In community detection, many methods require the user to specify the number of clusters in advance since an exhaustive search over all possible values is computationally infeasible. While some classical algorithms can infer this number directly from the data, this is typically not the case for graph neural networks (GNNs): even when a desired number of clusters is specified, standard GNN-based methods often fail to return the exact number due to the way they are designed. In this work, we address this limitation by introducing a flexible and principled way to control the number of communities discovered by GNNs. Rather than assuming the true number of clusters is known, we propose a framework that allows the user to specify a plausible range and enforce these bounds during training. However, if the user wants an exact number of clusters, it may also be specified and reliably returned.

Machine learning techniques face numerous challenges to achieve optimal performance. These include computational constraints, the limitations of single-view learning algorithms and the complexity of processing large datasets from different domains, sources or views. In this context, multi-view clustering (MVC), a class of unsupervised multi-view learning, emerges as a powerful approach to overcome these challenges. MVC compensates for the shortcomings of single-view methods and provides a richer data representation and effective solutions for a variety of unsupervised learning tasks. In contrast to traditional single-view approaches, the semantically rich nature of multi-view data increases its practical utility despite its inherent complexity. This survey makes a threefold contribution: (1) a systematic categorization of multi-view clustering methods into well-defined groups, including co-training, co-regularization, subspace, deep learning, kernel-based, anchor-based, and graph-based strategies; (2) an in-depth analysis of their respective strengths, weaknesses, and practical challenges, such as scalability and incomplete data; and (3) a forward-looking discussion of emerging trends, interdisciplinary applications, and future directions in MVC research. This study represents an extensive workload, encompassing the review of over 140 foundational and recent publications, the development of comparative insights on integration strategies such as early fusion, late fusion, and joint learning, and the structured investigation of practical use cases in the areas of healthcare, multimedia, and social network analysis. By integrating these efforts, this work aims to fill existing gaps in MVC research and provide actionable insights for the advancement of the field.

Mining data streams with multi-label outputs poses significant challenges due to evolving distributions, high-dimensional label spaces, sparse label occurrences, and complex label dependencies. Moreover, concept drift affects not only input distributions but also label correlations and imbalance ratios over time, complicating model adaptation. To address these challenges, structured learners are categorized into local and global methods. Local methods break down the task into simpler components, while global methods adapt the algorithm to the full output space, potentially yielding better predictions by exploiting label correlations. This work introduces iHOMER (Incremental Hierarchy Of Multi-label Classifiers), an online multi-label learning framework that incrementally partitions the label space into disjoint, correlated clusters without relying on predefined hierarchies. iHOMER leverages online divisive-agglomerative clustering based on \textit{Jaccard} similarity and a global tree-based learner driven by a multivariate \textit{Bernoulli} process to guide instance partitioning. To address non-stationarity, it integrates drift detection mechanisms at both global and local levels, enabling dynamic restructuring of label partitions and subtrees. Experiments across 23 real-world datasets show iHOMER outperforms 5 state-of-the-art global baselines, such as MLHAT, MLHT of Pruned Sets and iSOUPT, by 23\%, and 12 local baselines, such as binary relevance transformations of kNN, EFDT, ARF, and ADWIN bagging/boosting ensembles, by 32\%, establishing its robustness for online multi-label classification.

Internal clustering validity indices (ICVIs) assess clustering quality without ground truth labels. Comparative studies consistently find that no single ICVI outperforms others across datasets, leaving practitioners without principled ICVI selection. We argue that inconsistent ICVI performance arises because studies evaluate them based on matching human labels rather than measuring the quality of the discovered structure in the data, using datasets without formally quantifying the structure type and quality. Structure type refers to the mathematical organisation in data that clustering aims to discover. Validity theory requires a theoretical definition of clustering quality, which depends on structure type. We demonstrate this through the first validity assessment of clustering quality measures for correlation patterns, a structure type that arises from clustering time series by correlation relationships. We formalise 23 canonical correlation patterns as the theoretical optimal clustering and use synthetic data modelling this structure with controlled perturbations to evaluate validity across content, criterion, construct, and external validity. Our findings show that Silhouette Width Criterion (SWC) and Davies-Bouldin Index (DBI) are valid for correlation patterns, whilst Calinski-Harabasz (VRC) and Pakhira-Bandyopadhyay-Maulik (PBM) indices fail. Simple Lp norm distances achieve validity, whilst correlation-specific functions fail structural, criterion, and external validity. These results differ from previous studies where VRC and PBM performed well, demonstrating that validity depends on structure type. Our structure-type-specific validation method provides both practical guidance (quality thresholds SWC>0.9, DBI<0.15) and a methodological template for establishing validity for other structure types.

