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Received October 22, 2020, accepted November 12, 2020, date of publication November 17, 2020,

date of current version November 30, 2020.

Digital Object Identifier 10.1109/ACCESS.2020.3038645

A Machine Learning Approach to Predict the

Average Localization Error With Applications

to Wireless Sensor Networks

ABHILASH SINGH 1, (Member, IEEE), VAIBHAV KOTIYAL 2, SANDEEP SHARMA 2,

JAIPRAKASH NAGAR 3, (Member, IEEE), AND CHENG-CHI LEE 4,5, (Member, IEEE)

1Fluvial Geomorphology and Remote Sensing Laboratory, Indian Institute of Science Education and Research at Bhopal, Bhopal 462066, India

2Department of Electronics and Communication Engineering, Gautam Buddha University, Greater Noida 201312, India

3Subir Chowdhury School of Quality and Reliability, IIT Kharagpur, Kharagpur 721302, India

4Research and Development Center for Physical Education, Health, and Information Technology, Department of Library and Information Science, Fu Jen Catholic

University, New Taipei City 242, Taiwan

5Department of Photonics and Communication Engineering, Asia University, Taichung 41354, Taiwan

Corresponding authors: Sandeep Sharma (sandeepsvce@gmail.com) and Cheng-Chi Lee (cclee@mail.fju.edu.tw)

ABSTRACT Node localisation is one of the signiﬁcant concerns in Wireless Sensor Networks (WSNs).

It is a process in which we estimate the coordinates of the unknown nodes using sensors with known

coordinates called anchor nodes. Several bio-inspired algorithms have been proposed for accurate estimation

of the unknown nodes. However, use of bio-inspired algorithms is a highly time-consuming process. Hence,

ﬁnding optimal network parameters for node localisation during the network set-up process with the desired

accuracy in a short time is still a challenging task. In this article, we have proposed an efﬁcient way

to evaluate the optimal network parameters that result in low Average Localisation Error (ALE) using a

machine learning approach based on Support Vector Regression (SVR) model. We have proposed three

methods (S-SVR, Z-SVR and R-SVR) based on feature standardisation for fast and accurate prediction of

ALE. We have considered the anchor ratio, transmission range, node density and iterations as features for

training and prediction of ALE. These feature values are extracted from the modiﬁed Cuckoo Search (CS)

simulations. In doing so, we found that all the methods perform exceptionally well with method R-SVR

outperforming the other two methods with a correlation coefﬁcient (R =0.82) and Root Mean Square Error

(RMSE = 0.147m).

INDEX TERMS ALE, modiﬁed CS algorithm, SVR model, GPR model, WSNs.

I. INTRODUCTION

A WSN consists of a set of miniature and inexpensive sensors

that are spatially distributed over an area to measure the phys-

ical parameters or monitor the habitat conditions and also

have many practical areas of implementation such as target

tracking, precision agriculture, etc., [1]–[6]. In most of the

applications, these sensors need to estimate their coordinates

accurately with minimum resource requirements. These sen-

sors can quickly locate their coordinates using an integrated

Global Positioning System (GPS) system. However, it is not

practically feasible to integrate GPS in all the sensors due to

its size and cost. An alternate approach is to use the concept of

localisation algorithms in which several anchor nodes (with

The associate editor coordinating the review of this manuscript and

approving it for publication was Tie Qiu .

integrated GPS) will assist the unknown nodes to determine

their coordinates accurately.

A large number of localisation algorithms have been intro-

duced to solve different localisation problems [7]. These

algorithms are expected to be ﬂexible so that it can work well

in various diverse indoor and outdoor scenarios and topolo-

gies. These localisation algorithms have been divided into

two categories, viz., range-based algorithms and range-free

algorithms. In range-based algorithms, the location of the

unknown nodes is computed with the help of distance

between the anchor and unknown sensor nodes. They utilise

the ranging metrics such as the angle of arrival, time of arrival,

and the Received Signal Strength Indication (RSSI) [8]–[10].

