TECHNICAL REVIEW: PERFORMANCE OF EXISTING IMPUTATION METHODS FOR MISSING DATA IN SVM ENSEMBLE CREATION

International Journal of Data Mining & Knowledge Management Process (IJDKP) Vol.7, No.5/6, November 2017
DOI: 10.5121/ijdkp.2017.7606 75
TECHNICAL REVIEW: PERFORMANCE OF EXISTING
IMPUTATION METHODS FOR MISSING DATA IN
SVM ENSEMBLE CREATION
Shahid Ali and Simon Dacey
Department of Computing, Unitec Institute of Technology, Auckland, New Zealand
ABSTRACT
Incomplete data is present in many study contents. This incomplete or uncollected data information is
named as missing data (values), and considered as vital problem for various researchers. Even this missing
data problem is faced more in air pollution monitoring stations, where data is collected from multiple
monitoring stations widespread across various locations. In literature, various imputation methods for
missing data are proposed, however, in this research we considered only existing imputation methods for
missing data and recorded their performance in ensemble creation. The five existing imputation methods
for missing data deployed in this research are series mean method, mean of nearby points, median of
nearby points, linear trend at a point and linear interpolation respectively. Series mean (SM) method
demonstrated comparatively better to other imputation methods with least mean absolute error and better
performance accuracy for SVM ensemble creation on CO data set using bagging and boosting algorithms.
KEYWORDS
Ensemble, Bagging, Boosting, Imputation, Aggregation
1. INTRODUCTION
Air quality is monitored to detect any pollutant concentrations that has adverse effects on human
beings [1]. For this air quality is monitored at various locations through various monitoring
stations. However, to conduct air pollution analysis which has large observations of missing data
makes the task difficult to evaluate [13]. The missing data is a result of equipment failure, human
error, routine maintenance, changes in sitting of monitors or due to some other factors [19]. This
missing data or incomplete data set creates results that are different from those that would have
been monitored through complete data set [15].
The occurrence of missing data requires a serious consideration on analysing the data. In fact,
there are three main problems associated in dealing with incomplete data set [33] [23]. Firstly, the
loss of missing information results in reduction of efficiency. Secondly, the missing data leads to
problems in data handling, computation analysis and further minimizing the efforts to use the
standard software. Thirdly, which is the most important, the results produced via missing data
may be biased due to the difference between the observed data and unobserved data. Currently,
there are some statistical packages such as SPSS which can handle missing data and can perform
replacement for missing values.
Our approach to handle missing values or incomplete data set in current research is limited to five
imputation options. These are implemented in SPSS and our goal for this research is to determine
the best imputation method to replace missing values for Carbon monoxide(CO) concentrations in
our research. These five imputation methods for missing data are explained later in this chapter.
The remainder of this research is organized as follows: Section 2 provides the types of missing
data. Section 3 provides a literature review on previous computational studies for missing data.
Section 4 discusses the reasons for using imputation methods for missing data. Section discuses
about SVM ensemble for air pollution data analysis and methods for constructing SVM ensemble.

