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                                 Vol. 6, No. 1 | January – June 2023 
 

 

 

SJET | P-ISSN: 2616-7069 |E-ISSN: 2617-3115 | Vol. 6 No. 1 January – June 2023 
23 

Harris’ Hawks Optimization-Tuned Density-based 

Clustering 

Muhammad Shoaib Omar1, Syed Muhammad Waqas2, Kashif Talpur3*, Sumra Khan4, 

Shakeel Ahmad3 

Abstract: 

Clustering is a machine learning technique that groups data samples based on similarity and 

identifies outliers with distinct features. Density-based clustering outperforms other methods 

because it can handle arbitrary shapes of clustering distributions. However, it has a limitation of 

requiring empirical values for the cluster center and the nominal distance between the cluster 

center and other data points. These values affect the accuracy and the number of clusters obtained 

by the algorithm. This paper proposes a solution to optimize these parameters using Harris’ 

hawks optimization (HHO), an efficient optimization technique that balances exploration and 

exploitation and avoids stagnation in later iterations. The proposed HHO-tuned density-based 

clustering achieves better performance as compared to other optimizers used in this work. This 

research also provides a reference for designing efficient clustering techniques for complex-

shaped datasets. 

Keywords: Machine learning; density-based clustering; metaheuristic algorithm; Harris’ hawk 

optimization; clustering.

1. Introduction 

Unlabeled data is being generated 
exponentially by today’s information systems, 
which demands accuracy and high efficiency 
for analysis, in order to draw logical 
conclusions. Clustering is the most studied and 
broadly used learning technique of its kind. It 
endeavors to divide a dataset into numerous 
usually separate subsets where each one is 
called a cluster. Through this partition, each 
cluster may assimilate to some prospective 
categories, which the clustering algorithm is 
not aware of prior to working on it. Based on 
the diverse learning approaches, researchers 
have considered many types of clustering 

                                                           
1 Department of Computer Science, Bahria University, Karachi, Pakistan 
2 Department of Computer Science, Muhammad Ali Jinnah University, Karachi, Pakistan 
3 Department of Science and Engineering, Solent University, Southampton, United Kingdom 
4 Department of Information Technology, Salim Habib University, Karachi, Pakistan 

Corresponding Author: [kashif.talpur@solent.ac.uk] 

algorithms, based on different features. These 
methods can be characterized into density-
based, portioning-based, hierarchy-based, 
model-based, and grid-based approaches [1]. 

A density-based clustering algorithm 
groups data points based on cut-off distance 
and minimum number of points in each radius. 
In 1996, an algorithm was proposed by Martin 
Ester et. al [2] as a clustering algorithm with 
arbitrary cluster shapes without specifying the 
number of clusters beforehand, and they 
named it density-based spatial clustering of 
applications with noise (DBSCAN). 
DBSCAN, by design, has several advantages 
when compared to its counterparts; as it does 



 

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not need to define the number of clusters as 
prior information, and it can work with 
datasets with varying densities. DBSCAN 
algorithm is a novel technique to deal with 
unlabeled data as it promises great success. 

Initially, using DBSCAN, several past 
works have focused on clustering spatial data, 
however, its success has been noticed in 
various other data complexities [3,4,5]. 
Because it groups data points with respect to 
density, clusters in DBSCAN are considered to 
be the regions with dense data points, and these 
clusters are separated by the regions having 
low density, or noise. This core functionality 
of this algorithm makes it effective in 
identifying clusters with unusual arbitrary 
shapes, as well as, determining noise or 
outliers [6]. DBSCAN performs clustering 
with the help of two user-defined parameters: 
epsilon (ɛ) which is the cluster radius and 
minimum points (minPts) to be present in that 
radius. Despite its efficacy in clustering 
applications, DBSCAN faces same limitations 
as other clustering methods, such as the 
determination of optimal values for user-
defined parameters (ɛ and minPts) is difficult 
and problem specific. This demands a 
significant amount of personal experience or 
several experimental trials, hence limiting its 
extensive use. 

