FOSC-X: An Extended Framework for Optimal Local Cuts and Non-Horizontal Cluster Selection from Clustering Hierarchies

2026-06-18 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

FOSC-X is an extended framework for extracting the top-M globally optimal flat clusterings from hierarchical cluster trees, addressing limitations of single-solution methods like the original FOSC. It supports optional cluster-count constraints, allowing users to specify lower (k_min) and upper (k_max) limits on desired granularity. The framework employs a dynamic programming strategy with feasibility-aware dominance pruning, which maintains compact sets of feasible candidates and prunes infeasible or dominated combinations. This guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without constraints. Experiments demonstrate FOSC-X efficiently uncovers alternative, high-quality clustering structures often missed by prior approaches. A Python library for FOSC-X is available.

Key takeaway

For Machine Learning Engineers extracting flat clusterings from hierarchical data, FOSC-X provides a significant advantage over traditional single-solution methods. You should explore its ability to enumerate top-M optimal solutions, as experiments show this often uncovers more meaningful and robust alternatives. Additionally, utilize the flexible k_min and k_max constraints to guide granularity, suppressing noise or fine-grained structures for improved interpretability and application-specific relevance.

Key insights

FOSC-X extends hierarchical clustering to extract top-M optimal flat solutions with flexible cluster-count constraints via dynamic programming.

Principles

• Optimal cluster extraction requires objective function locality and additivity.
• Cluster-count constraints break local optimality for global solutions.
• Dominance pruning is key for constrained multi-solution optimality.

Method

FOSC-X uses a bottom-up, feasibility-aware dynamic programming with dominance pruning to identify top-M clusterings, maintaining candidate sets with lower/upper feasibility bounds.

In practice

• Explore top-M solutions to reveal overlooked alternative cluster structures.
• Use k_min/k_max to guide extraction to desired granularity.
• Suppress insignificant branches or noise with k_max constraints.

Topics

• Hierarchical Clustering
• Optimal Cluster Selection
• Dynamic Programming
• Cluster-Count Constraints
• Top-M Solutions
• Dominance Pruning

Code references

• Campello-Lab/FOSC-X

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.