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Section 6 provides experimental design and imputation methods used to handle missing data.
Section 7 is dedicated towards results and discussion for the experiments. Finally, section 8
presents conclusion to this research.
2. TYPES OF MISSING DATA
Incomplete data is present in many study contents [28]. This incomplete or uncollected data
information is named as missing data (values), and considered as vital problem for various
researchers. Even this missing data problem is faced more in air pollution monitoring stations
[16], where data is collected from multiple monitoring stations which are widespread across
various locations [3]. Generally, there are two types of missing data encountered in air quality
monitoring [30]. The first form of missing data is non-ignorable data, where missing datum
probability is dependent on its value, and ignoring missing data probability of missing datum does
not rely on its value. The second form of missing data is ignorable missing data, which is of two
types. The first type of ignorable missing data is linked to sampling, which refers to the situations
where it is not possible to obtain data from whole population. In this case probability sampling is
used to get a representative population sample. The second type of ignorable missing data is
where data is missing at random (MAR), it refers to the pattern of missing that vary for subsets
for a variable. It is determined that the air quality data referred to MAR.
To test the accuracy of imputation method, from a complete data set incomplete data sets need to
be generated [32]. For the imputation of missing values of air quality, various patterns of air
quality missing data sets are created to evaluate the efficiency of each method. These missing
patterns helped researchers to select the best estimation imputation method for research analysis.
3. LITERATURE REVIEW
Missing data is a serious problem, that creates uncertainty in research results [20]. In literature,
various methods and techniques are proposed to address imputation of missing data which will be
discussed here briefly.
Mean top bottom technique was applied to replace the missing values in PM10 concentrations in a
data set [32]. It was found in the research that this method performed very well only when the
missing data was in small number.
Nearest neighbor method was proposed for the imputation of incomplete PM10 concentration data
[13]. Further in this study three other methods namely, mean substitution, expectation
maximisation (EM) and hot deck were also considered for imputation of missing data.
Mean, median, hot deck, KNN and mean method by step depression imputation methods were
used to improve the imputation accuracy of each method through well know classifiers KNN,
SVAR, SVMP, C4.5, RIPPER and LSVM [25]. Statistical results of this study shown that mean
method by step depression (MMSD) results were more acceptable compare to other methods and
resulted in better performance of the classifier with missing values of 7.72% to 20% [25].
Traffic control, traffic management and control applications require complete and accurate data
because of various reasons, however, such data is sometime unavailable [34]. For this typical
problem researchers categorized the imputation methods into three categories i.e., prediction
methods, statistical methods and interpolation methods. Results from various studies
demonstrated that statistical methods were effective in imputing missing data resulted in better
performance results and low reconstruction errors [17]. A similar study for traffic flow missing
data with ten methods was conducted [7]. The performance of those methods was compared with
Bayesian Principal Component Analysis (BPCA) imputation methods [7]. Experiment analysis
outperformed the results of BPCA imputation methods and demonstrated good choices in dealing
with missing data.

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Incomplete data plays important role in prediction accuracy, as the incomplete data is present
both in training and testing data set tends to produce biased results [27]. It is quite evident from
various researches that combining the output of various classifiers results in the prediction
accuracy [2]. In this regard two ensemble based imputation techniques namely, Bayesian multiple
imputation and nearest neighbor single imputation [26] for imputation of missing data were
proposed. Results of this study demonstrated better results with decision trees support method.
Environmental monitors, scientific researchers and process controllers have widely used time
series data for analysis. However, in the presence of missing data time series results enforce big
question mark. In this regard to address the time series missing data imputation method based on
Genetic Programming (GP) and Lagrange Interpolation was proposed [9]. The results of this
study were promising and produce efficient results on imputation missing data in time series and
further possessed no loss to data sets statistical properties leading to better understanding of
missing data pattern.
From the previous literature, it is quite evident that various methods based on machine learning
for imputation of missing data were proposed. However, for our research we will take a different
approach for imputation of missing data of Carbon monoxide (CO) concentrations in Auckland
region for air pollution analysis by deploying series mean method, mean nearby point method,
median nearby point method, linear interpolation method and linear trend at point method. For all
above methods mean absolute error will be calculated and each method classification accuracy
will be determined by SVM ensemble creation. The above imputation methods are explained
further in this research.
4. REASONS FOR USING IMPUTATION METHODS
Researchers have used various alternative methods for imputation of missing data [22]. The
missing data is in various researches is handled by three traditional reasons:
1. The computer programs are defined in such a way that an empty space is a missing value.
Therefore, computer programs ignore these missing values as defined, in other words they
do not include them in the analyses [11].
2. Another common method to interfere into missing values is to remove the variable or
subjects for which missing values are there [14]. However, deleting the subjects may result
in loss of data and will produce biased results, because of the systematic difference between
the collected and uncollected data [21].
On the other side if the missing values are presented in a group of variables, then if the
variable(s) is/are of no such importance then the variable can be deleted. However, in case
where the available variables are distributed, then deleting such variable(s) will be of
serious loss of data [21]. Moreover, variables who have missing values are not distributed
randomly, then deleting those variable data may result in skewness of the distribution [8].
For such reasons, it is proposed that imputation of missing values helps to protect the
sample size as well [28].
3. Another way to solve missing data problem is to make predictions of missing values and
use them in the analysis [5] [6]. However, prediction of missing values and imputation can
only be used for quantitative variables. The three most common methods for predictions of
missing quantitative variables [8] [24], are prior knowledge, regression and average (mean)
imputation.
5. SVM ENSEMBLE
Computational air pollution data analysis is spatio-temporal in nature [2], this research focuses on
constructing dynamic computing environment through SVM ensemble. Various individual SVMs

