First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. The paper introduces max-margin Bayesian clustering (BMC) that extends Bayesian clustering techniques to include the max-margin criterion. This includes, for example, the Dirichlet process max-margin Gaussian mixture that relaxes the underlying Gaussian assumption of Dirichlet process Gaussian mixtures by incorporating max-margin posterior constraints, and is able to infer the number of clusters from data. The resulting techniques (DPMMGM and a further one classed MMCTM) are compared to a variety of other techniques in several numerical experiments. The paper combines two clustering approaches: Deterministic and Bayesian clustering.

Neural Information Processing Systems http://nips.cc/

Data clustering is a central tenet of unsupervised machine learning.

Data clustering is a central tenet of unsupervised machine learning.

Cons: - Some amount of discussion on proof techniques / open questions in the main text would be useful.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. In this paper the authors analyze theoretically two common graph clustering algorithms using low rank + sparsity, showing bounds on the parameter of these methods for them to work, and they present experimental validations of the results. The paper is very well written in general, although there are some minor typos. For instance, I think that the about in line 314 should be an above. Also, it seems more reasonable to me to put subsection 3.1.1

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Designing categorical kernels is a major challenge for Gaussian process regression with continuous and categorical inputs. Despite previous studies, it is difficult to identify a preferred method, either because the evaluation metrics, the optimization procedure, or the datasets change depending on the study. In particular, reproducible code is rarely available. The aim of this paper is to provide a reproducible comparative study of all existing categorical kernels on many of the test cases investigated so far. We also propose new evaluation metrics inspired by the optimization community, which provide quantitative rankings of the methods across several tasks. From our results on datasets which exhibit a group structure on the levels of categorical inputs, it appears that nested kernels methods clearly outperform all competitors. When the group structure is unknown or when there is no prior knowledge of such a structure, we propose a new clustering-based strategy using target encodings of categorical variables. We show that on a large panel of datasets, which do not necessarily have a known group structure, this estimation strategy still outperforms other approaches while maintaining low computational cost.

This work introduces a hybrid quantum-classical method to correlation clustering, a graph-based unsupervised learning task that seeks to partition the nodes in a graph based on pairwise agreement and disagreement. In particular, we adapt GCS-Q, a quantum-assisted solver originally designed for coalition structure generation, to maximize intra-cluster agreement in signed graphs through recursive divisive partitioning. The proposed method encodes each bipartitioning step as a quadratic unconstrained binary optimization problem, solved via quantum annealing. This integration of quantum optimization within a hierarchical clustering framework enables handling of graphs with arbitrary correlation structures, including negative edges, without relying on metric assumptions or a predefined number of clusters. Empirical evaluations on synthetic signed graphs and real-world hyperspectral imaging data demonstrate that, when adapted for correlation clustering, GCS-Q outperforms classical algorithms in robustness and clustering quality on real-world data and in scenarios with cluster size imbalance. Our results highlight the promise of hybrid quantum-classical optimization for advancing scalable and structurally-aware clustering techniques in graph-based unsupervised learning.