To address the said problem, different 
approaches have been proposed in the 
literature. Lai et. al [7] used multi-verse 
optimizer (MVO) algorithm for automatic 
selection of ɛ and minPts parameters. The 
authors claimed to have achieved improved 
clustering performance of DBSCAN while 
employed on three public datasets. In this 
research, the authors first improved MVO and 
then used it for finding the optimum range of 
values for the DBSCAN parameters. 
Researchers in [8] proposed the unsupervised 
patterns in multi-dimensional data, also known 
as data cubes, using genetic algorithm (GA). 
While tuning GA parameters (mutation and 
crossover), the researchers utilized fuzzy 
inference mechanisms: Mamdani's rules and 
Takagi-Sugeno's rules. When compared with 
the existing DBSCAN, they found the GA-
tuned DBSCAN achieved better clustering 

quality on six datasets of data cubes, for OLAP 
(online analytical processing) purposes. 
Another successful application of 
metaheuristic algorithms on DBSCAN 
parameter optimization is done by Zhu et. al 
[9] where the authors used harmony search 
(HS) optimization algorithm for the similar 
purposes. The experiments of this new 
clustering scheme, on six clustering problems 
of varying complexity, showed superior 
performance than the canonical DBSCAN, 
based on Rand index (RI) and Jaccard 
coefficient (JC) evaluation metrics. These 
significant research efforts have developed and 
extended the applicability of DBSCAN by 
benefiting from optimization capability of 
metaheuristic algorithms that select more 
reasonable values of clustering parameters 
from an optimal range. 

Metaheuristic algorithms have proved to be 
powerful optimization techniques, while 
implemented over a range of optimization 
problems. By mimicking intelligent behaviors 
from nature, researchers have developed 
efficient search mechanisms. The well-
established metaheuristic algorithms are 
particle swarm optimization (PSO) [10], 
artificial bee colony (ABC) [11], genetic 
algorithms (GA) [12], and ant colony 
optimization (ACO) [13]. However, some of 
the latest counterparts have also been effective 
in research, such as grey wolf optimization 
(GWO) [14], Archimedes optimization 
algorithm (AOA) [15], honey badger 
algorithm (HBA) [16], and chaos game 
optimization (CGO) [17]. These and many 
others are used in data mining tasks [18], 
wireless sensors node localization [19], power 
flow optimization in smart grids [20], stock 
price prediction [21], etc. Most of these 
metaheuristic algorithms are based on 
collective intelligence displayed by a group of 
search agents, which makes them simple, 
efficient, and ready to deploy on any 
optimization problem. Harris' hawks 
optimization (HHO) is a recent induction in the 
paradigm of optimization methods, developed 
by Heidari et. al paradigm of optimization 
methods, developed by Heidari et. al [22]. 
HHO maintains a robust global search strategy 
by integrating balanced exploration and 



 

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exploitation tools. Its performance is rightfully 
validated by several research works, such as 
engineering design optimization [23], satellite 
imaging breakdown threshold optimization 
[24], drug design and discovery [25] and 
wireless sensor node localization [26], and 
many other constrained and unconstrained 
problems [7,27,28,29]. 

Keeping in view the outstanding global 
search ability of HHO and its effective 
exploration and exploitation strategies, we 
utilize it to improve clustering performance of 
DBSCAN. We optimize the DBSCAN 
parameters (ɛ and minPts) using HHO, since 
the manual parameter selection process is 
based on trial and error which is considered as 
an ineffective approach. The optimal 
parameters result in high clustering accuracy. 
The rest of the paper is organized as follows. 
The upcoming section explains about materials 
and methods like fundamentals of DBSCAN 
and HHO. Section 
\ref{sec:MaterialsAndMethods} elaborates on 
the methodology of HHO for DBSCAN 
parameter optimization. The experimental 
settings and results are discussed in Section 
\ref{sec:Results}, whereas Section 
\ref{sec:Conclusion} duly concludes the 
findings of this research. 