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are aggregated for the purpose of data mining, where SVM aggregation results in outstanding
generalizability and speedy parallel computation [1][2].
(1)
The air pollution dataset can be represented as (1) and (2), which is a three dimensional matrix. It
can be further simplified as time series of two dimensional data matrix (1), as environmental data
is gathered over time line. Similarly, in time series one time instance is a matrix (2). Air pollution
states are represented by elements in various geometric location, where Elements are represented
as data and are collected by various sensor devices in different locations.
(2)
The individual SVMs decisions are aggregated by majority of vote method to analyse the air
pollution problem.
5.1 METHODS OF SVM ENSEMBLE CONSTRUCTION
Bagging and boosting algorithms are used for the construction of SVM ensemble and the
imputation methods are evaluated based on that.
5.1.1 Bagging
Bagging algorithm generates various bootstrap training sets from the original training set and
deploys each of them to produce a classifier for the enclosure in ensemble. The bagging
algorithm and bootstrap sampling with replacement is illustrated below [36].
BAGGING(T,M)
1 For each m = 1,2,...,M,
2 Tm = Sample With Replacement(T,N)
3 hm = Lb(Tm)
4 Return
SAMPLE WITH REPLACEMENT(T,N)
1 S = ϕ
2 for i = 1,2,...,N
3 r = randominteger(1,N) 4 Add T[r] to S
5 Return S.
In order to create a bootstrap sample from a training set of N, we execute N multinomial trials and
in each trial we draw one of the N samples. In this case each sample has a probability of 1/N to be
drawn in each trial.
The second algorithm shown above exactly does this N times, the algorithm selects a number
from 1 to N and then adds the rt
h training example, to bootstrap training set S. Noticeably, some

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of the original training examples will not be selected for inclusion of bootstrap training set and
others will be selected one time or more. In bagging, the number of base classifiers that need to be
learned M, are created through bootstrap training sets and further classifiers are generated using
each of them. Bagging yields a function h(x) that classifies new examples by yielding the class y
that receives the maximum number of votes from the base models {h1,h2,h3 ...hm}. In bagging, the
M bootstrap training sets produced are likely to have some differences. If these differences are
enough to show obvious differences among the M base models, then in that case the ensemble
will perform better than the base models individually [35] [12].
Models are said to be unstable [18], if the differences in their training sets show significant
differences in the models and stable if not. In other way, we can say that bagging method does
more to reduce the variance in base models instead of bias. So, bagging performs better relative to
its base models, when the base models have low bias and high variance.
5.1.2 BOOSTING
Adaboost is a boosting algorithm which we used with other algorithms for spatial and temporal
air pollution analysis in our research. Adaboost algorithm generates a sequence of based models
along with different weight distributions over training set. Adaboost algorithm is illustrated below
[36].
ADABOOST(
{(x1,y1),...,(xN,yN)},Lb,M)
1 Initialize D1(n) = 1/N for all n ∈ {1,2,...,N}
2 for m = 1,2,...,M,
3 hm = Lb({(x1,y1),...,(xN,yN)},Dm))
4 Calculate the error of≥ hm : ϵm = ∑n:hm(xn)≠ yn Dm(n)
5 If ϵm 1/2 then
6 set M = m − 1 and abort this loop
7 Update distribution Dm:
8 Dm+1(n) = Dm(n) × { 2(11m− m) m(xn) = yn if h
2ϵ otherwise
9 Output the final hypothesis:
h log ϵ
It has a set of N training examples, a base model learning algorithm Lb and the number of base
models M, that we want to combine. Adaboost algorithm was designed for two class
classification. However, it is regularly used in previous researches for more than two classes.
The first step in Adaboost algorithm is the construction of weights distribution D1 over the
training set. In Adaboost algorithm the first distribution is one that assigns equal weight to all N
training examples. By now, we enter into the loop of the Adaboost algorithm. In order to make
first base model, we call the base model learning algorithm Lb with distribution D1 over the
training set. Failure of Lb to take weighted training set, one can derive it by sampling with
replacement from the original training set with the help of distribution Dm. After getting h1
hypothesis and calculating error E1 on the training set, which is the sum of the weights of the
training examples that h1 misclassifies.
We want E1 < 1/2, if this condition is not satisfied then we stop here and will to ensemble that
consists previously generated base models. In this case if ϵ1 < 1/2 is satisfied, then we calculate
D2 over the training examples as follows. Correctly classified examples by h1 have their weights
multiplied by . Misclassified examples by h1 their weights will be multiplied by 2(
1
ϵ1).
According to our condition ϵ1 < 1/2, the weights of correctly classified examples will be reduced
and the weights of misclassified examples will be increased [36]. In other words, examples that h1
misclassified their aggregate weight will increase to 1/2 under D2 and examples that h1 correctly

