ECA-CE: An Evolutionary Clustering Algorithm with Initial Population

by Clustering Ensemble

Chao Xu

, Chunlin Xu

and Shengli Wu

School of Computer Science, Jiangsu University, Zhenjiang, China

School of Computer Science,Guangdong Polytechnic Normal University, Guangzhou, China

Keywords:

Evolutionary Clustering, Clustering Ensemble, Supervised Classiﬁer.

Abstract:

Evolutionary clustering is a type of algorithm that uses genetic algorithms to optimize clustering results.

Unlike traditional clustering algorithms which obtain clustering results by iteratively increasing the distance

between clusters and reducing the distance between instances within a cluster, the evolutionary clustering al-

gorithm tries to search for the optimal clustering result in the solution space. Not surprisingly, the initial pop-

ulation set in an evolutionary clustering algorithm has signiﬁcant inﬂuence on the ﬁnal results. To ensure the

quality of the initial population, this paper proposed a clustering ensemble-based method, ECA-CE, to do the

initial population for the evolutionary clustering algorithm. In ECA-CE, a clustering ensemble method, Hy-

brid Bipartite Graph Formulation, is applied. Extensive experiments are conducted on 20 benchmark datasets,

and the experimental results demonstrate that the proposed ECA-CE is more effective than two evolutionary

clustering algorithms F1-ECAC and ECAC in terms of Adjusted Rand index.

1 INTRODUCTION

In most real-world situations, data is unlabeled. Clus-

tering is an unsupervised learning algorithm that takes

an unlabeled dataset as input and divides it into a cer-

tain number of clusters, where data with similar char-

acteristics are grouped. The ideal clustering result

should be that all the clusters generated are indepen-

dent of each other and data within a cluster are rela-

tively compact.

Traditional clustering algorithms can be mainly

divided into three groups, including partition-based,

hierarchy-based, and graph-theory-based clustering

algorithms. The main idea of the partition-based algo-

rithms is to discover the groupings in the data by op-

timizing a speciﬁc objective function and iteratively

improving the quality of partitions (Kang et al., 2019).

The shortcoming of partition-based clustering algo-

rithms is that they can easily be trapped in a local op-

timum. Hierarchy-based clustering algorithms divide

data at different levels to form a tree-like structure

(Nielsen, 2016). The graph-based clustering algo-

rithms (Von Luxburg, 2007) construct an undirected

graph with similarity weights deﬁned in a matrix and

then apply a clustering algorithm to partition the undi-

rected graph.

Different from those traditional methods, evo-

lutionary clustering algorithms utilize genetic algo-

rithms to search for the global optimal clustering re-

sults. F1-ECAC (Sainz-Tinajero et al., 2021b) and

ECAC (Sainz-Tinajero et al., 2021a) are two re-

cently proposed evolutionary clustering algorithms

that achieve good performance. However, one prob-

lem of F1-ECAC and ECAC is that the quality of the

initial population is unstable, which impacts the ﬁnal

clustering results. If the evolutionary clustering al-

gorithm cannot start with a good initial population, it

will require more time to obtain the optimal clustering

result, or cannot ﬁnd that at all.

To alleviate the above problem, this paper pro-

poses an evolutionary clustering algorithm, ECA-CE

(Evolutionary Clustering Algorithm with initial pop-

ulation by Clustering Ensemble), whose initial popu-

lation is produced by a clustering ensemble and em-

ploys multiple supervised classiﬁers to evaluate each

individual’s ﬁtness. Our experimental results show

that the proposed method achieves better performance

than F1-ECAC and ECAC do.

The rest of the paper is organized as follows: Sec-

tion II summarizes related work. Section III describes

ECA-CE. The experimental settings and results for

the evaluation of the proposed method are presented

in Section IV. Finally, a summary is given in Section

132

Xu, C., Xu, C. and Wu, S.

ECA-CE: An Evolutionary Clustering Algorithm with Initial Population by Clustering Ensemble.

