New Criterion Optimizes K-Means++ Restarts for Better Clustering Quality

The k-means++ algorithm, a popular clustering method, often requires multiple restarts to avoid suboptimal local solutions. However, the number of these restarts is typically chosen arbitrarily, leading to inconsistent results and wasted computational resources on simpler datasets, while potentially underperforming on more complex ones. This new research addresses this issue by proposing the Good-Turing Restart Criterion (GTRC). GTRC provides a principled and interpretable way to determine when to stop restarting k-means++. It combines a Good-Turing estimate with unconditional and confidence-based bounds to calculate the probability that further restarts would improve the current clustering result. The algorithm stops once this probability falls below a user-defined tolerance. Evaluations across 36 diverse datasets showed that GTRC achieved clustering quality comparable to carefully chosen fixed restart counts. Crucially, the number of restarts used by GTRC varied appropriately with the dataset's difficulty, driven by an interpretable, data-dependent signal rather than a rigid rule. This offers a more robust and transparent alternative for practitioners, allowing for more reliable comparisons and efficient resource allocation in clustering tasks.