2. Materials and Methods 

2.1. DBSCAN Clustering Algorithm 

DBSCAN (Density-based spatial 
clustering of applications with noise), 
introduced by Martin et al. in 1996 [2], is a 
density-based clustering algorithm, which 
identifies clusters by density of objects found 
in dense regions. The benefits of this technique 
are that it can identify clusters of arbitrary 
shapes, clusters within a cluster (nested 
clusters) as well as outliers (the points not 
belonging to any cluster). This algorithm is 
mainly based on two integer value parameters: 
ɛ and minPts, where ɛ is the maximum radius 
of the neighborhood and minPts are the 
minimum number of points in that radius. A 
user has to provide values of these two 
parameters based on some past experience or 
on hit and trial basis. These two parameters 

play an important role in accuracy of the 
clusters being identified by the algorithm. Let's 
say if ɛ is a larger number, it will include many 
points in a cluster. Some of the points might 
occur there, which may not actually belong to 
that cluster. On the contrary, if it is initialized 
with a small value, it may create more clusters 
as compared to the correct number of required 
clusters. The parameter minPts also acts in 
same manner. DBSCAN also identifies 
outliers, the points that do not belong to any 
cluster. There are some core definitions related 
to the DBSCAN, which are: 

 ɛ-neighborhood: Points within the 
radius of the center point ɛ. 

 Core point: A point within its radius 
has at least minimum points (minPts). 

 Boundary point: A point that is not a 
center point and has less than 
minimum points in its neighborhood 
but at least has one center point within 
its radius. 

 Noise points: Points that are neither 
midpoints nor boundary points and do 
not belong to any cluster. 

 Direct-density reachable: If point q is 
within the radius and p is the core 
point, then point q is directly density 
accessible from point p. 

 Density-Reachable: Point q is the 
density reachable of point p if point q 
is within the radius and point p is not a 
center point. Point q is connected to 
point p through other points (q1, q2, q3, 
... qn). 

 Density-Connectivity: If points p and 
q are densities accessible from center 
point o, then points p and q are 
connected to each other relative to 
point o. 

 Cluster: Defined as the largest set of 
densely connected points. 

The algorithmic steps of DBSCAN are 
illustrated in Algorithm 1. 

 



 

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Algorithm 1: Pseudo-code of DBSCAN 

Procedure DBSCAN(Dataset X, 𝜖, minPts) 

Step-1: Explore all core points in the eld 
space X using 𝜖 and minPts and add it to 
the set of core objects. A core point is 
when |Nɛ(xi)| > minPts 

Step-2: Select any core object from the set 
and make a cluster with other core points 
using ɛ and minPts until all core points are 
visited and no more core point is left. 

Step-3: Add unvisited border points in the 
current cluster one-by-one. But border 
point cannot extend the cluster further as 
it is not a core point. 

Step-4: If a point is neither core nor a 
border point, mark it as noise and put it in 
a separate set, and label it. 

Step-5: When all border points are added 
to the cluster; pick another core point for 
the set and repeat above steps until a 
cluster is made. 

return Labeled data space of cluster index. 

End procedure 

2.2. Harris' Hawks Optimization 

In 2019, Ali Asghar et al. [22] presented an 
optimization technique after observing the 
hunting behavior of Harris' hawks, which is 
called Harris' hawks optimization (HHO). This 
algorithm exhibits the hunting behavior of the 
Harris' hawks. For these hawks, the primary 
tactic for hunting prey is the “raid”. This 
strategy is also known as the “seven-kill 
strategy”. In this strategy, sometimes the 
surprised prey is caught within a few seconds 
or otherwise, these attacks are kept in 
continuity till the prey is caught. This search 
approach may include several brief and smart 
dives from different directions within seconds 
and minutes to confuse the exhausted prey that 
it is now and then is caught by the attacking 
hawk. 

The Harris' hawks can apply a variety of 
attacking styles keeping in view the hunting 
environment, escaping behavior, and energy of 
their prey. There may be some hard and soft 

besieges while attacking the prey till it is 
finally caught. These abruptly changing 
attacking behavior of the hawks are beneficial 
in a way that this strategy brings rabbits to a 
complete exhaustion and become 
defenselessness. 

The HHO algorithm consists of three 
phases, in which these attacks are taken place. 
These are: 

2.2.1. Exploration Phase 

Firstly, in the exploration phase, hawks 
wait in the hunting field and use their extended 
and strong visual power to locate a prey 
(rabbit). Sometimes the rabbits are explored 
very easily and other times, they have to wait 
for hours to locate one. If the hawks are unable 
to locate any rabbit for a certain period of time, 
they change their place and use random 
perching in other locations to look for the prey. 
This strategy in the form of mathematical 
representation is depicted in Eq. 1: 

