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An equidistance index intuitionistic fuzzy c-means clustering algorithm based on local density and membership degree boundary

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Qianxia Ma
Qianxia Ma
Qianxia Ma
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Xiaomin Zhu at China University of Petroleum, Beijing
Xiaomin Zhu
Xiangkun Zhao
Xiangkun Zhao
Xiangkun Zhao
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Butian Zhao at Beijing University of Chinese Medicine
Butian Zhao
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Abstract and Figures

Fuzzy c-means (FCM) algorithm is an unsupervised clustering algorithm that effectively expresses complex real world information by integrating fuzzy parameters. Due to its simplicity and operability, it is widely used in multiple fields such as image segmentation, text categorization, pattern recognition and others. The intuitionistic fuzzy c-means (IFCM) clustering has been proven to exhibit better performance than FCM due to further capturing uncertain information in the dataset. However, the IFCM algorithm has limitations such as the random initialization of cluster centers and the unrestricted influence of all samples on all cluster centers. Therefore, a novel algorithm named equidistance index IFCM (EI-IFCM) is proposed for improving shortcomings of the IFCM. Firstly, the EI-IFCM can commence its learning process from more superior initial clustering centers. The EI-IFCM algorithm organizes the initial cluster centers based on the contribution of local density information from the data samples. Secondly, the membership degree boundary is assigned for the data samples satisfying the equidistance index to avoid the unrestricted influence of all samples on all cluster centers in the clustering process. Finally, the performance of the proposed EI-IFCM is numerically validated using UCI datasets which contain data from healthcare, plant, animal, and geography. The experimental results indicate that the proposed algorithm is competitive and suitable for fields such as plant clustering, medical classification, image differentiation and others. The experimental results also indicate that the proposed algorithm is surpassing in terms of iteration and precision in the mentioned fields by comparison with other efficient clustering algorithms.
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Vol.:(0123456789)
Applied Intelligence (2024) 54:3205–3221
https://doi.org/10.1007/s10489-024-05297-1
An equidistance index intuitionistic fuzzy c‑means clustering
algorithm based onlocal density andmembership degree boundary
QianxiaMa1· XiaominZhu1· XiangkunZhao1· ButianZhao2· GuanhuaFu3· RuntongZhang2
Accepted: 28 January 2024 / Published online: 27 February 2024
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024
Abstract
Fuzzy c-means (FCM) algorithm is an unsupervised clustering algorithm that effectively expresses complex real world
information by integrating fuzzy parameters. Due to its simplicity and operability, it is widely used in multiple fields such as
image segmentation, text categorization, pattern recognition and others. The intuitionistic fuzzy c-means (IFCM) clustering
has been proven to exhibit better performance than FCM due to further capturing uncertain information in the dataset. How-
ever, the IFCM algorithm has limitations such as the random initialization of cluster centers and the unrestricted influence of
all samples on all cluster centers. Therefore, a novel algorithm named equidistance index IFCM (EI-IFCM) is proposed for
improving shortcomings of the IFCM. Firstly, the EI-IFCM can commence its learning process from more superior initial
clustering centers. The EI-IFCM algorithm organizes the initial cluster centers based on the contribution of local density
information from the data samples. Secondly, the membership degree boundary is assigned for the data samples satisfying the
equidistance index to avoid the unrestricted influence of all samples on all cluster centers in the clustering process. Finally,
the performance of the proposed EI-IFCM is numerically validated using UCI datasets which contain data from healthcare,
plant, animal, and geography. The experimental results indicate that the proposed algorithm is competitive and suitable for
fields such as plant clustering, medical classification, image differentiation and others. The experimental results also indicate
that the proposed algorithm is surpassing in terms of iteration and precision in the mentioned fields by comparison with
other efficient clustering algorithms.
Keywords Equidistance index· Local density· Membership degree boundary· Intuitionistic fuzzy c-means· Equidistance
index intuitionistic fuzzy c-means
1 Introduction
As an essential branch of machine learning, clustering analy-
sis aims to gather high similarity data samples into the same
group. As an unsupervised learning algorithm, clustering
has been widely used in many fields, such as image segmen-
tation [1], evaluation of credit risk prediction [2], and pattern
recognition [3]. In various clustering algorithms [4–7], the
fuzzy c-means clustering (FCM) proposed by Bellman etal.
[8] can integrate the uncertainty of the actual datasets by
combining Zada’s fuzzy theory [9]. The use of fuzzy infor-
mation is mostly driven by the ability to understand opera-
tions in a manner akin to human logical thinking, which
can capture more information about actual problems [10]. In
FCM clustering, the interaction between different clusters is
generated by FCM, which can effectively avoid falling into
the local optimal solution [11, 12]. Due to the uncertainty in
data collection in practical problems, FCM may experience
uncertainty when calculating the membership value of a
given sample [13]. In other words, due to the fact that fuzzy
theory only obtains uncertain information through mem-
bership functions in expressing fuzzy information, this can
result in the loss of some fuzzy information [14]. Therefore,
FCM has certain limitations in comprehensively obtaining
uncertain information [15].
In order to improve the problem of fuzzy sets being
unable to obtain more uncertain information, Atanassov
* Xiaomin Zhu
xmzhu@bjtu.edu.cn
1 School ofMechanical, Electronic andControl Engineering,
Beijing Jiaotong University, Beijing100044, China
2 School ofEconomics andManagement, Beijing Jiaotong
University, Beijing100044, China
3 Rail Transit Department, Tianjin Jinhang Computing
Technology Research Institute, Tianjin300308, China
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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