In contrast, the range-free algorithms such as ad-hoc posi-

tioning system [11] and centroid [12], etc., make use of

simple operations related to the connectivity to localise the

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

unknown node. They only need the existence of the beacon

signal in the medium by the anchor node. Among both,

the range-based algorithms are widely employed and pre-

ferred over the range-free algorithms [13]–[15].

To design a less complicated algorithm; various bio-

inspired algorithms have been proposed for range-based

approach [16]. Initially, Gopakumar and Jacob [17] rendered

a node localisation method formed on Particle Swarm Opti-

misation (PSO) [18], which imitated the behaviour of a ﬁsh

swarm to search for food. This algorithm showed good initial

results, but the implementation tended to get caught in a local

optimum, which results in premature convergence. In 2014,

Goyal and Patterh [19] implemented CS for node locali-

sation in WSNs. It showed noticeable results to minimise

the localisation error. This is mainly because of the tuning

parameters in the CS algorithm, which ease the calculation

process. Recently, a modiﬁed version of CS was proposed by

Cheng and Xia [20], which improved the convergence rate

of the conventional CS algorithm. They modiﬁed the random

walk step size and the mutation probability to improve the

search process.

ALE metrics assess the accuracy of these localisation algo-

rithms. We select an algorithm that has the minimum ALE

value. The major problem after selecting a bio-inspired algo-

rithm for node localisation is the computational time. During

any network set-up, we need to run the algorithm many times

in order to ﬁnd the optimal network parameters (such as

anchor ratio, transmission range, node density, etc.,) and to

tune the ALE below the threshold for the desired scenario.

To deal with this limitation, we have proposed an efﬁcient

machine learning approach for accurate and fast prediction

of ALE in such a scenario. As far as we know, no other study

has been conducted and published to address this issue.

In this article, we have presented three methods based on

the SVR model. We have selected and extracted four features,

namely anchor ratio, transmission range, node density and

number of iterations from the modiﬁed CS algorithm. Even-

tually, we input this data to train the SVR model and obtained

the predicted ALE using the trained SVR model for all the

three methods.

Further, we have divided this article into six sec-

tions. In Section II, we have discussed the related works.

In Section III, we have discussed the system model for

the node localisation problem. Furthermore, we have also

discussed the details of the features importance, hyper-

parameter tuning and SVR model. Afterwards, in Section IV,

we have discussed the simulation scenarios and parameters

for the modiﬁed CS and SVR model. In Section V, we have

discussed the results of all the three methods for ALE predic-

tion. Finally, in Section VI and VII, we have presented the

discussion and conclusion respectively.

II. RELATED WORKS

In this section, we have discussed the several methods

for improving the node localisation accuracy. Several stud-

ies have been conducted to improve localisation accuracy

using machine learning. Morelande et al. [21] introduced

a Bayesian algorithm for node localisation in WSNs. The

proposed algorithm is a reﬁnement of a previous work

referred to as progressive correction [22]. Both these methods

are compared in different scenarios keeping Cramér–Rao

bound (CRB) as the benchmark. The proposed algorithm

proved to be more accurate than its predecessor. Further,

Ghargan et al. [23] presented an approach in which Artiﬁ-

cial Neural Network (ANN) is hybridised individually with

three optimisation algorithms: Particle Swarm Optimisation

(PSO), Backtracking Search Algorithm (BSA) and Gravi-

tational Search Algorithm (GSA). The GSA-ANN hybrid

proved to outperform the other methods with a mean absolute

distance estimation error of 0.02m and 0.2m for outdoor and

indoor scenarios, respectively. In a recent survey, Ahmadi

and Bouallegue [24] compiled the different state-of-the-art

machine learning techniques utilised in node localisation in

WSNs. It compared the cumulative localisation error distri-

bution curve of various techniques like ANN, Support Vector

Machine (SVM), Decision Tree (DT) and Naive Bayes (NB)

method. This study reported that NB outperformed all the

other machine learning techniques based on their cumula-

tive localisation error distributions. Bhatti et al. [25] devel-

oped an outlier detection algorithm named ‘‘iF_Ensemble’’

for an indoor localisation environment using a combina-

tion of different supervised, unsupervised, and ensemble

machine learning methods. Here, the supervised learning

techniques are K-nearest neighbour (KNN), Random For-

est (RF) classiﬁers and SVM, whereas unsupervised learning

techniques is isolation Forest (iForest). These techniques are

used with stacking, that is an ensemble learning method.

