Classification fields are infinite recursive hierarchical cluster structures generated by a local refinement rule, and a ReLU network predictor learned from finite prefixes can approximate the generator and extend it to deeper levels with exponential convergence in the completed cell metric.
Approximation bounds for hierarchical clustering: Average linkage, bisecting k-means, and local search.Journal of Machine Learning Research, 24(1):1–36
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Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples
Classification fields are infinite recursive hierarchical cluster structures generated by a local refinement rule, and a ReLU network predictor learned from finite prefixes can approximate the generator and extend it to deeper levels with exponential convergence in the completed cell metric.