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classified their aggregate weight will reduce to 1/2 under D2. From here we go into the next
iteration of the loop to construct base model h2 using training the set and new distribution D2. We
build M based models in this way. The ensemble derived from Adaboost is a function that takes
new example as an input and returns the class that gets the maximum weighted vote over the M
base models.
Each base model’s weight is , which is proportional to accuracy of base model on the
weighted training set presented on it.
It is quite clear from the above explanation that the core of Adaboost algorithm is the distribution
updating step. In the Adaboost algorithm we perceive that ϵm represents the sum of the weights of
misclassified examples. The weights of misclassified examples are multiplied by , by doing
this, sum of their weights increased by
.
Correctly classified examples weight is (1 − ϵm) but their weights are multiplied by
, hence, sum of their weights decreases by
.
The adjustment of this weight results in the next model is to be generated by weak learner, which
will have an error less than 1/2. From this misclassified example of previous base model will be
learned.
In general boosting algorithm reduces the bias than variance. For this boosting algorithm tends to
improve its base models when they have high bias and low variance. The reduction of bias in
boosting algorithm derives from the fact that it adjusts distribution over the training set. The
weights of misclassified examples by base model increases, resulting in base model algorithm to
focus more on those examples. In an instance, when the base model learning algorithm is biased
to certain examples gets more weight resulting the possibility of correcting that bias. This
mechanism of adjusting the training set distribution results in difficulty for boosting algorithm,
when the training data is noisy [37]. Noisy examples are difficult to operate and learn in boosting
algorithm [37]. Because high weights are assigned to noisy examples compare to others, causing
boosting algorithm to focus more on those examples and overfit the data.
6. EXPERIMENTAL DESIGN AND IMPUTATION METHODS
For simulation of missing data an annual hourly monitoring records for CO concentrations is
collected from seven stations in Auckland region, Takapuna, Khyber Pass road, Henderson,
Pakuranga, Queen Street, Glen Eden and Pukekohe. The data set contains CO concentrations on a
time scale of one per hour (hourly averaged) spread over a year.
For calculation of missing values of CO concentrations of seven monitoring stations and for the
calculation of mean absolute error of each imputation method we use IBM SPSS Statistics version
22 for our experiments. Whereas, for the classification accuracy of each imputation method we
run Matlab on Windows 7 Enterprise with system configuration Intel Core i5 processor (3.2 Ghz)
with 4 GB 1067 MHz DDR3of RAM.
Characteristics of CO are shown in table Table 1. Table 1 shows that a total of 8783 observations
of CO are available for experiment purposes of which 2169 (24.69 %) are missing. Number of
extremes of seven monitoring stations is provided, which was varies from station to station.

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Table 1. Characteristics of CO data
Stations N Mean Std.
Missing No. of Extremes
Count Percent Low high
Station 1 8544 .427 .5505 239 2.7 0 332
Station 2 8656 1.212 1.1644 127 1.4 0 412
Station 3 8487 .256 3484 296 3.4 0 399
Station 4 8504 .501 .6049 279 3.2 0 351
Station 5 8477 .695 .6247 306 3.5 0 349
Station 6 8564 .310 .4121 219 2.5 0 412
Station 7 8080 .254 .3083 703 8.0 0 309
Figure 1 is an illustration of concentrations of CO data skewness. Figure 1 shows that there is
some variability in range as shown in concentrations of CO data from 3.9 to 8.9 µg/m3
of various
monitoring stations. Whereas, the data is skewed towards the right demonstrating most of the time
low concentrations of CO were observed across Auckland region. Environmental Performance
Indicators (EPIs) are calculated relative to the National Environmental standards for Air Quality
for each gas. Since these values are different the EPI classes are different. The data for this study
includes five classes for monitoring CO in Auckland region according to EPIs: (class ”a”:
excellent (meaning, air quality is considered fantastic and no risk at all to people), class ”b”: good
(meaning, air quality is considered satisfactory and there is little to people health), class ”c”:
acceptable (meaning, air quality is acceptable, however, there is risk to people health), class ”d”:
alert (meaning, air quality is not acceptable and there is serious risk to people health), class ”e”:
action (meaning, air quality is deteriorating and a quick response is required).
Hence to deal with the missing data of CO on annual hourly monitoring records of various
stations in Auckland region requires a method(s) for imputation of missing data.
For this analysis in our experiments for missing data of seven monitoring stations of CO
concentrations we applied five imputation methods that are implemented in SPSSM. These
methods are named as series mean (SM) method, mean of nearby points (MNP), median of
nearby points (MDNP), linear trend at a point (LTAP) and linear interpolation (LI). Each method
mean absolute error is calculated for seven monitoring stations and based on that its effectiveness
determined. Similarly, each imputation method classification accuracy is calculated and further
evaluation of each imputation method on performance accuracy using boosting and bagging
algorithms is conducted. With the help of each method imputed data ensemble is build and its
classification accuracy is computed.
6.1 IMPUTATION METHODS
The existing five imputation methods for missing CO data of seven monitoring stations of
Auckland region are explained below with their significance.