The model, including stacking, is compared with the indi-

vidual performances of the machine learning algorithms

involved. The stacking model provides high localisation

accuracy of 97.8% with proposed outlier detection methods.

Recently, Wang et al. [26] introduced a node localisation

algorithm named Kernel Extreme Learning Machines based

on Hop-count Quantization (KELM-HQ). The trained KELM

computes the locations of the unknown nodes. The proposed

algorithm proves the localisation error to be improved by

34.6% when compared with fast-SVM, 19.2% when com-

pared with GADV-Hop algorithm, and 11.9% when com-

pared with DV-Hop-ELM algorithm.

Overall, this study aims to overcome the limitation

of localisation accuracy in previous studies by using a

regression-based machine learning approach.

III. SYSTEM MODEL

In this section, ﬁrst, we have discussed the system architec-

ture designed for the node localisation process. Then we have

discussed the method to compute the distance between the

anchor and unknown nodes. Afterwards, we have discussed

the objective function formation and working of the mod-

iﬁed CS algorithm for node localisation. Finally, we have

discussed the details of the machine learning model used.

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A. SYSTEM ARCHITECTURE

The sensor nodes are considered to be deployed randomly

inside a region with area X×Ysquare units. The system

consists of Manchor nodes. These anchor nodes act as a

reference for all Nunknown nodes of the network, which

need to be localised. All the sensors can transmit/receive

data within a transmission range of Rdistance units. The

anchor’s positional information is utilised as a reference to

evaluate the coordinates of all the localisable unknown nodes.

An unknown node is considered localisable only if it has at

the minimum three anchor nodes inside its communication

range.

B. DISTANCE CALCULATION AND OPTIMISATION

PROBLEM FORMATION

The RSSI is used by the unknown nodes to calculate their

distances from the anchor nodes. Sensors experience a power

loss during the exchange of information because of shad-

owing and multipath fading. This path loss is modelled as

log-normal shadowing [27], which is expressed as shown

in Eq.(1):

PL(d)=PL0+10 ×η×log10 (d

d0

)+Xg(1)

In Eq.(1), PL(d), PL0, and drepresent total path loss

(transmitted power – received power), path loss at a reference

distance d0, and the distance between the transmitter and

the receiver respectively. Besides, ηdenotes the path loss

exponent showing how the strength of the received signal

decreases with the increase in distance between transmitter

and receiver [28]. The value of ηrelies on various parameters

such as signal frequency, antenna height, and the propagation

environment [27]. Generally, the value of ηlies in the range

of 2-6 [29] and is higher than 4 for indoor or shadowed

environment [30]. Furthermore, σrepresents the standard

deviation of shadowing effects, and its value varies with the

signal propagation environment and is generally higher than

4 dB [31]. Xgis a Gaussian random value representing the

attenuation caused by fading.

A ranging error is experienced as the result of log-normal

shadowing. This ranging error observes a zero-mean Gaus-

sian distribution. Its variance σ2is expressed in Eq.(2):

σ2=γ2×D2

ij (2)

where, γrepresents the localisation error between the actual

and measured Euclidean distance Dij between ith node (xi,yi)

and the jth node (xj,yj) and is known as Gaussian noise having

mean zero and standard deviation one. We have considered

the value of γequal to 0.1 as it is the most appropriate value

used in literature [20], [32]. Eq. (2) shows that the standard

deviation of the ranging error varies linearly with the actual

distance between two nodes. The real distance Dij can be

calculated using the following Eq.(3):

Dij =q(xi−xj)2+(yi−yj)2(3)

A circular disk model has been adopted to establish net-

work connectivity: two nodes iand jcan converse with each

other only if Dij 6R, where Ris the transmission range of

both the sensor nodes.

