Box-K-Means symbolic data analysis: A k-means algorithm for boxplot variables with application to global climate Variability
DOI:
https://doi.org/10.64497/jssci.12Keywords:
Symbolic Data Analysis, Clustering, K-Means, Boxplot Variables, Climate Science, Pattern Recognition, Unsupervised LearningAbstract
A foundational methodology for the hierarchical clustering of boxplot-valued symbolic data was established in 2006 by addressing an interesting gap in the literature of Symbolic Data Analysis (SDA). Against this background, a robust partitioning-based clustering method for this data type has remained an open area of research. We develop a novel k-means-style algorithm specifically designed for boxplot variables, termed "Box-K-Means." The proposed algorithm defines a "mean boxplot" as a cluster prototype and utilizes the robust, weighted Ichino-Yaguchi distance metric for measuring dissimilarity between objects and prototypes. To validate the method, we apply it to a large-scale, contemporary climate dataset derived from the Berkeley Earth Surface Temperature Study, summarizing multi-decade temperature records from thousands of global weather stations into symbolic boxplot variables. The performance of Box-K-Means is evaluated against the original hierarchical method using internal validation metrics (Silhouette Score, Davies-Bouldin Index) and externally using the Adjusted Rand Index (ARI) for climate classification. The results demonstrate that the Box-K-Means algorithm provides a computationally efficient alternative for large symbolic datasets and successfully identifies coherent clusters in agreement with established climate zones. This work proposes a new tool for the SDA toolkit, expanding the potential for partitioning-based analysis of complex, distribution-based data in fields such as climatology, finance, and beyond.
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Copyright (c) 2025 Babangida Ibrahim BABURA, Lawan Muhammad Bulama , Dau Abba Umar
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