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Figure 1. Concentrations of CO data Skewness
6.1.1 Series Mean (SM) Method
In this method missing values are imputed with mean of the entire data. The missing CO
concentrations of seven monitoring stations were replaced to their station’s mean.
6.1.2 Mean of Nearby Points (MNP) Method
In this method missing values are imputed by the mean of nearby points (surrounding) values.
The number of nearby points is derived from ’span of nearby points’ option in SPSS. The default
value in the SPSS program is ’2 digits’. In other words, the mean is calculated by using complete
station’s data from above and below missing values, and this value is imputed instead of entire
data.
6.1.3 Median of Nearby Points (MDNP) Method
In this method missing values are imputed by the median of nearby (surrounding) values. The
number nearby points are derived from ’span of nearby points’ option in SPSS program. The
default value in the SPSS program is ’2 digits’. The median is calculated by using the complete
values of a station’s data from above and below, the missing data and the derived value is used
to replace the missing value.
6.1.4 Linear Interpolation (LI) Method
This method replaces missing values by interpolation. The last incomplete information in the
CO monitoring station’s data before the missing value and the first value after the missing data
in the CO monitoring station’s data are used for interpolation [4]. In case where the first or last
data in a series is missing, then the missing value is not replaced.
6.1.5 Linear Trend at Point (LTP) Method
Missing values in this method are replaced in accordance with the trend of current structure
data. The imputed missing data is replaced based on an index variable scale 1 to n [10].
The performance of each above method is determined based on the mean absolute error
(MAE). The selection of best method is based on to estimate the missing values with least
error. MAE is the average between actual and predicted data values. It can be represented from
(1.1) [13].
(1.1)

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MAE values range from zero to infinity, however, a perfect fit cab only be achieved when
MAE=0.
Classification accuracy in building ensemble was another consideration of each method which
is considered in evaluation of each method imputation accuracy for missing data. SVM
ensemble is developed based on each imputation method using boosting and bagging
algorithms. Confusion matrices are obtained for each method in building ensemble for CO
analysis.
7. RESULTS AND DISCUSSIONS
The descriptive statistics of mean absolute errors with SM method are shown in Table 2. Table
2 shows that with SM method the best result of least MAE of .1533 is obtained for station 7 of
CO monitoring. The second least error result is of .2237 for imputing missing data of station 6.
Hence, the lower .1533 MAE with SM method shows that prediction imputation of missing
data to actual values with this result showed least error when it comes to imputation of missing
data.
Table 2. Mean Absolute Errors with SM Method
Stations N Minimum Maximum Mean Std.Deviation
Station 1 8783 .00 6.97 .2992 .45308
Station 2 8783 .00 7.49 .9134 .70834
Station 3 8783 .00 3.64 .2246 .25858
Station 4 8783 .00 7.20 .3551 .47763
Station 5 8783 .00 8.21 .4405 .42733
Station 6 8783 .00 5.19 .2237 .33987
Station 7 8783 .00 6.45 .1533 .25284
The descriptive statistics of mean absolute errors with MNP method are shown in Table.1.3.
Table 3 shows that .165 MAE for station 7 is obtained, this is the best result which is available
with this method. The second best result is achieved with a MAE of .228 for station 6. The results
of .254 and .256 MAEs are obtained in imputation of predicted actual values. Further results of
this method showed how close the results are in terms of MAE for predicting missing values for
each monitoring station.
Table 3. Mean Absolute Errors with MNP Method
Station 1 8544 .03 6.97 .3075 .45657
Station 2 8783 .01 7.49 .9242 .70189
Station 3 8783 .01 3.64 .2309 .25621
Station 4 8782 .00 7.20 .3645 .47509
Station 5 8781 .01 8.21 .4499 .42179
Station 6 8783 .01 5.19 .2283 .33967
Station 7 8771 .00 6.45 .1650 .25036
The descriptive statistics of mean absolute errors with MDNP method are shown in Table 4.
Table 4 shows that the minimum MAE of .1607 is obtained for station 7. However, MAE of
.9236 is highest for station 2. The results of this method demonstrated that least .1607 of MAE is
obtained through this method imputation compare to actual values.

