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arXiv · 2609.06468

Sector-Mean: Deterministic Initialization of K-Means Centroids via Angular Sector Partitioning

Abhiyan Dhakal·Pranish Kafle·Rajani Chulyadyo
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Abstract

K-Means is one of the most widely used clustering algorithms, but its susceptibility to initial centroid selection remains a primary bottleneck for its convergence speed and clustering accuracy. This paper proposes Sector-Mean Initialization, a deterministic initialization strategy with O(N) time complexity that partitions the two-dimensional data space into angular sectors around the global centroid and initializes centroids using sector-wise means. We evaluate the method on established two-dimensional benchmarks (SIPU, Birch) and multiple real-world datasets, comparing against random, K-Means++, and Max-Min initialization under identical Lloyd iterations. The statistical analysis of Friedman's test (p<0.05) and Nemenyi post-hoc comparison indicates that, while delivering equivalent clustering quality as K-Means++ and Max-Min, Sector-Mean offers significant computational efficiency. Experimental results show that Sector-Mean reduces the initialization time by 74.9% and 59.8% in comparison to K-Means++ and max-min, respectively. And, it yields the lowest average number of iterations, achieving approximately 5% fewer iterations than K-Means++ and 16% fewer than max-min. These results highlight that Sector-Mean initialization offers a deterministic and computationally efficient initialization strategy while preserving cluster quality.

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Abhiyan Dhakal, Pranish Kafle, Rajani Chulyadyo. 2026-09-06. Sector-Mean: Deterministic Initialization of K-Means Centroids via Angular Sector Partitioning. https://arxiv.org/abs/2609.06468

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