DOI: 10.5220/0011621700003393

In Proceedings of the 15th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2023) - Volume 3, pages 132-139

ISBN: 978-989-758-623-1; ISSN: 2184-433X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

2 RELATED WORK

2.1 Traditional Clustering Algorithms

There are several types of traditional clustering algo-

rithms.

1. Partition-based algorithm: For a given initial

central point, a heuristic search method is used to it-

eratively update each cluster and its centroid until the

distance between any two instances within a cluster

is small enough and the distance between clusters is

large enough.

2. Hierarchy-based algorithm: To create clusters

in a hierarchical tree-like structure in which the root

node corresponds to the entire dataset, and branches

are created from the root node to form hierarchical

clusters. Mainly there are two types of hierarchy-

based clustering algorithms: fused hierarchical clus-

tering and partitioned hierarchical clustering. The

fused hierarchical clustering algorithm generates all

the nodes in a bottom-up style, while the latter does it

in a top-down style.

3. Graph-based algorithm: Each data point in a

dataset is represented as a node, the distance between

two data points is modeled by an edge between the

two nodes with a weight. In this way, the cluster-

ing problem can be transformed into a graph partition

problem, and the clustering results can be obtained by

applying some partition criteria such as minimum cut

on the graph.

In this study, we choose a typical method from

each category as the baseline for performance com-

parison. Also they are used as base clustering algo-

rithms for the clustering ensemble.

a) K-means: It is a well-known partition-based

method with multiple variants, such as k-medoids, k-

medians, etc. K-means is a centroid-based cluster-

ing algorithm. This method tries to shorten the av-

erage Euclidean distance from each data point to the

centroid of the cluster through iterative membership

change. Since K-means intends to build sufﬁciently

tight clusters, the algorithm is likely to fall into lo-

cal optima and is exceptionally sensitive to noisy data

points.

b) BIRCH: It constructs a cluster feature tree

(CFT) for the dataset. Since the algorithm uses a tree

model, then it is well-interpretable and can solve non-

spherical problems that cannot be solved by K-means.

However, the construction of the tree structure leads

to high time complexity. Therefore, BIRCH may not

be able to handle high-dimensional data.

c) Spectral Clustering: Spectral Clustering is a

graph-based algorithm. Spectral Clustering requires a

similarity matrix between instances to work. It is ef-

fective in dealing with sparse datasets. Due to the use

of dimensionality reduction, it is a more appropriate

solution for high-dimensional datasets than BIRCH.

However, as Spectral Clustering relies on similarity

matrices, different similarity matrices may yield dif-

ferent clustering results.

Algorithm 1: HBGF.

Require: dataset D =

{

..,X

}

{

..,x

}

 n is the number of instances and

m is the number of features.

graph partitioning algorithm package

L(SPEC (Shi and Malik, 2000) or METIS

(Karypis and Kumar, 1998)) )

1: V = D ∪C;  C contains all

clusters,C =



|1 ≤ j ≤ k

∗



∗

is the number of

clusters

2: E = φ;

3: for i = 1,...,n do:

4: for j = 1,...,k

∗

do:

5: if v

∈ v

then:  v

is an instance.v

is a

cluster

6: E = E ∪



i j



 add edge

= (v

);

7: w

i j

= 1  Set equal weights for e

i j

;

8: end if

9: end for

10: end for

11: G = (V,E);

12: σ = L(G);  Apply the speciﬁed graph

partitioning algorithm package on G

2.2 Evolutionary Clustering Algorithm

The evolutionary clustering algorithm generally ap-

plies the genetic search method to try to ﬁnd the op-

timal results. In order to solve the density-related

clustering problem, Zhang et al. (Zhang et al., 2013)

proposed an evolutionary clustering algorithm based

on DBSCAN(Ester et al., 1996), and applied the time

smoothing degree penalty framework in the calcula-

tion process. Sainz Tinajero et al. (Sainz-Tinajero

et al., 2021a) proposed a single objective evolution-

ary clustering algorithm (ECAC) based on a super-

vised classiﬁer, which uses random functions to ini-

tialize the population of solutions. After performing

selection, crossover, and mutation operations, a new

population is obtained. For the evaluation of a clus-

tering solution, we transform the solution to a classi-

ﬁcation problem, in which each instance is composed

of all the original attributes with a label correspond-

ing to a speciﬁc cluster. In order to let a classiﬁer

ECA-CE: An Evolutionary Clustering Algorithm with Initial Population by Clustering Ensemble

