Universal NP-Hardness of Clustering under General Utilities

Researchers prove that clustering problems in machine learning are universally NP-hard, providing theoretical explanation for why clustering algorithms often produce unstable results. The study demonstrates that major clustering methods like k-means and spectral clustering inherit fundamental computational intractability, explaining common failure modes like local optima.

• →All major clustering paradigms including k-means, GMMs, and DBSCAN are proven to be NP-hard problems.
• →The Universal Clustering Problem framework unifies diverse clustering approaches under a single theoretical foundation.
• →Common clustering failures like local optima and greedy merge-order traps are explained by fundamental computational constraints.
• →The research motivates development of stability-aware objectives and interaction-driven formulations for clustering.
• →Clustering limitations arise from interacting computational and epistemic constraints rather than algorithmic deficiencies.