Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.

In this paper, we study the fundamental problems of maintaining the diameter and a k-center clustering of a dynamic point set P Rd, where points may be inserted or deleted over time and the ambient dimension dis not constant and may be high. Our focus is on designing algorithms that remain effective even in the presence of an adaptive adversary--an adversary that, at any time t, knows the entire history of the algorithm's outputs as well as all the random bits used by the algorithm up to that point. We present a fully dynamic algorithm that maintains a 2-approximate diameter with a worst-case update time of poly(d,logn), where n is the length of the stream. Our result is achieved by identifying a robust representative of the dataset that requires infrequent updates, combined with a careful deamortization. To the best of our knowledge, this is the first efficient fully-dynamic algorithm for diameter in high dimensions that simultaneously achieves a 2-approximation guarantee and robustness against an adaptive adversary. We also give an improved dynamic (4+ϵ)-approximation algorithm for the k-center problem, also resilient to an adaptive adversary.

Incomplete multi-view deep clustering is an emerging research hot-pot to incorporate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to a fixed set of data samples in all views. Meanwhile, the pair-wise similarities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment.

Motivated by the privacy, sensitivity and sharing limitations of health data, we present a comprehensive pipeline for inference of Bayesian mixture models within a federated learning setting, i.e. when data cannot be fully shared or pooled across compute nodes. We adopt a Consensus Monte Carlo (CMC) approach, in which an MCMC algorithm is run independently within each data silo to estimate local posterior distributions, which are then aggregated to approximate the posterior over the full data. The variational CMC approach of Rabinovich, Angelino and Jordan (2015) [1] frames the aggregation step as a variational inference problem, but their application to mixtures assumes the number of clusters and key mixture parameters to be known. Our main methodological contributions are: (i) an extension of variational CMC to over-fitted Bayesian mixture models that infer the number of clusters and all model parameters, without requiring conjugacy; (ii) novel cluster-matching algorithms suitable for cross-silo settings in which not every cluster appears in each local dataset; (iii) a number of inference strategies for the aggregation step, matched to different federated learning constraints; and (iv) guidelines for choosing among these in practice. A comprehensive simulation study validates the framework and allows us to compare to state-of-the-art federated learning alternatives. Notably, we show that when the composition of local datasets reflects the underlying clustering structure in the data, our approach can recover small clusters with greater accuracy than standard MCMC applied to the pooled data. We illustrate the framework on large-scale electronic health record data, identifying multi-morbidity patterns in a British geriatric population.

Clustering tabular data remains a significant open challenge in data analysis and machine learning. Unlike for image data, similarity between tabular records often varies across datasets, making the definition of clusters highly dataset-dependent. Furthermore, the absence of supervised signals complicates hyperparameter tuning in deep learning clustering methods, frequently resulting in unstable performance. To address these issues and reduce the need for per-dataset tuning, we adopt an emerging approach in deep learning: zero-shot learning. We propose ZEUS, a selfcontained model capable of clustering new datasets without any additional training or fine-tuning. It operates by decomposing complex datasets into meaningful components that can then be clustered effectively. Thanks to pre-training on synthetic datasets generated from a latent-variable prior, it generalizes across various datasets without requiring user intervention. To the best of our knowledge, ZEUS is the first zero-shot method capable of generating embeddings for tabular data in a fully unsupervised manner. Experimental results demonstrate that it performs on par with or better than traditional clustering algorithms and recent deep learning-based methods, while being significantly faster and more user-friendly.

In this work, we introduce TreeGen, a novel generative framework modeling distributions over hierarchies. We extend Bayesian Flow Networks (BFNs) to enable transitions between probabilistic and discrete hierarchies parametrized via categorical distributions. Our proposed scheduler provides smooth and consistent entropy decay across varying numbers of categories. We empirically evaluate TreeGen on the jet-clustering task in high-energy physics, demonstrating that it consistently generates valid trees that adhere to physical constraints and closely align with ground-truth log-likelihoods. Finally, by comparing TreeGen's samples to the exact posterior distribution and performing likelihood maximization via rejection sampling, we demonstrate that TreeGen outperforms various baselines.

Measuring the alignment between representations lets us understand similarities between the feature spaces of different models, such as Vision Transformers trained under diverse paradigms. However, traditional measures for representational alignment yield only scalar values that obscure how these spaces agree in terms of learned features. To address this, we combine alignment analysis with concept discovery, allowing a fine-grained breakdown of alignment into individual concepts. This approach reveals both universal concepts across models and each representation's internal concept structure. We introduce a new definition of concepts as non-linear manifolds, hypothesizing they better capture the geometry of the featurespace. A sanity check demonstrates the advantage of this manifold-based definition over linear baselines for concept-based alignment. Finally, our alignment analysis of four different ViTs shows that increased supervision tends to reduce semantic organization in learned representations.

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. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable -- e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method 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 cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.

Although receiving notable improvements, current multi-view clustering (MVC) techniques generally rely on feature library mechanisms to propagate accumulated knowledge from historical views to newly-arrived data, which overlooks the information pertaining to basis embedding within each view. Moreover, the mapping paradigm inevitably alters the values of learned landmarks and built affinities due to the uninterruption nature, accordingly disarraying the hierarchical cluster structures. To mitigate these two issues, we in the paper provide a named BSTM algorithm. Concretely, we firstly synchronize with the distinct dimensions by introducing a group of specialized projectors, and then establish unified anchors for all views collected so far to capture intrinsic patterns. Afterwards, departing from per-view architectures, we devise a shared bipartite graph construction via indicators to quantify similarity, which not only avoids redundant data-recalculations but alleviates the representation distortion caused by fusion.

Most existing multi-view clustering methods aim to generate a consensus partition across all views, based on the assumption that all views share the same sample arrangement. However, in real-world scenarios, the collected data across different views is often unsynchronized, making it difficult to ensure consistent sample correspondence between views. To address this issue, we propose a scalable sample-alignment-based multi-view clustering method, referred to as SSA-MVC. Specifically, we first employ a cluster-label matching (CLM) algorithm to select the view whose clustering labels best match those of the others as the benchmark view. Then, for each of the remaining views, we construct representations of nonaligned samples by computing their similarities with aligned samples. Based on these representations, we build a similarity graph between the non-aligned samples of each view and those in the benchmark view, which serves as the alignment criterion. This alignment criterion is then integrated into a late-fusion framework to enable clustering without requiring aligned samples. Notably, the learned sample alignment matrix can be used to enhance existing multi-view clustering methods in scenarios where sample correspondence is unavailable. The effectiveness of the proposed SSA-MVC algorithm is validated through extensive experiments conducted on eight real-world multi-view datasets.