The measured distance is represented by D0

ij, and is given

by the expression in Eq.(4):

D0

ij =Dij +Nij (4)

where, Nij is the ranging error between node iand j.

While calculating the position of the unknown nodes, there

always exists a ranging error. So, we need to evaluate the

position of the unknown nodes as precisely as possible,

considering this inevitable ranging error. To achieve this,

we formulate an Optimisation Function (OF), which is the

mean of the square of the error between the actual distance

of evaluated node coordinates and the estimated distance

of actual unknown node coordinates from the neighbouring

anchor nodes. Let, (xi,yi) and (xj,yj) be the position of ith

unknown node and jth anchor node respectively. The OF is

given in Eq.(5):

OF(xi,yi)=1

M×

M

X

j=1

(Dij −D0

ij)2(5)

where, M>3, because an unknown node should have

at the minimum three anchor nodes within its transmission

range to be considered as localisable (trilateration rule). The

(xi,yi) corresponding to the minimum value of the OF is the

evaluated position of the unknown node.

C. MODIFIED CS ALGORITHM FOR NODE LOCALISATION

Modiﬁed CS is a bio-inspired meta-heuristic algorithm [20]

used for node localisation in WSNs. It estimates the coordi-

nates of the unknown nodes in the network by initialising a

random population of candidate solutions for every unknown

node. Afterwards, it calculates the ﬁtness value for each

solution using the OF (using Eq.(5)). The worst out of the

candidate solutions are replaced by a new set of randomly

allocated candidate solutions. This process continues over

a predetermined number of iterations, then the coordinates

corresponding to the global best solutions are selected as the

coordinates of the unknown nodes in the network for each of

the node.

D. MACHINE LEAR NING MODEL

Broadly, learning algorithms are divided into supervised and

unsupervised learning. Further, supervised learning is classi-

ﬁed into classiﬁcation and regression learning, whereas unsu-

pervised learning is classiﬁed into clustering and dimension

reduction techniques [33].

In this article, our objective is to assess the potentiality

of regression-based machine learning algorithms for esti-

mating the node localisation error. The key objective of

regression-based machine learning algorithms is to predict

the predictand based on a mapping function. This mapping

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

FIGURE 1. Predictor importance graph.

function is modelled by feeding a set of features and predic-

tand data known as training data set. In doing so, we have

selected the SVR algorithm. SVR is used in many appli-

cations such as image processing [34], [35], remote sens-

ing [36], and blockchain [37]. It has superb generalisation

competence along with high accuracy. Also, the computa-

tional complexity is independent of the input feature data

set [38].

1) FEATURE IMPORTANCE

In this article, we have evaluated the feature’s importance

by regression ensemble approach. First, we have trained a

regression ensemble model. It contains the results of boosting

hundred regression trees (number of ensemble learning cycle)

using LSBoost ensemble aggregation approach, feature data

and the predictand data. We have used the regression tree,

weak learner, with unity learning rate. After creating an

ensemble, we calculated the estimate of the predictor or fea-

ture importance by summing these estimates over all the weak

learners in it. In doing so, we plotted the feature importance

graph (Fig. 1). We found that out of the four features, the node

density is the most important feature followed by the number

of iterations. In contrast, the anchor ratio and the transmis-

sion range has nearly equal importance. Further, we have

estimated the partial dependency of the features on the pre-

dictand (Fig. 2). In the same plot, we have also plotted the

individual conditional expectation of each data.

2) HYPER-PARAMETER OPTIMISATION

SVR is used to learn from data indicating excellent per-

formance in prediction and pattern recognition. It is also

beneﬁted from the big data collected from onboard analysis.