133

work, they divide all the instances into two partitions:

Training and testing partitions. The training part is

used to train the classiﬁer, and then the trained model

is applied to the testing part. Its AUC index is used

as the ﬁtness metric of the clustering results. Multiple

supervised classiﬁers are used to make the evaluation

results more reliable. The best solution is kept in the

iterative process. The iteration stops when the end-

ing condition, either a predeﬁned number of iterations

or a given AUC value, is satisﬁed. The author sub-

sequently proposed F1-ECAC (Sainz-Tinajero et al.,

2021b), a variant of ECAC, which uses F1 score to

replace AUC as the evaluation index.

Additionally, Mardi and Keyvanpour(Mardi and

Keyvanpour, 2021) applied the evolutionary cluster-

ing algorithm to set the initial points for the K-means

algorithm, which they believe can reduce the sensitiv-

ity of K-means to abnormal data.

3 PROPOSED ALGORITHM

3.1 ECA-CE

In this section, we describe ECA-CE in detail. We

will also discuss Hybrid Bipartite Graph Formula-

tion(HBGF) (Fern and Brodley, 2004), a clustering

ensemble algorithm, and how to use HBGF in ECA-

CE.

HBGF, a graph-based clustering ensemble algo-

rithm, was proposed by Fern et al. The pseudo-code

for the HBGF algorithm is shown in Algorithm 1. It

is expected that the clustering results generated by an

ensemble of multiple clustering algorithms are more

stable.

In ECA-CE, ﬁrstly we run three traditional clus-

tering algorithms including the aforementioned K-

means, BIRCH, and Spectral Clustering algorithm to

obtain three different clustering results. Then HBGF

is used to fuse them, and the fused clustering re-

sults are taken as an initial solution for the evolution-

ary clustering algorithm. We think that such an ini-

tial solution can help the evolutionary clustering al-

gorithm to ﬁnd better solutions more quickly. Algo-

rithm 2 shows the process of the ECA-CE algorithm.

For a dataset D =

{

..,X

}

{

..,x

}

where n denotes the number of instances and m de-

notes the number of features. ECA-CE calculates the

individual’s ﬁtness in a supervised manner (Caruana

and Niculescu-Mizil, 2006).

Algorithm 2: ECA-CE.

Require: dataset D,the population size α ,number of

iterations β,number of clusters k

1: θ =



,...,g

,...g



= HBGF(D);

2: fmax = 0;

3: bestCrs = [];

4: for i = 1,...,α do:

5: θ

= random(θ);  Using random functions to

increase the dissimilarity between chromosomes

6: f (i) = f itness(θ

);  Calculate the ﬁtness of

the individual θ

7: if f (i) > f max then:

8: fmax = f(i);

9: bestCrs = θ

;

10: end if

11: end for

12: for i = 1, 2, ..., β do:

13: for j = 1,2,...,α do:

14: P

= TournamentSelection(α); 

Use tournament operator to obtain parent chro-

mosomes

15: end for

16: K

,...,K

= Single −

pointCrossover(P

,...,Pα);  Generate

children using the single-point crossover operator

17: K

‘

,...,K

‘

= Mutationi(K

,...,K

);

18: for j = 1,2,...,α do:

19: f ( j) = fitness(K

‘

) ;

20: if f ( j) > f max then:

21: fmax = f(j);

22: bestCrs = K

‘

;

23: end if

24: end for

25: end for

26: return bestCrs;

