Universal NP-Hardness of Clustering under General Utilities
Quick summary
arXiv:2603.00210v2 Announce Type: replace-cross Abstract: Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation. Existing theoretical results are largely objective-specific and do not explain these behaviours at a unifying level. We formalise the common optimisation core underlying diverse clustering paradigms by defining the Universal Clustering Problem (UCP): the maximisation of a polynomial-time computable partition utility over a finite me
Key takeaways
- arXiv:2603.00210v2 Announce Type: replace-cross Abstract: Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation.
- Existing theoretical results are largely objective-specific and do not explain these behaviours at a unifying level.
- We formalise the common optimisation core underlying diverse clustering paradigms by defining the Universal Clustering Problem (UCP): the maximisation of a polynomial-time computable partition utility over a finite me
Why it matters
The importance of “Universal NP-Hardness of Clustering under General Utilities” will be measured by what changes in practice. User behavior, access conditions, verifiable performance and responsible-use outcomes are the signals worth following.
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