculate the accuracy under different k values.
The second one is to cross calculate the classification accuracy of each distance
metric by transforming the dataset into different types of normalization. This
will help to identify the effects of distance metric and normalization in KNN
classifier on the classification of PD dataset.
MATERIALS AND METHODS
The Parkinson dataset used in this study, obtained from UCI machine learning
repository. The dataset is composed of 22 attributes sustained biomedical voice
measurements including 32 subjects from both sexes, of which 23 were diagnosed
with PD. There are 195 instances in the data set, including 48 normal and 147
PD patients. The main purpose is to distinguish between healthy people with
PD from the data, according to “status” variable which is assign to
0 for healthy people and 1 for PD. The attributes of dataset are given in Table
1 (Little et al., 2007).
KNearest neighbor classifier: KNN is a supervised learning algorithm
and perceived as a simple but powerful classification, even for complex applications,
capable of yielding highperformance results (Dzuida, 2010).
In the beginning of 1970’s, KNN has been already used in statistical estimation
and pattern recognition as a nonparametric technique. The k samples which are
closest to the query sample are found based on a similarity measure among the
training data. The class label of the query sample is determined by using majority
voting (Shakhnarovich et al., 2005). In the study,
distance measurements like Euclidean and Manhattan are used to calculate the
distances of the samples.
Table 1: 
Describing the attribute information presented by some kind
of vocal signals with Parkinson’s disease 

The various kvalues in KNN classifier are used and compared with each other,
which effects have been investigated and pointed out the best one.
Euclidean distance: The euclidean distance between any two instances is the length of the line segment connecting them. In this study, the dataset is composed of 22 attributes is represented in 22dimensional space. If x = (x_{1}, x_{2}, ..., x_{22}) and y = (y_{1}, y_{2}, ..., y_{22}) are two points in Euclidean 22space, then the distance from x to y is given by:
Manhattan distance: The manhattan distance is the distance that would be traveled to get from one data point to the other, measured along axes at right angles. The name implies the Manhattan street in grid layout which causes the shortest path between two points. The equation for this distance between a point x = (x_{1}, x_{2}, ..., x_{22}) and a point y = (y_{1}, y_{2}, ..., y_{22}) is given by:
Normalization: Distance measure calculated directly from the training
set has one major shortcoming, that is, the variable has a different measurement
scales or a mixture of numerical and categorical variables. For example, in
this study, attribute “MDVP: Fo (Hz)” is based on Hertz, and MDVP:
Jitter (%) is based on percent then Hertz will have a much higher influence
on the distance calculated. One of the solutions is to standardize the training
set, such as normalization. It is a data preprocessing tool used in data mining
system. By normalizing the attributes of a dataset, their values are scaled
to a smallspecified range, such as 0.01.0. Normalization is particularly useful
for classification algorithms. There are many methods for data normalization.
In this study, KNN classifier predicts the results of classification adopting
raw data and data after four normalization approaches, includes minmax normalization,
zscore normalization, max normalization and normalization by decimal scaling.
Generally, the data subjected to preprocessing in the classification process
will improve the performance of classification (Kumar and
Zhang, 2007; Polat et al., 2008). Twenty
two continuousvalued attributes in Parkinson's disease dataset are normalized
by following methods. Details about these four normalization methods are described
as below:
• 
Minmax normalization: Linear transformation of the
raw data was carried out. Suppose that v_{min} and v_{max}
are the minimum and maximum of attribute variable. Every value v from the
raw dataset will be mapped into value v’ using the following equation: 
• 
Zscore normalization: The values of attribute are
normalized using the mean and standard. A new value v’ is obtained
using the following expression: 

where, v_{ave} and v_{std} are the mean and
standard deviation of attribute X, respectively 
• 
Max normalization: The values of attribute are normalized
using every value v from the original interval divided by the maximum of
attribute variable v_{max}. New value v’ is obtained using
the following expression: 

