Variance-Inter-Quartile Range Hierarchical Clustering Method with Applications (VIQR)

Clustering is the task of grouping a set of objects in such a way that objects in the same group (cluster) are more similar  to each other than to those in other groups (clusters).  In this paper, a new procedure of linkage hierarchical clustering method (Variance-inter-quartile Range Hierarchical clustering method) was developed to reduce the effect of extreme values in the classification of groups into clusters. The new proposed method makes use of the variance to get the variance matrix and inter-quartile range for the construction of the dendogram which is used for the comparative analysis of the newly proposed method and the existing methods. A performance evaluation was carried out using the visual dendogram inspection and silhouette score on the newly proposed method VIQR (Variance-inter-quartile Range Hierarchical clustering method) and the existing methods (Single and Complete linkage). From the result, using visual dendogram inspection, It was observed that VIQR Hierarchical clustering method performs better than the existing methods for the classification of objects as it has similar dendogram with fewer steps in the classification procedure. Using Shilouette score as a method of validation of the clusters, from the result, the score for the proposed method is 0.53 which is higher than the scores of the existing methods; single linkage (0.23) and complete linkage linkage (0.30). In summary, VIQR is more efficient and robust classification method in terms of shorter algorithm, better control of extreme values, and less complexity. Therefore the VIQR should be adopted  as a better method for classification of observations or variables especially when dealing with problems that have to do with classification.

Clustering, Variation, Similarity, Dendogram, Hierarchical, Dispersion

1. Alvin C. R. (2002). Methods of Multivariate Analysis. John Wiley and Sons, Inc. publication Second Edition. Page 456 [Google Scholar] [Crossref]

2. Banfield J. D. and Raftery A. E. (1993): “Model-based Gaussian and non-Gaussian clustering”. Biometrics, 49:803-821. [Google Scholar] [Crossref]

3. Bharat Chaudhari, Manan Parikh (2012): “A Comparative Study of clustering Algorithms”. International Journal of Application or Innovation in Engineering & Management. [Google Scholar] [Crossref]

4. bezas, L. M. C., Izbicki, R., & Stern, R. B. (2023). Hierarchical Clustering: Visualization,Feature Importance And Model Selection. Applied Soft Computing, 141, 110303. [Google Scholar] [Crossref]

5. Brian S. Everitt., Sabine Landau and Morven Leese (2001). Cluster Analysis (Fourth ed.) London: Arnold. [Google Scholar] [Crossref]

6. Chen, H., Zhang, R., Duan, Y., Wang, R., & Nie, F. (2025). Fast Multi-View Clustering Via Anchor Label Transmit With Tensor Structure Constraint. Expert Systems With Applications, 274, 126878. [Google Scholar] [Crossref]

7. Chris ding and Xiaofeng He (2002): “Cluster merging and Splitting In hierarchical clustering Algorithms”, International Conference on Data Mining (ICDM 2002) IEEE, pg139. [Google Scholar] [Crossref]

8. Hamidi S.S, Akbari. E, Motameni .H. (2019): Consensus clustering algorithm based on the automatic partitioning similarity graph, Data Knowl.Eng., 124, p.101754 [Google Scholar] [Crossref]

9. J.A.S. Almeida, L.M.S. Barbosa, A.A.C.C. Pais and S.J. Formosinho (2007): “A new method with outlier detection and automatic clustering. Chemometrics and Intelligent Laboratory Systems 87, pp. 208–217 [Google Scholar] [Crossref]

10. Jiawei Han and Micheline Kamber, Jian Pei, B Data Mining: Concepts and Techniques, 3rd Edition, 2007. [Google Scholar] [Crossref]

11. Jin, T., Sun, X., Huang, B., & Wang, T. (2026). A Novel Hierarchical Clustering Approach Based On Granular-Ball Computing. Neurocomputing, 665, 132200. [Google Scholar] [Crossref]

12. Krishnamurthy, P. (2006): Approaches to clustering Gene expression Time course Data, M.Sc Thesis: Department of Computer Science and Engineering, State University of New York at Buffalo. [Google Scholar] [Crossref]

13. Martin Ester, Hans-Peter Kriegel, J&g Sander and Xiaowei Xu (1996): “A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise. Institute for Computer Science, University of Munich. Pp. 226-231. [Google Scholar] [Crossref]

14. May Thu Lwin and Moe Moe Aye (2016): “Modified Agglomerative Hierarchical Clustering (MAHC) Algorithm for Document Clustering”, International Journal of Advances in Electronics and Computer Science, Vol. 3, Issue-8. [Google Scholar] [Crossref]

15. Myatt, Glenn J, (2009): “Making Sense of Data II”, 2009, Wiley, Canada. [Google Scholar] [Crossref]

16. Onyeagu S. I (2003): A first course in Multivariate Statistical Analysis, Textbook. [Google Scholar] [Crossref]

17. Pelin Yildirim and Derya Birant (2017): K-Linkage: A New Agglomerative Approach for Hierarchical Clustering, Advances in Electrical and Computer Engineering, 17(4) pp 77-88. [Google Scholar] [Crossref]

18. Stuetzle, w and Nugent, R. (2010): A generalized Single linkage method for estimating the cluster tree of a destiny. Technical Report. University of Washington, Washington, USA. [Google Scholar] [Crossref]

19. Sruthi, K and B.V. Reddy (2013), “Document clustering on various similarity measures”, International Journal of Advanced Research in Computer Science and Software Engineering, IJARCSSE, Vol.3, Issue-8. [Google Scholar] [Crossref]

20. Tian Zhang, Raghu Ramakrishnan and Miron Livny (1996): “Birch: An Efficient Data Clustering Method for Very Large Databases. Computer Sciences Dept. Univ. of Wisconsin-Madison. Pp. 103-114 [Google Scholar] [Crossref]

21. Rokach, Lior, and Oded Maimon (2005),"Clustering methods." Data mining and knowledge discovery handbook. Springer US, pp 321-352. [Google Scholar] [Crossref]

22. Yogita Rani and Harish Rohil (2013): “A Study of Hierarchical Clustering Algorithm. International Journal of Information and Computation Technology, 3(10), pp. 1115-1122. [Google Scholar] [Crossref]

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