3.2 Chromosome Coding and

Population Initialization

First, the individual’s chromosomes (solution) of the

genetic algorithm are encoded with integers as shown

in Figure 1. For the ith individual, its chromosomes



,...,g

,...g



can be represented as a

vector with n positions where n is the number of the

instances of the dataset and g

denotes the cluster

number for the jth instance. The initialization proce-

dure for the ﬁrst generation of the parent individual is

as follows: ﬁrstly, three different types of clustering

algorithms K-means, BIRCH, and Spectral Cluster-

ing, are used to generate three clustering results, and

then HBGF is used to fuse the three clustering results

into one cluster result. At this point, the fused cluster-

ing results can only be the chromosome of one indi-

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

134

vidual. There are three common ways to ensure diver-

sity among the initialized individuals: 1) data pertur-

bation, such as autonomous sampling of bagging; 2)

attribute perturbation of the dataset, such as attribute

sampling of the random subspace; 3) algorithm pa-

rameter perturbation, such as setting different hyper-

parameters of the base learner. After trying the above

three methods in our experiments, we found that nei-

ther of them could obtain good results. Therefore, we

use K-means, BIRCH, and Spectral Clustering to do

the clustering and combine their clustering results by

HBGF. After obtaining the ﬁrst solution θ, we gener-

ate more solutions by making some moderate changes

to θ: 30% of the chromosomes (instances) randomly

chosen and changed clustering groups. The process is

shown in Figure 2.

Figure 1: Results of clustering with ﬁve groups and n chro-

mosomes (instances).

Figure 2: 30% of the instances are randomly chosen and

changed clustering groups.

3.3 Objective Function

The choice of the objective function will affect the

speed of convergence of the genetic algorithm and the

ability to ﬁnd an optimal solution. In ECA-CE, we

use supervised classiﬁers to get the ﬁtness of an in-

dividual and Figure 3 shows how ECA-CE employs

multiple supervised classiﬁers to get the individual’s

ﬁtness. Instead of calculating the similarity between

features as in traditional clustering algorithms, the

objective function is treated as a supervised learning

task. The objective function pseudo-code is shown in

Algorithm 3. The calculation of the individual’s ﬁt-

ness of ECA-CE is based on a single objective, which

makes it easier to calculate the individual’s ﬁtness and

speeds up the convergence of the algorithm.

When using supervised classiﬁers to calculate the

ﬁtness of an individual, the bias of a single classiﬁer

can be reduced by having multiple supervised clas-

siﬁers involved in the calculation at the same time.

In this paper, we choose three supervised classiﬁers.

Algorithm 3: Objective function: ﬁtness.

Require: dataset D,individual chromosomes θ

1: X

train

test

train

test

= train test split(D,θ);

2: res = 0;

3: for i = 1,...,c do:  c is the number of

supervised classiﬁers

4: model

= C

.train(X

train

);

5: Y

pred

= model

.predict(X

test

);

6: res = res + f 1 score(Y

test

pred

);

7: end for

8: return res/c;

A certain number of training sets are chosen to train

each supervised classiﬁer, and a test set is evaluated

to calculate the F1 score of each supervised classiﬁer

on the test set and summed to ﬁnd the mean value.

3.4 Genetic Algorithm Operators

a) Tournament selection: In each round of the tour-

nament operator (Blickle and Thiele, 1995), two or

more individuals are randomly selected from the pop-

ulation, and the individual with the greatest ﬁtness be-

comes the parent.

b) Single-point crossover: In the single-point

crossover operator (Deb et al., 1995), a position on the

parent chromosome is chosen at random. This posi-

tion becomes the crossover point. As shown in Figure

4, at the crossover point of the parents’ chromosomes,

the left and right chromosomes are swapped with each

other to obtain two offsprings, each carrying the ge-

netic information of the parent’s generation.

c) Mutation operator: The mutation operation is

generally applied to an offspring produced using se-

lection and crossover operators. Because the mutation

operator (Das et al., 2009) generally compromises the

genetic information of the offspring, mutations usu-

ally occur with very low probability. As shown in

Figure 5, using the swap mutation operator, two chro-

mosomes are randomly selected and their values are

swapped.

