arXiv:2606. 18972v1 Announce Type: cross Abstract: Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem.
Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution.
arXiv:2607. 13217v1 Announce Type: cross Abstract: Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton.
arXiv:2604. 23628v2 Announce Type: replace-cross Abstract: Hierarchical clustering is a fundamental task in data analysis, but classical methods have long lacked a principled objective function.
arXiv:2502. 08397v3 Announce Type: replace-cross Abstract: Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together.
Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton. We relax the halting condition of the recursive process to stop whenever the remaining cluster is a graph belonging to a class $\mathcal{F}$.
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
The paper introduces the Universal Clustering Problem (UCP), a framework that captures the optimisation core common to many clustering methods by maximizing a polynomial‑time computable partition utility over a finite metric space. It proves UCP is NP‑hard through reductions from graph colouring and exact cover by 3‑sets, showing that popular algorithms such as k‑means, GMMs, DBSCAN, spectral clustering, and affinity propagation inherit this intractability. The authors argue that this unified hardness explains typical failure modes—like local optima and greedy merge traps—and suggest moving toward stability‑aware objectives and interaction‑driven formulations with explicit guarantees.
arXiv:2607. 24237v1 Announce Type: new Abstract: Many existing clustering methods are designed based on a set-oriented definition---a cluster is a set of similar points---relying a point-to-point similarity function to find similar points.
arXiv:2606. 00327v1 Announce Type: cross Abstract: Clustering is widely used across the sciences as the foundation for downstream data-driven scientific discoveries.
arXiv:2411. 01576v3 Announce Type: replace Abstract: The explainable clustering problem was first posed by Moshkovitz et al.
arXiv:2606. 05230v1 Announce Type: cross Abstract: Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data.
The paper introduces ICOMT, a framework for interpretable clustering using optimal multi-way decision trees. It proposes a new discretization technique based on one-dimensional K‑means, formulates a binary linear optimization problem to ensure tree optimality, and demonstrates superior clustering accuracy and shallow tree structures on four public datasets.