where v_{max} is the maximum of attribute variable 
Normalization by decimal scaling: Normalizes by moving the decimal point of values of attribute. The number of decimal points depends on the maximum absolute value. A new value v’ corresponding to v is obtained using the following expression:
where i is the smallest integer such that max (v’)<1.
Crossvalidation: Choosing the optimal value for kneighborhood is best done by first inspecting the data. In general, a large kneighborhood value is more precise as it reduces the overall noise but there is no guarantee. Crossvalidation is another way to determine a good kneighborhood value by using an independent data set to validate the value of kneighborhood.
In Kfold crossvalidation, the original sample is randomly divided into K
subsamples of approximately equal size. One of the K subsamples is keep as
the testing data, and the rest of the K1 subsamples are used as training data.
The process is repeated K times, with each of the K subsamples used for validation
exactly once. The average of K results from the folds is yielded to a single
estimation.
In this study, started with 3fold crossvalidation, 67% training and 33% testing data split, has been used and randomly chosen from dataset. The best accuracy of classification is yielded with such a matrix out of a given set of data and a given distance function. This phase mainly discusses the value of k and these different data patterns, what the impacts will be on the best classification accuracy. Then, this study will use a series of data split which the percentage of training data gradually increase from 5% to LOOCV (Leave one out crossvalidation). The data set is tested further for finding the causes of the true optimum value of k. That is, this study will try to find the best value of k under a variety of split ratio of training dataset and with the different distance function.
RESULTS AND DISCUSSION
Range of k: This study was conducted by the value of k = 1, progressively increasing k neighboring points from 1133 (67% training dataset) to test the range of k. Euclidean distance is used here to examine the accuracy by different raw dataset and normalized datasets. The results indicate that if k is even number, the accuracy is less than the condition of odd, k+1 and k1. In addition, as k increases to 65 or more, the accuracy of all data patterns is almost close to 75.38%. This means that when the k neighboring points is large enough, the accuracy will naturally tends to the expected value of the sample, in this data set including 48 normal and 147 PD patients.
Excluding all even numbers of k, this study redefines the range of k value, which is odd and less than 65. In training and testing of KNN classifier, still 6733% traintest data split has been randomly chosen from the dataset. The effects of kvalue in KNN classifier on the classification accuracy including Euclidean and Manhattan distance have been investigated. Both of the obtained classification results are plotted in Fig. 1 and 2. As can be seen from these figures, the classification accuracy in the classification of raw PD dataset, either Euclidean distance or Manhattan distance is used to calculate the accuracy that are almost the lowest. On the other hand, it is noteworthy that the accuracy from normalized datasets is relatively better, especially normalized by the minmax normalization or decimal scaling has a higher accuracy and make no difference around k = 1 among the two figures.
Best accuracy of classification: The overall data set splits into training
and testing sets as following.

Fig. 1: 
KNN accuracy for different kvalue based on euclidean distance,
training data (67%)/testing data (33%) , k is odd and less than 65 

Fig. 2: 
KNN accuracy for different kvalue based on Manhattan distance,
training data (67%)/testing data (33%), k is odd and less than 65 
The percentage of the training data set at least 5%, gradually up to LOOCV,
is randomly selected. Using the chosen raw and normalized datasets estimate
the classification accuracy of the KNN classifier. The above steps performed
repeatedly 100 times under each percentage shown in Table 2.
The results from the calculations then can be averaged to yield a single estimation.
As can be seen from the table, found that the less the percentage of training
set, the lower the accuracy, if there lower enough, the accuracy will tends
to the expected value of the sample also. As the percentage is greater than
75%, the accuracy of normalized datasets reaches 95% or more. The results imply
that the percentage of training sets shall split the larger the better, the
classification accuracy will be relatively close to the optimum value, accordingly,
and then it can obtain an acceptable optimum value, not exactly one. This is
why in most studies; researchers always use a 10folds crossvalidation, 90%
training and 10% testing data split, to find their answers. In fact, the results
from 10folds crossvalidation may not hit the target, but close.
In addition, each best k value is acquired from different training and testing
data split respectively, only a small portion of k is likely to belong to 3,
5 or 7, the others are almost equal to 1.
Table 2: 
Effects of kvalue in KNN classifier on the classification
accuracy used different percentage of the training data set on raw and normalized
datasets, (based on euclidean distance and manhattan distance) 

(k)*: Optimal accuracy in k value 
This represents under a different ratio of training and testing data, its
best classification accuracy corresponds to the k neighboring points is different.
However, there are many scholars mostly used arbitrarily chosen k values to
be calculated, such as preselected k = 3 (Yang et al.,
2012), k = 1, 2,…, 10 (Sierra et al., 2011),
k = 1, 2, …, 50 (Wang et al., 2007) or
k = Square (number of samples) (Mitra et al., 2002;
Bhattacharya et al., 2012). How should determine
the value of k, there are no specific description. This case uses nearly global
search methods to explore the range of k. It is feasible to calculate a smaller
dataset. As the training set = 95.0%, using normalization by minmax normalization
with Euclidean distance, have the highest average accuracy which is 96.73±5.97
(k = 1). As to the accuracy of the LOOCV, 96.41 (k = 1), is very close to the
optimum value and there is no variation, the results would have been more popular
in the case of stringent forecast.
CONCLUSION
Constantly improved algorithm techniques have been developed so far to secure the accuracy of classification. As mentioned above, there are many methods that are in use for recognizing PD today, whether in the field of medical research or public health. KNN is a simple but useful algorithm technology. It has the potential to become a good supportive for the experts to improve the accuracy and reliability of diagnosis, as well as making the diagnosis fewer possible errors and more timeefficient.
From the results of this study and by comparing other literature, such as,
Ene (2008) using neural networkbased approach has
derived the highest classification accuracy 81.28%. Resul
(2010) also uses four wellknown classification methods, best classification
accuracy achieved by the neural network classifier 92.9%. As can be seen from
this study, the classification accuracy in the classification of raw PD dataset,
either Euclidean distance or Manhattan distance is used to calculate the accuracy
that are almost the lowest and under a different ratio of training and testing
data, its best classification accuracy corresponds to the k neighboring points
is also different. That means that k can not be arbitrarily chosen, it should
be calculated carefully. The training set = 95.0%, using normalization by minmax
normalization with Euclidean distance, have the highest average accuracy 96.73±5.97
(when k = 1). The results points out different distance functions with different
normalized methods also have a decisive influence on the optimum value. As to
the accuracy of the LOOCV, 96.41 (k = 1), is very close to the optimum value
and there is no variation. Although, the results of LOOCV would not the best,
it has been more popular in the case of stringent forecast.