𝑋(𝑡 + 1) =

{
𝑋𝑟𝑎𝑛𝑑(𝑡) − 𝑟1|𝑋𝑟𝑎𝑛𝑑(𝑡) − 2𝑟2𝑋(𝑡)| if 𝑞 ≥ 0.5

𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝑟1|𝑋𝑚(𝑡) − 𝑟3(𝑈𝐵 − 𝑟4𝐿𝐵)| otherwise
(1) 

where Xrabbit(t) is the current optimal solution 
whereas the next possible solution in terms of 
hawk's position is denoted by X(t+1). X(t), 
Xrand(t), and Xm(t) show the positions of all 
hawks (total solutions-set), randomly selected 
hawks, and average positions, respectively. 
The lower and upper bounds of the search 
space are given by LB and UB, whereas r1-r4 
represent random variables between [0-1]. 

2.2.2. The Transition from Exploration 
to Exploitation 

This is the second phase of HHO 

algorithm, which takes place between 

exploration and exploitation. When a prey is 

found, then different exploitation behaviors 

are used to reduce its escaping energy so that 

some of the hawks are able to catch it easily. 

In HHO, it is called energy component, 

formulated in Eq. 2: 

 

𝐸 = 2𝐸0(1 −
𝑡

𝑡𝑚𝑎𝑥
)                      (2) 

 



 

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where initial energy of the rabbit is denoted by 

E0, and t and tmax represent current and 

maximum number of iterations respectively. 

2.2.3. Exploitation Phase 

The hawks bout on their target using different 
attacking techniques as required in that 
situation. The situation depicts the escaping 
pattern of the prey and attacking style of the 
hawks, and energy of the rabbits as well. There 
are four likely strategies in the HHO 
algorithms. These are as depicted in Eqs. 3 - 6: 

 Soft besiege: If chance of escape ≥0.5 and 
absolute energy ≥0.5: 

𝑋(𝑡 + 1) = ∆𝑋(𝑡) − 𝐸|𝐽𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝑋(𝑡)|

∆𝑋(𝑡) = 𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝑋(𝑡), 𝐽 = 2(1 − 𝑟5)
 (3) 

where ∆𝑋(𝑡) is the difference between the 
current position of a hawk X(t) and rabbit 
𝑋𝑟𝑎𝑏𝑏𝑖𝑡  and r5 being a random variable. 

 Hard besiege: If chance of escape ≥0.5 
and absolute energy <0.5: 

𝑋(𝑡 + 1) = 𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝐸|∆𝑋(𝑡)|       (4) 

 Soft besiege with rapid progressive 
dives: If chance of escape <0.5 and 
absolute energy ≥0.5: 

𝑋(𝑡 + 1) =

{
𝑌 𝑖𝑓 F(Y ) < F(X(t)), 𝑌 = 𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝐸|𝐽𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝑋(𝑡)|

𝑍 𝑖𝑓 F(Z ) < F(X(t)), 𝑍 = 𝑌 + 𝑆 × 𝐿𝑒𝑣𝑦𝐹𝑙𝑖𝑔ℎ𝑡(𝐷)
     

  (5) 

where D and S denote problem 
dimensions and a random vector of size D, 
respectively. LevyFlight(D) is Levy 
Flight function. 

 Hard besiege with rapid progressive 
dives: If chance of escape <0.5 and 
absolute energy <0.5: 

 𝑋(𝑡 + 1) =

{
𝑌 𝑖𝑓 F(Y ) < F(X(t)), 𝑌 = 𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡) − 𝐸|𝐽𝑋𝑟𝑎𝑏𝑏𝑖𝑡 (𝑡)−𝑋𝑚 (𝑡)|

𝑍 𝑖𝑓 F(Z ) < F(X(t)), 𝑍 = 𝑌 + 𝑆 × 𝐿𝑒𝑣𝑦𝐹𝑙𝑖𝑔ℎ𝑡(𝐷)
     

  (6) 

 The step-by-step procedure of HHO 
algorithm can be defined in Algorithm 2. 

