OpenNovelty.org

Metric kk-clustering using only Weak Comparison Oracles

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 7.2Download Report PDF
clustering$k$-center$k$-median$k$-meanscomparison oracleslearned rankerslearning-augmented algorithms
Abstract:

Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for kk-clustering (such as kk-median and kk-means) assume access to exact pairwise distances---an unrealistic requirement in many modern applications. We study clustering in the \emph{Rank-model (R-model)}, where access to distances is entirely replaced by a \emph{quadruplet oracle} that provides only relative distance comparisons. In practice, such an oracle can represent learned models or human feedback, and is expected to be noisy and entail an access cost.

Given a metric space with nn input items, we design randomized algorithms that, using only a noisy quadruplet oracle, compute a set of O(k⋅polylog(n))O(k \cdot \mathsf{polylog}(n)) centers along with a mapping from the input items to the centers such that the clustering cost of the mapping is at most constant times the optimum kk-clustering cost. Our method achieves a query complexity of O(n⋅k⋅polylog(n))O(n\cdot k \cdot \mathsf{polylog}(n)) for arbitrary metric spaces and improves to O((n+k2)⋅polylog(n))O((n+k^2) \cdot \mathsf{polylog}(n)) when the underlying metric has bounded doubling dimension. When the metric has bounded doubling dimension we can further improve the approximation from constant to 1+ε1+\varepsilon, for any arbitrarily small constant ε∈(0,1)\varepsilon\in(0,1), while preserving the same asymptotic query complexity. Our framework demonstrates how noisy, low-cost oracles, such as those derived from large language models, can be systematically integrated into scalable clustering algorithms.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper develops randomized algorithms for k-clustering in metric spaces using only noisy quadruplet oracles, achieving constant-factor approximation with O(n·k·polylog(n)) query complexity. It resides in the 'Metric Clustering via Weak Comparison Oracles' leaf, which contains four papers total. This leaf sits within the broader 'Comparison-Based Clustering with Noisy Oracles' branch, indicating a moderately populated research direction focused on clustering without exact distances. The taxonomy shows this is an active but not overcrowded area, with sibling leaves addressing noisy pairwise queries and top-k selection problems.

The taxonomy reveals neighboring work in 'Clustering with Noisy Pairwise Queries' (three papers) and 'Ordinal and Ranking-Based Clustering' (five papers across three leaves). The paper's focus on quadruplet comparisons in metric spaces distinguishes it from ordinal methods that avoid metric assumptions and from pairwise-query frameworks that use different oracle models. The scope note for this leaf explicitly excludes non-metric or ordinal embedding approaches, positioning the work at the intersection of metric geometry and weak supervision. Related branches explore semi-supervised constraints and correlation clustering, but these assume different information models.

Among 21 candidates examined across three contributions, no clearly refuting prior work was identified. Contribution A (randomized algorithms using noisy quadruplet oracles) examined one candidate with no refutation. Contributions B (improved approximation for bounded doubling dimension) and C (framework for noisy low-cost oracles) each examined ten candidates, again with no refutations found. This suggests that within the limited search scope—top-K semantic matches plus citation expansion—the specific combination of quadruplet oracles, metric clustering objectives, and doubling-dimension analysis appears relatively underexplored. The absence of refutations does not imply exhaustive novelty but indicates limited overlap in the examined candidate set.

Based on the restricted literature search of 21 papers, the work appears to occupy a distinct position within comparison-based clustering. The taxonomy structure and contribution-level statistics suggest the paper addresses a specific gap—metric k-clustering via quadruplet oracles with doubling-dimension refinements—that neighboring work does not directly cover. However, the analysis is constrained by the search scope and does not capture the full landscape of comparison-based learning or metric clustering beyond the examined candidates.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
21
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: clustering using only weak comparison oracles. This field addresses the challenge of grouping data when direct feature measurements are unavailable or expensive, relying instead on limited pairwise comparisons or ordinal feedback. The taxonomy reveals several complementary directions. Comparison-Based Clustering with Noisy Oracles focuses on algorithms that tolerate imperfect or probabilistic similarity judgments, often analyzing sample complexity and robustness guarantees. Ordinal and Ranking-Based Clustering exploits relative ordering information—such as top-k lists or partial rankings—to infer cluster structure without metric embeddings. Semi-Supervised Clustering with Weak Supervision incorporates sparse human feedback or constraints to guide partitioning, while Feature-Based and Multi-View Clustering leverages multiple data representations when available. Correlation Clustering and Graph Synchronization tackle consensus problems over noisy pairwise relationships, and Specialized Clustering Applications and Models address domain-specific scenarios ranging from entity resolution to face clustering in videos. A particularly active line of work examines the trade-off between query efficiency and noise tolerance in comparison oracles. Studies such as Noisy Comparison Oracle[3] and Metric Clustering Weak Oracles[2] investigate how many noisy triplet or pairwise queries suffice to recover ground-truth clusters with high probability, balancing statistical guarantees against practical query budgets. Weak Comparison Oracles[0] sits squarely within this branch, emphasizing metric clustering under minimal oracle assumptions and analyzing the interplay between oracle noise models and algorithmic sample complexity. Compared to Noisy Comparison Oracle[3], which explores broader noise regimes, and Metric Clustering Weak Oracles[2], which refines query strategies for specific metric spaces, Weak Comparison Oracles[0] contributes refined theoretical bounds and algorithmic techniques for handling weak feedback. This work exemplifies ongoing efforts to understand the fundamental limits of clustering when only indirect, noisy relational information is accessible.

Claimed Contributions

Randomized algorithms for k-clustering using only noisy quadruplet oracles

The authors develop algorithms that construct an O(1)-Coreset+ for k-clustering in metric spaces using only a noisy quadruplet oracle (R-model), without requiring any distance oracle. The algorithms achieve query complexity of O(n·k·polylog(n)) for general metrics and O((n+k²)·polylog(n)) for bounded doubling dimension metrics.

1 retrieved paper
Improved approximation for bounded doubling dimension metrics

For metrics with bounded doubling dimension, the authors present an algorithm that constructs an ε-Coreset+ for k-median and k-means clustering, achieving (1+ε)-approximation for any small constant ε while maintaining O((n+k²)·polylog(n)) query complexity using only the quadruplet oracle.

10 retrieved papers
Framework for integrating noisy low-cost oracles into clustering

The authors establish a systematic framework showing how noisy quadruplet oracles, which can be implemented via large language models or learned models, can replace expensive distance computations in clustering algorithms while maintaining theoretical guarantees on clustering quality.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Randomized algorithms for k-clustering using only noisy quadruplet oracles

The authors develop algorithms that construct an O(1)-Coreset+ for k-clustering in metric spaces using only a noisy quadruplet oracle (R-model), without requiring any distance oracle. The algorithms achieve query complexity of O(n·k·polylog(n)) for general metrics and O((n+k²)·polylog(n)) for bounded doubling dimension metrics.

Contribution

Improved approximation for bounded doubling dimension metrics

For metrics with bounded doubling dimension, the authors present an algorithm that constructs an ε-Coreset+ for k-median and k-means clustering, achieving (1+ε)-approximation for any small constant ε while maintaining O((n+k²)·polylog(n)) query complexity using only the quadruplet oracle.

Contribution

Framework for integrating noisy low-cost oracles into clustering

The authors establish a systematic framework showing how noisy quadruplet oracles, which can be implemented via large language models or learned models, can replace expensive distance computations in clustering algorithms while maintaining theoretical guarantees on clustering quality.

Table of Contents