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Table 4. Mean Absolute Errors with MDNP Method
Station 1 8544 .03 6.97 .3075 .45657
Station 2 8783 .01 7.49 .9236 .70298
Station 3 8783 .00 3.65 .2295 .25715
Station 4 8782 .01 7.21 .3629 .47628
Station 5 8781 .01 8.21 .4494 .42276
Station 6 8783 .01 5.19 .2275 .33991
Station 7 8771 .01 6.46 .1607 .25324
The descriptive statistics of mean absolute errors with LI method are shown in Table 5. Table 5
shows imputation for missing data prediction through Linear Interpolation (LI) received .1620
MAE for station 7. However, the second best result for this method is achieved with a MAE of
.2280 for station 6.
Table 5. Mean Absolute Errors with LI Method
Station 1 8544 .04 6.96 .3250 .44736
Station 2 8783 .01 7.49 .9220 .70219
Station 3 8783 .00 3.65 .2281 .25681
Station 4 8783 .00 7.20 .3616 .47535
Station 5 8783 .01 8.20 .4573 .41793
Station 6 8783 .00 5.19 .2269 .33914
Station 7 8773 .00 6.45 .1597 .25134
The descriptive statistics of mean absolute errors with LTP method are shown in Table.1.6.
Table.1.6 shows that the best result with LTP is obtained with minimum MAE of .1597 for station
7 for prediction of missing values. Whereas, second best result is obtained with a MAE of .2269
for station 6.
Table 5. Mean Absolute Errors with LTP Method
Station 1 8544 .03 6.97 .3075 .45657
Station 2 8783 .01 7.49 .9239 .70339
Station 3 8783 .00 3.65 .2305 .25769
Station 4 8783 .00 7.20 .3637 .47602
Station 5 8782 .01 8.21 .4505 .42326
Station 6 8783 .01 5.19 .2280 .34028
Station 7 8771 .00 6.46 .1620 .25268
Overall, the SM method demonstrated best in prediction for missing data having lowest MAE of
.1533 for station 7. This is followed by the LTP method having MAE of .159 for station 7 also.
Relatively all the five imputation methods utilised in this study performed considerably well,
however, among the five imputation methods best results are obtained through SM method
followed by LTP method with least MAE.
We try to classify the CO data set by using all the above five imputation methods for missing CO
data by creating an SVM ensemble with each method missing imputed data. We deployed five
imputation methods used in this research for filling missing data in CO analysis, each method
classification accuracy was evaluated by creating an ensemble using bagging and boosting
algorithms.

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Firstly, we deployed SM method for imputation of missing data and created an SVM ensemble
with this data. The ensemble obtained with SM method imputed data using adaBoostM1
algorithm resulted in a classification accuracy of 76.9% based on confusion matrix illustrated in
Figure 2.
Figure 2. SM method Confusion Matrix AdaBoostM1 Algorithm
Ensemble obtained with SM method using bagging algorithm resulted in 74.6% classification
accuracy base on confusion matrix illustrated in Figure 3.
Figure 3. SM method Confusion Matrix Bagging Algorithm
Ensemble obtained with imputed method MDNP with adaBoostM1 algorithm resulted in 76.7%
of classification based on confusion matrix as shown in Figure 4. However, ensemble using
MDNP method with bagging algorithm resulted in 75.0% classification accuracy based on
confusion matrix illustrated in Figure 5.
Figure 4. MDNP method Confusion Matrix AdaBoostM1 Algorithm

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Figure 5. MDNP method Confusion Matrix Bagging Algorithm
Ensemble based on MNP method resulted in 76.7% classification accuracy based on confusion
matrix using adaBoostM1 algorithm as shown in Figure 6. With this method classification
accuracy of ensemble resulted same i.e. 76.7% using bagging algorithm based on confusion
matrix as illustrated in Figure 7.
Figure 6. MNP method Confusion Matrix AdaBoostM1 Algorithm
Figure 7. MNP method Confusion Matrix Bagging Algorithm
A 76.9% of classification accuracy based is obtained in ensemble creation with LI method using
adaBoostM1 algorithm based on confusion matrix as shown in Figure 8. A similar percentage of
76.9% is obtained using bagging algorithm deploying LI method based on confusion matrix as
shown in Figure 9.