4 EXPERIMENTAL SETUP

In this section, the traditional algorithmic hyperpa-

rameters and datasets required for the ECA-CE algo-

rithm are described in detail. All experiments were

done on a PC with an Intel Core i7 2.9GHz, 8-core

processor, 16GB, and the python programming lan-

guage.

ECA-CE: An Evolutionary Clustering Algorithm with Initial Population by Clustering Ensemble

135

Figure 3: ECA-CE uses supervised classiﬁers to calculate the ﬁtness of an individual.

Figure 4: Single point crossover operator.

Figure 5: Exchange mutation operator.

4.1 Datasets and Evaluation Metrics

For this experiment, we selected 20 datasets from the

UCI (Asuncion and Newman, 2007) and Fr

anti and

Sieranoja’s Clustering Benchmark repository (Fr

anti

and Sieranoja, 2018),(Gionis et al., 2007),(Chang and

Yeung, 2008),(Veenman et al., 2002),(Jain and Law,

2005). Table I shows the information of them.

All the datasets used are labelled, which are suit-

able for classiﬁcation tasks. In this study, we use them

to test clustering algorithms. Therefore, we set the

number of clusters as the number of classes in each

dataset, then compare the similarity between a clus-

ter and its corresponding class. Adjusted RAND In-

dex(Steinley, 2004) is used for the comparison. The

larger the ARI value is, the better clustering result we

obtain.

Table 1: Information of the datasets used in experiment.

Dataset N. Features N. Classes N. Instances

aggregation 2 4 788

jain 2 2 373

pathbased 2 3 300

r15 2 15 600

spiral 2 3 312

breast-cancer-wisconsin 30 2 569

breast-tissue 9 6 106

dermatology 34 6 366

ecoli 7 8 336

forest 27 4 523

glass 9 6 214

iris 4 3 150

leaf 14 36 340

liver 5 16 345

parkinsons 22 2 195

seeds 7 3 210

segment 19 7 210

transfusion 4 2 748

wine 13 3 178

zoo 16 7 101

4.2 Hyperparameter Setting for all

Participating Algorithms

Apart from the proposed method, ﬁve other algo-

rithms F1-ECAC, ECAC, K-means, BIRCH, and

Spectral Clustering are also tested. Among them, F1-

ECAC and ECAC are recently proposed evolutionary

clustering algorithms and the rest are traditional clus-

tering algorithms. Each algorithm run 10 times and

its average performance is calculated for better reli-

able results. For each dataset, the number of clusters

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

136

is set to be the number of categories.

a) Three evolutionary clustering methods ECA-

CE, F1-ECAC, and ECAC:

Both ECA-CE and F1-ECAC generate 200 indi-

viduals per iteration for 200 iterations, while ECAC

generates 20 individuals per iteration for a total of

2000 iterations. When initializing the ECA-CE popu-

lation, the hyperparameters of the traditional cluster-

ing algorithm are as follows:

K-means: the number of times the algorithm is run

for different values of the initialization of the center

points is 10.

BIRCH: the threshold for merging a new sub-

cluster with the closest sub-cluster is 0.5.

Spectral Clustering: Constructing similarity ma-

trices using RBF kernels.

For all three methods, the probability of crossover

is set to 95%, and the probability of chromosome mu-

tation is set to 5%. They use the same method for

evaluation.

b) Other traditional clustering algorithms

For K-means, the maximum number of iterations

is set to 300. The algorithm is run 10 times and

the average performance of them is calculated. For

BIRCH, the threshold for merging new sub-clusters

with the closest sub-clusters is set to 0.5 and the num-

ber of CF sub-clusters per node is set to 55. For Spec-

tral Clustering, similarity matrices are constructed by

RBF kernels.

