A new validity clustering index-based on finding new centroid positions using the mean of clustered data to determine the optimum number of clusters

Abdalameer, Ahmed Khaldoon; Alswaitti, Mohammed; Alsudani, Ahmed Adnan; Isa, Nor Ashidi Mat

doi:10.1016/j.eswa.2021.116329

Cited by 21 publications

(6 citation statements)

References 40 publications

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“…In the literature, there are two main types of clustering algorithms that are often combined with IVIs to determine the ONC: hierarchical and partitional clustering [8]. For the hierarchical clustering, according to the direction of clustering, there are two types of methods: agglomerative hierarchical clustering (AHC) and divisive hierarchical clustering (DHC) [21], where the former follows the bottom-top strategy, which treats each sample as a complete cluster at the beginning, and then gradually merges them into some larger cluster based on a certain criterion, and on the contrary, the DHC adopts the top-down strategy, which initially regards the entire dataset as a complete cluster and then splits the dataset into some smaller clusters based on a certain criterion [22].…”

Section: Clustering Algorithmsmentioning

confidence: 99%

“…Let N be the number of samples, k is the NC, and the range of k is 2, √ N as in [7,8,11]. The object of this step is to get different clustering results corresponding to different NCs under a certain clustering algorithm.…”

Section: The Bwcon-based Onc Estimation Frameworkmentioning

confidence: 99%

“…Here the significance level in the Nemenyi test is 0.1 and CD is 3.640. 26)), where those unstable clustering algorithms are run 100 times as in [8].…”

Section: Performance Evaluation Of the Bwcon-nsdk-means++ Algorithmmentioning

confidence: 99%

“…In the state-of-the-art studies, there are two main ways to determine the ONS: (1) the researchers directly specify an ONS or a range based on their prior knowledge [5], and (2) the combination of a validity index and a clustering algorithm is used to determine the ONS due to a fact that the clustering analysis is the current dominant market segmentation technique and most clustering algorithms also require a pre-specified number of clusters (NC), which makes the process of finding the optimal NC (ONC) coincide with the purpose of determining the ONS [6]. Compared with the former, this combination strategy is more objective and user-friendly; and its basic idea is to perform a clustering algorithm many times with different NCs, choose an appropriate validity index to evaluate the clustering results, and determine the ONC (ONS) according to the evaluation values [7,8], in which the selections of the validity index and the clustering algorithm play the very important roles in whether a reasonable ONC can be obtained. And in our study, we also try to propose an effective method for determining the ONC based on such combinatorial idea.…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

Qi¹,

Li²,

Haibin³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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An appropriate optimal number of market segments (ONS) estimation is essential for an enterprise to achieve successful market segmentation, but at present, there is a serious lack of attention to this issue in market segmentation. In our study, an independent adaptive ONS estimation method BWCON-NSDK-means++ is proposed by integrating a new internal validity index (IVI) Between-Within-Connectivity (BWCON) and a new stable clustering algorithm Natural-SDK-means++ (NSDK-means++) in a novel way. First, to complete the evaluation dimensions of the existing IVIs, we designed a connectivity formula based on the neighbor relationship and proposed the BWCON by integrating the connectivity with other two commonly considered measures of compactness and separation. Then, considering the stability, number of parameters and clustering performance, we proposed the NSDK-means++ to participate in the integration where the natural neighbor was used to optimize the initial cluster centers (ICCs) determination strategy in the SDK-means++. At last, to ensure the objectivity of the estimated ONS, we designed a BWCON-based ONS estimation framework that does not require the user to set any parameters in advance and integrated the NSDK-means++ into this framework forming a practical ONS estimation tool BWCON-NSDK-means++. The final experimental results show that the proposed BWCON and NSDK-means++ are significantly more suitable than their respective existing models to participate in the integration for determining the ONS, and the proposed BWCON-NSDK-means++ is demonstrably superior to the BWCON-KMA, BWCON-MBK, BWCON-KM++, BWCON-RKM++, BWCON-SDKM++, BWCON-Single linkage, BWCON-Complete linkage, BWCON-Average linkage and BWCON-Ward linkage in terms of the ONS estimation. Moreover, as an independent market segmentation tool, the BWCON-NSDK-means++ also outperforms the existing models with respect to the inter-market differentiation and sub-market size.

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Section: Clustering Algorithmsmentioning

confidence: 99%

Section: The Bwcon-based Onc Estimation Frameworkmentioning

confidence: 99%

“…Here the significance level in the Nemenyi test is 0.1 and CD is 3.640. 26)), where those unstable clustering algorithms are run 100 times as in [8].…”

Section: Performance Evaluation Of the Bwcon-nsdk-means++ Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

Qi¹,

Li²,

Haibin³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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show abstract

“…The purpose of clustering is to partition objects into groups with criteria such that the similarity within the groups and the dissimilarity among different groups should be maximized [ 1 , 2 ]. Although clustering methods have been widely used in many applications, most clustering algorithms do not provide the optimal number of clusters.…”

Section: Introductionmentioning

confidence: 99%

Cluster Validity Index for Uncertain Data Based on a Probabilistic Distance Measure in Feature Space

Baek

Tavakkol

et al. 2023

Sensors

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Cluster validity indices (CVIs) for evaluating the result of the optimal number of clusters are critical measures in clustering problems. Most CVIs are designed for typical data-type objects called certain data objects. Certain data objects only have a singular value and include no uncertainty, so they are assumed to be information-abundant in the real world. In this study, new CVIs for uncertain data, based on kernel probabilistic distance measures to calculate the distance between two distributions in feature space, are proposed for uncertain clusters with arbitrary shapes, sub-clusters, and noise in objects. By transforming original uncertain data into kernel spaces, the proposed CVI accurately measures the compactness and separability of a cluster for arbitrary cluster shapes and is robust to noise and outliers in a cluster. The proposed CVI was evaluated for diverse types of simulated and real-life uncertain objects, confirming that the proposed validity indexes in feature space outperform the pre-existing ones in the original space.

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A Novel Genetic Algorithm with Specialized Genetic Operators for Clustering

Robles-Berumen,

Zafra,

Ventura

2023

Lecture Notes in Computer Science

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A new validity clustering index-based on finding new centroid positions using the mean of clustered data to determine the optimum number of clusters

Cited by 21 publications

References 40 publications

An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index

Cluster Validity Index for Uncertain Data Based on a Probabilistic Distance Measure in Feature Space

A Novel Genetic Algorithm with Specialized Genetic Operators for Clustering

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