 

Algorithm 2: Pseudo-code of HHO 
algorithm 

Procedure HHO(Dataset X, 𝜖, minPts) 

Initialization of population Xi, (i=1, 2,..., N) 

While t< tmax 

Calculate fitness values of hawks and 
best location of rabbit 

 For each hawk Xi(t) 

If E≥1 Then  

Exploration and position update via 
Eq. 1 

Else  

Exploitation and position update 
via Eqs. 3-6 

 End For 

End While 

return Optimum solution Xrabbit 

End procedure 

 As can be seen in Algorithm 2, it first 
initializes the population and then enters the 
exploration phase using Eq. 1 until it finds 
some prey in the search space. It will keep on 
searching and will wait until it finds a prey. 
After locating the prey, it will transit from the 
exploration to the exploitation phase using Eq. 
2. Then it will make some attacking 
movements using four strategies as mentioned 
using Eq. 3 to Eq. 6 called soft and soft 
besieges and soft/ hard besieges with 
progressive dives. 

2.3. HHO-Tuned DBSCAN 

In this research, HHO and DBSCAN are 
integrated, in order to enhance clustering 
capability of the DBSCAN algorithm. Here, 
DBSCAN is integrated with HHO in such a 
way that it achieves highest accurate values of 
ɛ and minPts. As can be seen from Algorithm 
3 the DBSCAN algorithm is called within 
HHO. HHO provides the values of best-fit 
rabbit and its energy as candidate values of ɛ 
and minPts, which are evaluated and then 
passed to HHO. The provided values are 



 

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compared to each other and convergence of the 
HHO is analyzed. At the point where it 
converges at global minima and with lowest 
clustering error, it is our desired values for ɛ 
and minPts. 

The HHO is used to search DBSCAN 
parameters for optimal clustering accuracy, as 
shown in Algorithm 3. 

Algorithm 2: Pseudo-code of HHO-
DBSCAN algorithm 

Procedure HHO-DBSCAN(Solution Size N, 
Maximum Iterations tmax) 

Initialization of population Xi (i = 1, 2,..., N) 

While t<tmax 

For each Xi(t) 

x =Xi(t) 

ɛ =x1 and MinPts = x2 

Calculate fitness of DBSCAN with 
given parameters  

End For 

For each hawk Xi(t) 

If E≥1 Then 

Exploration and position update via 
Eqs. 1 and 2 

Else 

Exploitation and position update via 
Eqs. 3-6 

End For 

End While 

Return Optimum solution Xrabbit 

End procedure 

3. Experimental Results 

To evaluate the HHO-tuned DBSCAN 
performance, we used a computing machine 
with a 1TB hard drive, 32 GB RAM, and a 
Core i7 processor, on a Windows 10 PC, the 
code was developed in MATLAB R2016a. For 
experiments, we used three real-world datasets 
namely Seed, Segment, and Iris. And, four 

synthetic datasets namely Flame, Path-based, 
D31, and Compound. 

3.1. HHO-DBSCAN on Real-World 
Datasets 

Three University of California machine 

learning datasets [30] are chosen: Iris has 

three classes and four attributes; Seeds has 

three classes and seven attributes; and 

Segment has seven classes and nineteen 

attributes. The results of HHO-DBSCAN are 

compared with improved multi-verse 

optimizer (IMVO2) from Lai et al. [7] which 

is used for searching best value for ɛ 

parameter. To evaluate IMVO2 search ability, 

the researchers chose 500 points at random 

from each interval [ɛmin, ɛmax] as the value of ɛ, 

and used it in DBSCAN. Whereas, our 

proposed method HHO is being more 

effective as the results indicated that it shows 

the highest accuracy in every case as 

compared to IMVO2. HHO-tuned DBSCAN 

achieves outstanding results, serving as a 

model for developing efficient clustering 

approaches for complex clustering-shaped 

datasets. 

Table 1 presents comparison results of 

HHO-DBSCAN and other counterparts 

(metaheuristic improved versions of 

DBSCAN i.e., PSO-DBSCAN [31], ACO-

DBSCAN [32], and IMVO-DBSCAN [7]) 

with respect to accuracy metric on real-world 

and synthetic datasets. It can be observed from 

the results that HHO-DBSCAN outperformed 

the other improved versions of DBSCAN, as 

it scores high in each evaluation. The indices 

of evaluation metric are almost near to 100\% 

in each case, which speaks of efficacy of the 

proposed method. 