4.3 Experimental Results

In this section we present the experimental results of

the experiment. Firstly, we look at the convergence

effect of the objective function of ECA-CE using two

different population initialization methods i.e., the

clustering ensemble algorithm initialized population

and the randomly initialized population. ECA-CE

searches the individual with the largest ﬁtness in each

generation as the best clustering result in that genera-

tion. As shown in Figure 6, when using the aggrega-

tion dataset, the ﬁgure shows the maximum ﬁtness of

the clustering ensemble initialization population and

random initialization population algorithms in each

iteration. When the initial population algorithm of

the clustering ensemble has about 100 iterations, the

ﬁtness converges to 0.93. The evolutionary cluster-

ing algorithm using a random method to initialize the

population shows no sign of convergence in 200 iter-

ations, and the maximum ﬁtness is 0.66 in the 200th

iteration. HBGF and Randomization: We compared

the quality of clustering results using different pop-

ulation initialization methods. As shown in Table 2,

HBGF initialization outperforms randomization ini-

Table 2: ARI values for random initialization and ensemble

clustering initialization of ECA-CE.

Dataset Randomization HBGF

aggregation 0.2597 0.6021

jain 0.2505 0.5525

pathbased 0.3100 0.4308

r15 0.5474 0.9899

spiral 0.0139 -0.0045

breast-cancer-wisconsin 0.0457 0.3441

breast-tissue 0.5058 0.5146

dermatology 0.0221 0.6230

ecoli 0.4569 0.4715

forest 0.0082 0.3088

glass 0.2703 0.3195

iris 0.8232 0.9242

leaf 0.4979 0.4875

liver 0.0804 0.0092

parkinsons 0.0549 0.1261

seeds 0.8277 0.8180

segment 0.6601 0.7550

transfusion 0.0522 0.0963

wine 0.8255 0.8485

zoo 0.1308 0.4442

Table 3: ARI for ECAC, F1-ECAC and ECA-CE.

Dataset ECAC F1-ECAC ECA-CE

aggregation 0.0403 0.2685 0.6021

jain 0.1022 0.3513 0.5525

pathbased 0.1070 0.2900 0.4308

r15 0.1406 0.5478 0.9899

spiral 0.0247 0.0134 -0.0045

breast-cancer-wisconsin 0.0134 0.0570 0.3441

breast-tissue 0.2778 0.5046 0.5146

dermatology 0.0235 0.0283 0.6230

ecoli 0.0899 0.4506 0.4715

forest 0.0049 0.0100 0.3088

glass 0.0863 0.2880 0.3195

iris 0.3776 0.9169 0.9242

leaf 0.3320 0.4993 0.4875

liver 0.0522 0.0880 0.0092

parkinsons 0.0275 0.0419 0.1261

seeds 0.2099 0.7763 0.8180

segment 0.2342 0.6777 0.7550

transfusion 0.0058 0.0542 0.0963

wine 0.1584 0.7577 0.8485

zoo 0.0599 0.1173 0.4442

tialization on 16 out of 20 datasets in terms of ARI,

which demonstrates the effectiveness of using a clus-

tering ensemble for population initialization.

Secondly, we compare the difference in cluster-

ing quality between ECA-CE and two other evolu-

tionary clustering algorithms, F1-ECAC, and ECAC.

The difference in clustering quality between ECA-CE

and other traditional clustering algorithms is also pre-

sented in Table 3. As shown in Table 3, ECA-CE is

doing better than ECAC on 18/20 datasets. Especially

on three datasets zoo, R15, and aggregation, the ARI

ECA-CE: An Evolutionary Clustering Algorithm with Initial Population by Clustering Ensemble

137

Table 4: ARI for ECA-CE and baseline algorithms.

