The Condition-Number Principle for Prototype Clustering
We develop a geometric framework that links objective accuracy to structural recovery in prototype-based clustering. The analysis is algorithm-agnostic and applies to a broad class of admissible loss functions. We define a clustering condition number that compares within-cluster scale to the minimum loss increase required to move a point across a cluster boundary. When this quantity is small, any solution with a small suboptimality gap must also have a small misclassification error relative to a benchmark partition. The framework also clarifies a fundamental trade-off between robustness and sensitivity to cluster imbalance, leading to sharp phase transitions for exact recovery under diffe...
| Authors | Romano Li, Jianfei Cao |
|---|---|
| Primary category | stat.ML |
| Published | 9 April 2026 |
| Last updated at source | 9 April 2026 |
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