Optimizing cluster centroids with improved quadratic interpolation: an Adaptive K-means algorithm

doi:10.1016/j.cam.2025.116921

2026-02-01

PRE

DOI：10.1016/j.cam.2025.116921

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The traditional k-means clustering algorithm is sensitive to initial centroids selection, prone to local optima, and inefficient on large-scale datasets. To address these limitations, this article proposes an Adaptive K-Means algorithm (AK-means) that integrates a density-based initialization strategy and an Improved Quadratic Interpolation Optimization (IQIO) method. Specifically, a novel density-aware initialization approach is introduced to generate initial centroids by evaluating data point sparsity and distance distribution, effectively mitigating centroid deviation, and an enhanced IQIO mechanism. In particular, IQIO is improved through two key innovations, including a dynamic neighborhood search mechanism based on the absolute slope of interpolated points and the position of known optima, which significantly reduces computational complexity compared to traditional methods; and the incorporation of gradient descent to refine local exploitation, accelerating convergence to high-accuracy solutions. To verify the effectiveness of IQIO, experiments on the CEC2017 benchmark suite demonstrate its superiority over 10 state-ofthe-art optimizers, with Wilcoxon rank-sum tests, confirming statistically significant improvements in 22 out of 29 test functions. Furthermore, evaluations on 18 UCI datasets reveal that AKmeans achieves superior clustering performance compared to 4 baseline methods, achieving lower Mean Squared Error (MSE) and reduction in Davies-Bouldin Index (DB) compared to traditional k-means, particularly on large-scale data. These results highlight the algorithm's ability to balance cluster compactness and separation while maintaining scalability for highdimensional data. The proposed hybrid optimization strategy provides a better program for real-world applications requiring efficient and precise clustering of large-scale datasets.

Keyword:

Data clustering

Improved quadratic interpolation

K -means algorithm

Initial center

Adaptive optimization