Dataset ECA-CE F1-ECAC ECAC K-means BIRCH SC

aggregation 0.6021 0.2685 0.0403 0.7622 0.8133 0

jain 0.5525 0.3513 0.1022 0.3181 0.5146 -0.0436

pathbased 0.4308 0.2900 0.1070 0.4613 0.4847 0.0024

r15 0.9899 0.5478 0.1406 0.9928 0.9820 0.8942

spiral -0.0045 0.0134 0.0247 -0.0059 -0.0009 0.0125

breast-cancer-wisconsin 0.3441 0.0570 0.0134 0.4914 0.2872 0

breast-tissue 0.5146 0.5046 0.2778 0.0943 0.0943 0

dermatology 0.6230 0.0283 0.0235 0.0258 0.0342 0

ecoli 0.4715 0.4506 0.0899 0.4313 0.4858 0.0398

forest 0.3088 0.0100 0.0049 0.4987 0.4652 0

glass 0.3195 0.2880 0.0863 0.2702 0.2620 0.0125

iris 0.9242 0.9169 0.3776 0.7302 0.7312 0.2818

leaf 0.4875 0.4993 0.3320 0.2795 0.2885 0.0354

liver 0.0092 0.0880 0.0522 0.0176 0.0273 0

parkinsons 0.1261 0.0419 0.0275 0 0.0058 0

seeds 0.8180 0.7763 0.2099 0.7166 0.7132 0.0056

segment 0.7550 0.6777 0.2342 0.4061 0.4002 0

transfusion 0.0963 0.0542 0.0058 0.0795 0.0795 -0.0389

wine 0.8485 0.7577 0.1584 0.3711 0.3684 0

zoo 0.4442 0.1173 0.0599 0.7098 0.6451 0.00042

Average ranking 2.2 3.2 5.075 3.85 3.55 6.675

Figure 6: Random initialization and ensemble clustering

initialization ﬁtness variation on the aggregation dataset.

of ECA-CE is twice as higher as that of ECAC. ECA-

CE is superior to F1-ECAC on 17 out of 20 datasets.

In Table 4, the ARI of ECA-CE, ECAC, F1-

ECAC, and the three traditional clustering algorithms

are shown for all tested datasets. ECA-CE is the best

in 10 of the 20 datasets, which is followed by K-

means with 4, BIRCH with 3, F1-ECAC with 2, and

ECAC with only 1.

4.4 Analysis of the Results

In Friedman’s test (Chatﬁeld and Mander, 2009), the

lower the average ranking of the algorithm, the bet-

ter its average performance. The average ranking of

ECA-CE (2.2) over the 20 datasets is shown in Ta-

ble 4 to be lower than the other ﬁve algorithms, thus

demonstrating the superiority of ECA-CE over the

other algorithms on the experimental datasets.

5 SUMMARY

In this paper, we have proposed an evolutionary clus-

tering algorithm ECA-CE that uses a clustering en-

semble to initialize population and employs multiple

supervised classiﬁers to evaluate the ﬁtness scores of

individuals. To ensure the diversity of the initial pop-

ulation, after using a clustering ensemble to obtain a

solution, 30% of chromosomes. Multiple supervised

classiﬁers are then used to jointly assess the ﬁtness

of the generated individual when designing the objec-

tive function. Furthermore, it was experimentally ver-

iﬁed that ECA-CE outperforms the two recently pro-

posed evolutionary clustering algorithms: F1-ECAC

and ECAC in terms of ARI.

In our future work, we would investigate the use

of other clustering ensemble methods to initialize the

population to ensure the generation of good genetic

parents. We also plan to apply ECA-CE to some more

practical clustering tasks.

REFERENCES

Asuncion, A. and Newman, D. (2007). UCI machine learn-

ing repository.

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

138

Blickle, T. and Thiele, L. (1995). A mathematical analysis

of tournament selection. In International Conference

on Genetic Algorithms.

Caruana, R. and Niculescu-Mizil, A. (2006). An empiri-

cal comparison of supervised learning algorithms. In

Proceedings of the 23rd International Conference on

Machine Learning, pages 161–168.

Chang, H. and Yeung, D.-Y. (2008). Robust path-based

spectral clustering. Pattern Recognition, 41(1):191–

203.