The hyper-parameters have a signiﬁcant inﬂuence on SVR’s

predictive efﬁciency. The SVR’s efﬁciency is determined by

the different hyper-parameters such as Cand , which helps

in identifying the training error. If the residual is higher than

hyper-parameter , then the parameter Cpenalises the train-

ing error. Thus, minimal Cvalues lead to computational com-

plexity, while too large Cvalues lead to model under-ﬁtting.

In this article, we have used the universal grid search

approach to optimise the hyper-parameter present in the SVR

model. In this study, we optimise the penalty factor, C, in the

SVR model by keeping the , constant. We have selected the

famous Mean Square Error (MSE) function as the loss or

objective function (using Eq. (6)) for optimisation.

1

n

n

X

i=1

(Yi−b

Yi)2(6)

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

FIGURE 2. Partial Dependence Plot (PDP) and Individual Conditional Expectation (ICE) plots.

We have selected the Cvalue, which corresponds to the

minimum value of the objective function for all the three

methods.

3) SUPPORT VECTOR REGRESSION MODEL

SVR was initially proposed by Drucker et al., which is a

supervised learning technique, based on the concept of Vap-

nik’s support vectors [39], [40]. SVR aims at reducing the

error by determining the hyperplane and minimising the

range between the predicted and the observed values. Min-

imising the value of win the Eq.(7) is similar to the value

deﬁned to maximise the margin, as shown in Fig. 3.

min ||w||2+C

n

X

i

(ξ+

i+ξ−

i) (7)

where, n

P

i

(ξi) represents an empirical error. Hence, to min-

imise this error, Eq.(8) is being used.

f(x)=

n

X

iα∗

i+aiK(x,xi)+B(8)

where,α∗

i,ai≥0 represents the Lagrange multiplier,

K(x,xi)represents the kernel function and Brepresents the

bias term. In this study, we have used the Polynomial kernel

given by:

K(x,xi)=γ(x∗xi+1)d(9)

where dis the polynomial degree and γis the polynomial

constant.

SVR performs better performance prediction than other

algorithms like Linear Regression, KNN and Elastic Net, due

to the improved optimisation strategies for a broad set of vari-

ables. Moreover, it is also ﬂexible in dealing with geometry,

transmission, data generalisation and additional functionality

of kernel [41]. This additional functionality enhances the

model capacity for predictions by considering the quality of

features [42].

The training samples inﬂuence the SVR model’s ﬁtting

performance since the SVR algorithm is sensitive to the

interference in the training data. Besides, SVR is useful in

resolving high dimensional features regression problem, and

well-function if the feature metrics is larger than the size of

the sample [43]. In this study, we have extracted four features,

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

FIGURE 3. Structure of support vector regression.

namely anchor ratio, transmission range, node density and the

number of iterations from modiﬁed CS algorithm simulation.

Feature scaling is essential for SVR because, when one

function has greater magnitudes than others, the other fea-

tures will dominate while measuring the distance. To avoid

this, we have used various standardisation approaches. Based

on which, we have proposed three methods, as shown

in Fig. 4. The method I is S-SVR (Scaling SVR). In this

method, we ﬁrst standardised the features using Eq.(10):

xs=x

σ(10)

where xis the feature vector, xsis the standardised data, and σ

is the standard deviation of the feature vector. The method II is

Z-SVR (Z-score SVR). In this method, we have standardised

the features using Eq.(11):

xs=x−x

σ(11)

where xis the mean of the feature vector. The method III is the

R-SVR (Range SVR). In this method, we have standardised

the features using Eq.(12):

xs=x−xmin

xmax −xmin

(12)

Afterwards, we trained and tested the SVR models

in 70:30 ratio, as shown in Fig. 4. In this study, the dimension

of the features vector are 107 ×1. Hence, we have used

75 data for training and the remaining 32 for testing.

IV. SIMULATION EXPERIMENT

In this section, we have discussed the simulation environment

of the modiﬁed CS algorithm and the SVR model.