Contrastive learning has proven to be highly efficient and adaptable in shaping representation spaces across diverse modalities by pulling similar samples together and pushing dissimilar ones apart. However, two key limitations persist: (1) Without explicit regulation of the embedding distribution, semantically related instances can inadvertently be pushed apart unless complementary signals guide pair selection, and (2) excessive reliance on large in-batch negatives and tailored augmentations hinders generalization. To address these limitations, we propose Variational Supervised Contrastive Learning (VarCon), which reformulates supervised contrastive learning as variational inference over latent class variables and maximizes a posterior-weighted evidence lower bound (ELBO) that replaces exhaustive pair-wise comparisons for efficient class-aware matching and grants fine-grained control over intra-class dispersion in the embedding space. Trained exclusively on image data, our experiments on CIFAR-10, CIFAR-100, ImageNet-100, and ImageNet-1K show that VarCon (1) achieves state-of-the-art performance for contrastive learning frameworks, reaching 79.36% Top-1 accuracy on ImageNet-1K and 78.29% on CIFAR-100 with a ResNet-50 encoder while converging in just 200 epochs; (2) yields substantially clearer decision boundaries and semantic organization in the embedding space, as evidenced by KNN classification, hierarchical clustering results, and transfer-learning assessments; and (3) demonstrates superior performance in few-shot learning than supervised baseline and superior robustness across various augmentation strategies. Our code is available at https://github.com/ziwenwang28/VarContrast.

This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating Individual Treatment Effects (ITEs) by capturing unobserved heterogeneity in treatment response driven by latent risk factors that affect only outcomes. CDVAE comes with theoretical guarantees on valid latent adjustment and generalization bounds for ITE error. Experiments on synthetic and real datasets show that CDVAE outperforms baselines, and that state-of-the-art models greatly improve when augmented with its latent substitutes, approaching oracle performance without access to true adjustment variables. The second contribution proposes an efficient framework for long-term counterfactual regression based on RNNs enhanced with Contrastive Predictive Coding (CPC) and InfoMax. It captures long-range dependencies under time-varying confounding while avoiding the computational cost of transformers, achieving state-of-the-art results and introducing CPC into causal inference. The third contribution advances CRL by addressing how latent causes manifest in observed variables. We introduce a model-agnostic interpretability layer based on the geometry of the decoder Jacobian. A sparse self-expression prior induces modular, possibly overlapping groups of observed features aligned with shared latent influences. We provide recovery guarantees in both disjoint and overlapping settings and show that meaningful latent-to-observed structure can be recovered without anchor features or single-parent assumptions. Scalable Jacobian-based regularization techniques are also developed.

Text clustering is a fundamental task in natural language processing, yet traditional clustering algorithms with pre-trained embeddings often struggle in domain-specific contexts without costly fine-tuning. Large language models (LLMs) provide strong contextual reasoning, yet prior work mainly uses them as auxiliary modules to refine embeddings or adjust cluster boundaries. We propose ClusterFusion, a hybrid framework that instead treats the LLM as the clustering core, guided by lightweight embedding methods. The framework proceeds in three stages: embedding-guided subset partition, LLM-driven topic summarization, and LLM-based topic assignment. This design enables direct incorporation of domain knowledge and user preferences, fully leveraging the contextual adaptability of LLMs. Experiments on three public benchmarks and two new domain-specific datasets demonstrate that ClusterFusion not only achieves state-of-the-art performance on standard tasks but also delivers substantial gains in specialized domains. To support future work, we release our newly constructed dataset and results on all benchmarks.

Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attacks is still not quite clear. In this paper, we investigate the adversarial learning from the perturbation analysis point of view. We characterize the robustness of learning models through the calmness of the solution mapping. In the case of convex clustering models, we identify the conditions under which the clustering results remain the same under perturbations. When the noise level is large, it leads to an attack. Therefore, we propose two bilevel models for adversarial learning where the effect of adversarial learning is measured by some deviation function. Specifically, we systematically study the so-called $δ$-measure and show that under certain conditions, it can be used as a deviation function in adversarial learning for convex clustering models. Finally, we conduct numerical tests to verify the above theoretical results as well as the efficiency of the two proposed bilevel models.

The Information Contrastive (I-Con) framework revealed that over 23 representation learning methods implicitly minimize KL divergence between data and learned distributions that encode similarities between data points. However, a KL-based loss may be misaligned with the true objective, and properties of KL divergence such as asymmetry and unboundedness may create optimization challenges. We present Beyond I-Con, a framework that enables systematic discovery of novel loss functions by exploring alternative statistical divergences. Key findings: (1) on unsupervised clustering of DINO-ViT embeddings, we achieve state-of-the-art results by modifying the PMI algorithm to use total variation (TV) distance; (2) supervised contrastive learning with Euclidean distance as the feature space metric is improved by replacing the standard loss function with Jenson-Shannon divergence (JSD); (3) on dimensionality reduction, we achieve superior qualitative results and better performance on downstream tasks than SNE by replacing KL with a bounded $f$-divergence. Our results highlight the importance of considering divergence choices in representation learning optimization.

Data science is a pillar of artificial intelligence (AI), which is transforming nearly every domain of human activity, from the social and physical sciences to engineering and medicine. While data-driven findings in AI offer unprecedented power to extract insights and guide decision-making, many are difficult or impossible to replicate. A key reason for this challenge is the uncertainty introduced by the many choices made throughout the data science life cycle (DSLC). Traditional statistical frameworks often fail to account for this uncertainty. The Predictability-Computability-Stability (PCS) framework for veridical (truthful) data science offers a principled approach to addressing this challenge throughout the DSLC. This paper presents an updated and streamlined PCS workflow, tailored for practitioners and enhanced with guided use of generative AI. We include a running example to display the PCS framework in action, and conduct a related case study which showcases the uncertainty in downstream predictions caused by judgment calls in the data cleaning stage.