Chatﬁeld, M. and Mander, A. (2009). The skillings–mack

test (friedman test when there are missing data). The

Stata Journal, 9(2):299–305.

Das, S., Abraham, A., Chakraborty, U. K., and Konar, A.

(2009). Differential evolution using a neighborhood-

based mutation operator. IEEE Transactions on Evo-

lutionary Computation, 13(3):526–553.

Deb, K., Agrawal, R. B., et al. (1995). Simulated binary

crossover for continuous search space. Complex Sys-

tems, 9(2):115–148.

Ester, M., Kriegel, H.-P., Sander, J., and Xu, X. (1996).

A density-based algorithm for discovering clusters in

large spatial databases with noise. In Proceedings of

the Second International Conference on Knowledge

Discovery and Data Mining, KDD’96, page 226–231.

AAAI Press.

Fern, X. Z. and Brodley, C. E. (2004). Solving cluster en-

semble problems by bipartite graph partitioning. In

Proceedings of the Twenty-First International Confer-

ence on Machine Learning, page 36.

anti, P. and Sieranoja, S. (2018). K-means properties

on six clustering benchmark datasets. Applied Intel-

ligence, 48(12):4743–4759.

Gionis, A., Mannila, H., and Tsaparas, P. (2007). Cluster-

ing aggregation. ACM Trans. Knowl. Discov. Data,

1(1):4–es.

Jain, A. K. and Law, M. H. (2005). Data clustering: A

user’s dilemma. In Pattern Recognition and Machine

Intelligence, pages 1–10. Springer.

Kang, Z., Guo, Z., Huang, S., Wang, S., Chen, W., Su, Y.,

and Xu, Z. (2019). Multiple partitions aligned clus-

tering. In Proceedings of the 28th International Joint

Conference on Artiﬁcial Intelligence, IJCAI’19, page

2701–2707. AAAI Press.

Karypis, G. and Kumar, V. (1998). A fast and high qual-

ity multilevel scheme for partitioning irregular graphs.

SIAM Journal on Scientiﬁc Computing, 20(1):359–

392.

Mardi, M. and Keyvanpour, M. R. (2021). Gbkm: A

new genetic based k-means clustering algorithm. In

2021 7th International Conference on Web Research

(ICWR), pages 222–226. IEEE.

Nielsen, F. (2016). Hierarchical clustering. In Introduction

to HPC with MPI for Data Science, pages 195–211.

Springer.

Sainz-Tinajero, B. M., Gutierrez-Rodriguez, A. E., Cebal-

los, H. G., and Cantu-Ortiz, F. J. (2021a). Evolution-

ary clustering algorithm using supervised classiﬁers.

In 2021 IEEE Congress on Evolutionary Computation

(CEC), pages 2039–2045. IEEE.

Sainz-Tinajero, B. M., Gutierrez-Rodriguez, A. E., Cebal-

los, H. G., and Cantu-Ortiz, F. J. (2021b). F1-ecac:

Enhanced evolutionary clustering using an ensemble

of supervised classiﬁers. IEEE Access, 9:134192–

134207.

Shi, J. and Malik, J. (2000). Normalized cuts and image

segmentation. IEEE Transactions on Pattern Analysis

and Machine Intelligence, 22(8):888–905.

Steinley, D. (2004). Properties of the hubert-arable adjusted

rand index. Psychological Methods, 9(3):386.

Veenman, C. J., Reinders, M. J. T., and Backer, E. (2002).

A maximum variance cluster algorithm. IEEE Trans-

actions on Pattern Analysis and Machine Intelligence,

24(9):1273–1280.

Von Luxburg, U. (2007). A tutorial on spectral clustering.

Statistics and Computing, 17(4):395–416.

Zhang, Y., Liu, H., and Deng, B. (2013). Evolutionary clus-

tering with DBSCAN. In 2013 Ninth International

Conference on Natural Computation (ICNC), pages

923–928.

ECA-CE: An Evolutionary Clustering Algorithm with Initial Population by Clustering Ensemble

139