A. ALE SIMULATION USING MODIFIED CS ALGORITHM

For the calculation of ALE, we set up a simulation envi-

ronment of 100 ×100 m2, and we vary the parameters like

node density, anchor ratio and transmission range of each

node to calculate ALE for different network conﬁgurations.

Modiﬁed CS has some tuning parameters like step size αand

mutation probability Pa, which lie in the ranges 0.9 to 1.0 and

0.05 to 0.25 respectively. The number of candidate solutions

is ﬁxed at 25. The maximum number of iterations allowed to

localise each unknown node is set to 100.

B. SVR SIMULATION FOR ALE PREDICTION

For simulating the SVR model, we performed the

hyper-parameter tuning through the grid search algorithm.

In doing so, we ﬁxed one of the hyper-parameter (i.e.,at

0.01) and applied the grid search algorithm to ﬁnd the value

of the other hyper-parameter. We created a 100 ×100 grid

for the penalty factor, C. Each grid represents a speciﬁc

value of C. On simulating the grid search algorithm, it ﬁnds

an optimal grid that corresponds to the minimum value of

the MSE. The range of optimal Cfor all the three methods

along with the other simulation parameter value is given

in Table 2.

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

FIGURE 4. Flowchart of the methodology.

TABLE 1. Simulation parameters for Modified CS algorithm.

TABLE 2. Simulation parameters for SVR model.

V. RESULTS

In this section, we have presented the results of the method I,

II and III for ALE prediction in the respective subsections.

We have plotted a linear regression curve between the pre-

dicted ALE and the simulated ALE for comparison.

A. PERFORMANCE OF THE METHOD I

We have compared the predicted ALE results, thus obtained

by the method I with the simulated results of the modiﬁed

CS algorithm. We found that predicted results accorded well

with the simulated results and gathered along the straight

regression line with mild scattering (Fig. 5). The shaded

grey region corresponds to the 95% Conﬁdence Interval

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

FIGURE 5. Prediction results for ALE using method I.

(CI) of the regression line and suggests that the predicted

result has a strong positive correlation with R =0.80 and

RMSE =0.23m.

B. PERFORMANCE OF THE METHOD II

Once we calculated the predicted ALE through method II,

we have evaluated its performance with the simulated results

of the modiﬁed CS algorithm. In doing so, we found a good

agreement between the both with R =0.81 and RMSE =

0.20m (Fig. 6). However, some observed values lie outside

the CI of the regression line due to the overestimation of the

ALE value by the SVR model. The overestimation probably

occurs due to the positive bias. This type of error comes under

systematic error which is mainly due to model or approach

used.

FIGURE 6. Prediction results for ALE using method II.

C. PERFORMANCE OF THE METHOD III

We have compared the predicted ALE of the method III with

the simulated ALE obtained through modiﬁed CS algorithm.

FIGURE 7. Prediction results for ALE using method III.

In this case, also, we found a strong correlation between the

variables (Fig. 7). Here, we found a pragmatic correlation of

R=0.82 with RMSE =0.15m.

FIGURE 8. Comparison of the computation time for method I, II, III with

different scenarios of modified CS algorithm.

VI. DISCUSSION

In this section, we have ﬁrst discussed the performance of

all the three methods in terms of computational efﬁciency.

In doing so, we have calculated the computational time

required to predict or calculate the ALE. Further, to ensure

a fair comparison of the proposed methods with the existing

modiﬁed CS, we have compared the obtained results with

the computational time of the modiﬁed CS simulated results

for three different conﬁgurations i.e., computational time for

node density 100, 200 and 300 have been plotted by taking

the transmission range of 20m and an anchor node of 20 in

100 ×100 m2area (Fig. 8). In this ﬁgure, the time axis is

in log scale. The dotted line shows the computational time

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A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

TABLE 3. Comparison of the proposed methods with the benchmark.

required by all the three methods when it is compiled in a

single script.