In Fig. 1, the trend of optimal accuracy 

of DBSCAN clustering for Seeds, Iris, and 

Segment is consistent with the tendency of 

clustering accuracy in their subsets, when 

minPts takes different values. Also, the 

optimal parameter minPts is the same, which 

are 18, 3, and 3 respectively in IMVO2. The 

optimal minPts is selected and then optimized 

for the parameter ɛ. The results are shown in 

Table 1, which indicates that the ɛ interval 



 

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corresponds to the optimal clustering accuracy 

of all the samples in a dataset. Furthermore, 

the interval of ɛ corresponding to the optimal 

clustering accuracy of all the samples in the 

dataset overlaps with the range of ɛ examined 

by IMVO2 to its subset in Table 1. On the 

other hand, when the proposed technique 

HHO-DBSCAN is applied to Seed Subsets, 

Seeds, Iris Subsets, Iris, Segment Subsets, and 

Segments, the accuracy obtained is 95.05\%, 

89.52\%, 99.47\%, 84.66\%, 76.42\%, and 

66.02\%, respectively. The results show that 

by using known label samples to tune the 

DBSCAN parameters, we can mine unknown 

label samples, which is unattainable with 

supervised learning methods. 

Table 2. Evaluation of HHO-DBSCAN on 
real-world datasets 

 
 

We can identify the optimal clustering 

accuracy of DBSCAN by incorporating HHO 

to optimize the parameters of DBSCAN. This 

helps us to choose a more suitable ɛ value for 

DBSCAN clustering. Fig. 1 depicts a graph of 

various datasets on IMVO2 and the proposed 

method with minPts ranging from 1 to 40 on 

the x-axis and accuracy on the y-axis. The 

graphs indicate accuracy of the proposed 

method is higher than IMVO2-DBSCAN, so 

we can conclude that our method is reliable, as 

it achieves the highest accuracy in every 

dataset. DBSCAN parameters determination 

and optimization for a dataset and its subset is 

presented in Table 2. In Fig. 1, the best 

DBSCAN clustering accuracy trend for Seeds, 

Iris, and Segment is consistent with the 

clustering accuracy trend of their subsets 

where minPts is provided with different 

values. Moreover, the optimal minPts 

parameters are the same, 18, 3, and 3 in 

IMVO2, respectively. 

On the other hand, when the proposed 

technique HHO-DBSCAN is applied to Seed 

Subsets, Seeds, Iris Subsets, Iris, Segment 

Subsets, and Segments, the accuracy obtained 

is 95.05\%, 89.52\%, 99.47\%, 84.66\%, 

76.42\%, and 66.02\%, respectively. The 

results show that by using known label 

samples to tune the DBSCAN parameters, we 

can mine unknown label samples. 

It can be seen from Table 2 that purity is 

more than 90\% i.e., 0.9505 and 0.9948 in 

Seeds Subset and Iris Subset, which clearly 

speaks of the results validity. The NMI, RI and 

Table 1. Accuracy comparison between HHO-DBSCAN and others based on optimized values 
for DBSCAN parameters. 



 

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ARI of Segment Subset are 0.9939, 0.9799, 

and 0.9887, respectively. For the Segment, 

values of NMI, RI, and ARI are 0.8834, 

0.9014, and 0.9112, which are also promising. 

However, NMI, RI, and ARI indices of Seeds 

and Seeds Subsets are not as expected, which 

shows that the method did not perform well on 

this dataset because it consists of 19 attributes 

and 7 classes of diverse natures. Since this 

dataset belongs to segments of a picture, hence 

it contains a high variance and dispersion 

among the values. The diverse nature of these 

values and increased number of classes, the 

results generated are not as expected. 

Fig. 1.  Accuracy comparison between IMVO2-DBSCAN and HHO-DBSCAN based on 

optimized values for minPts parameter. 



 

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3.2. HHO-DBSCAN on Synthetic 
Datasets 

The proposed method is then implemented 
on four synthetic datasets including 
Compound, D31, Flame, and Path-based. 
Here, Compound dataset has 788 points with 2 
dimensions and 7 clusters. Whereas the D31 
dataset which is made up of 31 similar 2-D 
Gaussian distributions. The Path-based dataset 
contains 300 points and has 2 dimensions and 
contains 6 clusters. The Flame dataset has 240 
data points, 2 dimensions, and contains 2 
clusters. The clustering results of HHO-
DBSCAN are evaluated on synthetic datasets 
based on Purity, NMI, RI, and the ARI 
evaluation measures. 