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Figure 8. LI method Confusion Matrix AdaboostM1 Algorithm
Figure 9. LI method Confusion Matrix Bagging Algorithm
Whereas, a classification accuracy of 76.5% is obtained in ensemble creation using LTP method
for imputation missing data by deploying adaBoostM1 algorithm based on confusion matrix as
shown in Figure 10.
A similar percentage of 76.5% classification accuracy is obtained in ensemble creation using
bagging algorithm with LTP method as illustrated in Figure 11. through confusion matrix.
Figure 10. LTP method Confusion Matrix AdaboostM1 Algorithm

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Figure 11. LTP method Confusion Matrix AdaboostM1 Algorithm
Based on the results of classification accuracy of all imputation methods, we can conclude that
the best result of classification accuracy of 76.9% is obtained with SM method using
adaBoostM1 and bagging algorithms. The other second best imputation method for filling
missing data is MNP having classification accuracy of 76.7% with bagging and adaBoostM1
algorithms.
8. CONCLUSION
This study examined the effectiveness of existing SM, MNP, MDNP, LI and LTP imputation
methods in terms of their error and classification accuracy in ensemble creation. There are
various other effective methods proposed for dealing with missing data and tends to produce
some realistic results. This research was limited to only SM, MNP, MDNP, LI and LTP
imputation methods that are already implemented in SPSS and are used by various researchers
resulted in useful results. However, these imputation methods performances in ensemble
creation are not evaluated in the previous researches, hence, this work lead to main
contribution in machine learning.
Experiment results of this research successfully identified that SM method produced lowest
MAE comparing to other imputation methods in ensemble creation. Further, ensemble creation
with SM method resulted in better classification accuracy compare to other methods using
bagging and boosting algorithms in our research. Importantly, it is noticeable that percentage
of performance accuracy margin among the imputation methods is not that high, however, SM
method comparatively possessed better imputation results for our experiments.
This research is limited to small data set i.e. 8783 observations. For future work, this research
work has few considerations, firstly, this research could be extended to larger data set.
Secondly, further work is required for the validity of SM method results by considering
various pattern of missing data. In the literature, various patterns of missing data have been
used for imputation of missing data and results were obtained successfully. Thirdly, how each
of these existing imputation methods in this study influences the performance of various
classifiers in ensemble creation, further research on this task is also essential. Fourthly, this
research could be further extended by widening the numbers of performance indicators for
these five imputation methods.
ACKNOWLEDGEMENTS
The authors would like to thanks Sreenivas Sremath Tirumala for his technical support.

89
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AUTHORS
Sh Shahid obtained his Master in Computer Sciences from the Auckland University
of Technology, Auckland in 2006. He got industry experience as an IT Analyst and
Business Analyst. He is a part time lecturer in Computer Sciences Department at
Unitec. He is in his final year Doctorate having thesis entitled, “SVM Aggregation
modeling for spatio-temporal air pollution analysis”. He also hold some Microsoft
and Cisco certifications i.e. MCP, MCSA, MCSE, CCNA, CCNP, CCDP.
http://dmli.info/index.php/member.html
Simon Dacey
Dr. Simon Dacey is lecturer at Unitec Institute of Technology, Auckland, New
Zealand and worked in software development for 17 years on applications as diverse
as a firing control system for anti-submarine warfare and a database application for
the management of wetland resources in Indonesia. He obtained his MSc in Applied
Remote Sensing from the University of Cranfield, UK (1995). From 1998 to 2002 he
worked as a lecturer at UCOL in Palmerston North, North Zealand. Since January
2002, he has been a full-time lecturer at the Department of Computing, Unitec
Institute of Technology. His research interests include Geographical Information Systems, Remote Sensing,
Digital Image Processing, Geographical Positioning Systems, and Database Management Systems.
http://www.unitec.ac.nz/about-us/contact-us/staff-directory/simon-dacey

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