On comparing, we found that the time taken by all the

three methods is signiﬁcantly lower than the time taken by

the modiﬁed CS algorithm. Further, method III taken the least

time followed by method II and method I respectively.

Various other studies have been carried out to improve

the localisation accuracy based on Adaptive Neural Fuzzy

Inference System (ANFIS) [44] with a Mean Absolute

Error (MAE) of 0.283 m and backpropagation based artiﬁcial

neural network (BP-ANN) model [45] with a mean locali-

sation error of 0.921 m. Both these studies have reported a

high localisation accuracy. In this study, we have reported

a minimal RMSE of 0.15m. However, to ensure a fair eval-

uation of the proposed methods, we need to compare the

results of SVR with other regression-based machine learning

model. We have selected Gaussian Process Regression (GPR)

for comparison because it is widely used, robust and accu-

rate model [46], [47]. In doing so, we have compared the

obtained results with the corresponding variants of GPR. The

three corresponding GPR variants are Scaling GPR (S-GPR),

Z-score GPR (Z-GPR) and Range GPR (R-GPR) as illus-

trated in Table 3. We have used R, RSME and computational

time for comparing the results of all the methods. In doing

so, we found that the method III is the most effective method

among all the methods.

Although the proposed methods perform better than the

corresponding variant of the GPR, the SVR based meth-

ods are susceptible to under-performance when dealing with

noisy data. In such scenarios, GPR is more likely to perform

better [48]. Also, the performance of the proposed methods

depends on the choice of the kernel and features.

VII. CONCLUSION

In this article, we presented and investigated three SVR based

machine learning model for ALE prediction. These meth-

ods are deﬁned based on the standardisation method used.

In the method I, II and III, we have used scaling, Z-score

and range standardisation methods respectively. Afterwards,

we trained the SVR model with the polynomial kernel using

the standardised data and evaluated its performance using

correlation of coefﬁcient and RMSE metrics. In doing so,

we found that range standardisation (using Eq.(12)) of the

features (i.e., method III) results in lower RMSE in ALE

prediction. Also, the coefﬁcient of correlation is highest in

method III.

Further, we have also compared the performance of all the

three models in terms of the computation time requirement.

Again, method III performs better than the other two methods.

It requires less time than the other two methods. Hence,

method III can be used for ALE prediction during network

set-up process to cut down the time requirements.

ACKNOWLEDGMENT

The authors would like to acknowledge IISER, Bhopal;

Gautam Buddha University, Greater Noida; IIT Kharagpur;

Fu Jen Catholic University, Taiwan; and Asia University,

Taiwan, for providing institutional support. They would like

to thank to the editor and all the anonymous reviewers for

providing helpful comments and suggestions.

CODE AVAILABILITY

The code for this work will be made available on a reasonable

request to the corresponding authors.

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ABHILASH SINGH (Member, IEEE) received the

integrated dual (B.Tech. and M.Tech.) degree in

electronics and communication engineering with

specialization in wireless communication and net-

works from Gautam Buddha University, Greater

Noida, India, in 2017. He is currently pursuing the

Ph.D. degree in the ﬁeld of remote sensing with the

Indian Institute of Science Education and Research

at Bhopal, Bhopal, India.

Since 2018, he has been working on the

NASA-ISRO Synthetic Aperture Radar (NISAR) Project at IISER Bhopal.

He has been publishing research papers in peer-reviewed conferences

and internationally reputed journals. His current research interests include

microwave remote sensing, machine learning, bio-inspired algorithms, wire-

less sensor networks, and wireless communication.

Mr. Singh is a member of the European Geophysical Union (EGU), ISPRS,

and the Indian Radio Science Society (InRaSS). He was a recipient of the

Gold Medal Awards from the University for been throughout the First Rank

Holder in his UG and PG. He received the prestigious ‘‘DST-INSPIRE’’

Fellowship to carried out his Ph.D. degree from the Department of Science

and Technology (DST), Ministry of Science and Technology, India. He also

received the DAAD Fellowship to attend a Summer School, in 2019.