On Compound, HHO-DBSCAN achieves 
the purity of 0.9607, NMI value.9510, RI value 
0.9863 and, the ARI value 0.9755. Overall, it 
achieves better results by using an efficient 
optimization method for finding ɛ parameter 
on different minimum parameter (minPts) 
ranging from 1 to 40. The clustering results of  

 

HHO-DBSCAN on Compound are shown in 
Fig.2(a), from which it can be inferred that the 
outcomes of projected solution are 
outperforming. The D31 is made up of 31 
similar 2-D Gaussian distributions. While 
applying HHO-DBSCAN, we get the highest 
purity value of 0.9900 for the D31 dataset. We 
can also suggest from the Fig.2(b) that the 
proposed approach is reliable and produces the 
best results. 

The clustering results of HHO-DBSCAN 
on the Flame dataset are shown in Fig.2(c) 
which clearly illustrate that this strategy for 
selecting DBSCAN parameters is the most 
efficient method available. HHO provides 
enhanced exploration and exploitation 
capabilities, which aids in avoiding solution 
stagnation in subsequent rounds. Table 2 
presents that using the Flame dataset, we attain 
purity of 0.9988 and NMI of 0.9714, while the 
RI and ARI are 0.9949 and 0.9717. Fig.2(d) 
demonstrates clustering results on the Path-
based dataset when HHO-DBSCAN is applied 



 

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Sukkur IBA Journal of Emerging Technologies - SJET | Vol. 6 No. 1 January – June 2023 

32 

to that data the highest results we achieve as 
Purity, NMI, RI, and ARI are 0.9533, 0.9144, 
0.9438, and 0.9398 respectively. 

From the overall results, it can be 
concluded that HHO is an efficient method for 
achieving the optimal values for the 
parameters for DBSCAN. The application of 
HHO to optimize DBSCAN parameters, 
allows us to discover the best clustering 
accuracy. The proposed algorithm optimally 
finds values of ɛ and minPts parameters to 
create clusters with maximum accuracy. The 
combination of DBSCAN and HHO 
algorithms enhanced the process of clustering 
with accuracy improvement. 

4. Conclusion  

DBSCAN is a clustering technique which 

has achieved appreciation from researchers 

and practitioners, mainly due to its ability to 

detect outliers and clustering efficiency for the 

data points distributed in arbitrary manner. 

However, manual selection of the DBSCAN 

parameters (ɛ and minPts) is a cumbersome 

job, as it requires past experience, as well as, 

several trials. This highly affects accuracy of 

the algorithm, since every dataset or clustering 

problem demands separate efforts to find best 

suitable DBSCAN parameters. This demands 

an effective approach to selecting these 

parameters in an automatic manner. Using 

metaheuristic algorithms, for this purpose, has 

overall resolved the problem, but with the 

existence of numerous optimization methods, 

the choice of the efficient one is crucial. This 

study applied an efficient metaheuristic 

algorithm HHO which has already generated 

comparatively better optimization results for a 

variety of optimization problems. 

Both of the algorithms are successfully 

integrated to achieve the objective of 

automatically getting values of minPts and 

Eps. These values are metaheuristically 

calculated by optimization algorithm HHO. 

The results and comparison show that the 

calculated values are more accurate as 

compared to previous methods proposed y 

different researchers. The evaluation metrics 

used in this study indicate that the proposed 

method outperforms its counterpart methods. 

Moreover efficiency of the proposed model is 

also tested with other alike methods found in 

literature. 

Based on insightful comparative analysis 

performed for HHO-DBSCAN and one of the 

recently introduced IMVO2-DBSCAN 

methods, it can be asserted that HHO is able 

to optimize DBSCAN parameters more 

efficiently, as it helps DBSCAN achieve 

clustering accuracy. Although the proposed 

method performs comparatively better for 

various datasets however, its performance is 

observed low in datasets having diverse data 

points. The lack of smoothness of data due to 

dispersion caused the proposed method to 

drop its efficiency, since it fails to identify the 

values of ɛ and minPts correctly. 

Moreover, remaining in our limited 

scope, the proposed solution is for now 

applied to real-world and synthetic datasets 

however, it can also be applied to 

industry/engineering problems to testify to its 

performance. Moreover, since DBSCAN, 

sometimes fails to perform properly in large-

scale and high-dimensional datasets, so in 

future DBSCAN and HHO can also be 

improved to work with large and high-

dimensional datasets. 

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