Open AccessOpen Access


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

Jianfang Qi1, Yue Li1,3, Haibin Jin1, Jianying Feng1, Dong Tian1, Weisong Mu1,2,*

1 College of Information and Electrical Engineering, China Agricultural University, Beijing, 100083, China
2 Key Laboratory of Viticulture and Enology, Ministry of Agriculture, Beijing, 100083, China
3 Institute of Population Research, Peking University, Beijing, 100871, China

* Corresponding Author: Weisong Mu. Email:

Computer Modeling in Engineering & Sciences 2023, 137(1), 197-232.


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, BWCONMBK, 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.


Cite This Article

Qi, J., Li, Y., Jin, H., Feng, J., Tian, D. et al. (2023). An Adaptive Parameter-Free Optimal Number of Market Segments Estimation Algorithm Based on a New Internal Validity Index. CMES-Computer Modeling in Engineering & Sciences, 137(1), 197–232.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1091


  • 393


  • 0


Share Link