208262 VOLUME 8, 2020

A. Singh et al.: Machine Learning Approach to Predict the ALE With Applications to WSNs

VAIBHAV KOTIYAL was born in New Delhi,

India, in 1998. He received the integrated dual

(B.Tech. and M.Tech.) degree in electronics and

communication engineering with specialization

in wireless communication and networks from

Gautam Buddha University, Greater Noida, India,

in 2020.

He ranked third in the University in the course.

He is currently working as a Junior Research Fel-

low (JRF) with the Department of Industrial and

Management Engineering, IIT Kanpur, India. His research area during

his M.Tech. degree was on node localization in wireless sensor networks

(WSNs). He trained with Airports Authority of India (AAI) in his summer

training period, learning about various equipment used by the organization

to ensure navigation to the air-crafts all over the Indian airspace. His current

research interests include machine vision, the IoT, and machine learning

application to wireless sensor networks.

SANDEEP SHARMA received the B.Tech. degree

in electronics engineering from RGPV, Bhopal,

India, in 1997, the M.Tech. degree in digital com-

munication from Devi Ahilya University, Indore,

India, in 2005, and the Ph.D. degree in electron-

ics and communication engineering from Gautam

Buddha University, Greater Noida, India, in 2016.

Since 2010, he has been working as a Faculty

Member with the Electronics and Communication

Engineering Department, School of ICT, Gautam

Buddha University. He has published 22 research articles in reputed inter-

national journals and more than 41 papers published in the international

conferences. His research interests include wireless sensor networks, wire-

less network security, physical layer authentication, intrusion detection in

wireless networks, cross-layer design, and machine learning applications in

WSNs.

Mr. Sharma was a recipient of the Best Conference Paper in the interna-

tional conference ICCCS, in 2016, and the Young Scientist Award in 2019 for

his research work. He is an Active Reviewer of IET Communications,

IEEE WIRELESS COMMUNICATIONS LETTERS,Journal of Information Technol-

ogy (Springer), Personal and Ubiquitous Computing (Springer), Multimedia

Tools and Applications (Springer), International Journal of Computer Appli-

cations in Technology (Inderscience), International Journal of Communica-

tion Systems (Wiley), Journal of The Institution of Engineers (India): Series

B, and the Journal of Intelligent and Fuzzy Systems.

JAIPRAKASH NAGAR (Member, IEEE) was born

in Nagla Vasdev, Mathura, Uttar Pradesh, India,

in 1991. He received the integrated B.Tech. (elec-

tronics and communication engineering) and

M.Tech. (wireless communication and networks)

degree from Gautam Buddha University, Greater

Noida, India, in 2015. He is currently pursu-

ing the Ph.D. degree with the Subir Chowdhury

School of Quality and Reliability, IIT Kharagpur,

India.

He has published six research articles in reputed SCI/Scopus indexed jour-

nals and international conferences (IEEE/Springer/Taylor and Francis). His

current research interests include analytical modeling of wireless multihop

networks, the Internet of Things (IoTs), machine learning techniques for the

IoTs, and block-chain implementation for real life applications.

CHENG-CHI LEE (Member, IEEE) received

the Ph.D. degree in computer science from

National Chung Hsing University (NCHU),

Taiwan, in 2007. He is currently a Distinguished

Professor with the Department of Library and

Information Science, Fu Jen Catholic University.

His current research interests include data security,

cryptography, network security, mobile commu-

nications and computing, and wireless communi-

cations. He has published more than 200 articles

on the above research ﬁelds in international journals. He is a member of

the Chinese Cryptology and Information Security Association (CCISA),

the Library Association of The Republic of China, and the ROC Phi Tau

Phi Scholastic Honor Society. He has also served as a Reviewer for many

SCI-index journals, other journals, and other conferences. He is also an

Editorial Board Member of some journals.

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