Abstract--Graph clustering plays a pivotal role in unsupervised learning methods like spectral clustering, yet traditional methods for graph clustering often perpetuate bias through unfair graph constructions that may underrepresent some groups. The current research introduces novel approaches for constructing fair k-nearest neighbor (kNN) and fair ϵ-neighborhood graphs that proactively enforce demographic parity during graph formation. By incorporating fairness constraints at the earliest stage of neighborhood selection steps, our approaches incorporate proportional representation of sensitive features into the local graph structure while maintaining geometric consistency. Our work addresses a critical gap in pre-processing for fair spectral clustering, demonstrating that topological fairness in graph construction is essential for achieving equitable clustering outcomes. Widely used graph construction methods like kNN and ϵ-neighborhood graphs propagate edge based disparate impact on sensitive groups, leading to biased clustering results. Providing representation of each sensitive group in the neighborhood of every node leads to fairer spectral clustering results because the topological features of the graph naturally reflect equitable group ratios. This research fills an essential shortcoming in fair unsupervised learning, by illustrating how topological fairness in graph construction inherently facilitates fairer spectral clustering results without the need for changes to the clustering algorithm itself. Thorough experiments on three synthetic datasets, seven real-world tabular datasets, and three real-world image datasets prove that our fair graph construction methods surpass the current baselines in graph clustering tasks. Machine learning algorithms are widely used for decision-making in a variety of fields, including criminal justice [1], healthcare [2], [3], and finance [4]. The reason for this is that these algorithms have been shown to be very accurate and effective at analyzing big datasets. The increasing prevalence of these algorithms has raised questions regarding their fairness and potential to reinforce societal biases [5], [6]. These biases can result in unfair treatment of certain groups of people thereby create significant societal implications. Recently, concerns have been raised about the fairness of clusters produced by popular clustering algorithms.

Large Language Models (LLMs) are transforming language sciences. However, their widespread deployment currently suffers from methodological fragmentation and a lack of systematic soundness. This study proposes two comprehensive methodological frameworks designed to guide the strategic and responsible application of LLMs in language sciences. The first method-selection framework defines and systematizes three distinct, complementary approaches, each linked to a specific research goal: (1) prompt-based interaction with general-use models for exploratory analysis and hypothesis generation; (2) fine-tuning of open-source models for confirmatory, theory-driven investigation and high-quality data generation; and (3) extraction of contextualized embeddings for further quantitative analysis and probing of model internal mechanisms. We detail the technical implementation and inherent trade-offs of each method, supported by empirical case studies. Based on the method-selection framework, the second systematic framework proposed provides constructed configurations that guide the practical implementation of multi-stage research pipelines based on these approaches. We then conducted a series of empirical experiments to validate our proposed framework, employing retrospective analysis, prospective application, and an expert evaluation survey. By enforcing the strategic alignment of research questions with the appropriate LLM methodology, the frameworks enable a critical paradigm shift in language science research. We believe that this system is fundamental for ensuring reproducibility, facilitating the critical evaluation of LLM mechanisms, and providing the structure necessary to move traditional linguistics from ad-hoc utility to verifiable, robust science.

With the adoption of multiple digital devices in everyday life, the cyber-attack surface has increased. Adversaries are continuously exploring new avenues to exploit them and deploy malware. On the other hand, detection approaches typically employ hashing-based algorithms such as SSDeep, TLSH, and IMPHash to capture structural and behavioural similarities among binaries. This work focuses on the analysis and evaluation of these techniques for clustering malware samples using the K-means algorithm. More specifically, we experimented with established malware families and traits and found that TLSH and IMPHash produce more distinct, semantically meaningful clusters, whereas SSDeep is more efficient for broader classification tasks. The findings of this work can guide the development of more robust threat-detection mechanisms and adaptive security mechanisms.

Pretrained language models offer strong text understanding capabilities but remain difficult to deploy in real-world text-attributed networks due to their heavy dependence on labeled data. Meanwhile, community detection methods typically ignore textual semantics, limiting their usefulness in downstream applications such as content organization, recommendation, and risk monitoring. To overcome these limitations, we present Dual Refinement Cycle Learning (DRCL), a fully unsupervised framework designed for practical scenarios where no labels or category definitions are available. DRCL integrates structural and semantic information through a warm-start initialization and a bidirectional refinement cycle between a GCN-based Community Detection Module (GCN-CDM) and a Text Semantic Modeling Module (TSMM). The two modules iteratively exchange pseudo-labels, allowing semantic cues to enhance structural clustering and structural patterns to guide text representation learning without manual supervision. Across several text-attributed graph datasets, DRCL consistently improves the structural and semantic quality of discovered communities. Moreover, a Mamba-based classifier trained solely from DRCL's community signals achieves accuracy comparable to supervised models, demonstrating its potential for deployment in large-scale systems where labeled data are scarce or costly. The code is available at https://github.com/wuanghoong/DRCL.git.

Process discovery algorithms automatically extract process models from event logs, but high variability often results in complex and hard-to-understand models. To mitigate this issue, trace clustering techniques group process executions into clusters, each represented by a simpler and more understandable process model. Model-driven trace clustering improves on this by assigning traces to clusters based on their conformity to cluster-specific process models. However, most existing clustering techniques rely on either no process model discovery, or non-stochastic models, neglecting the frequency or probability of activities and transitions, thereby limiting their capability to capture real-world execution dynamics. We propose a novel model-driven trace clustering method that optimizes stochastic process models within each cluster. Our approach uses entropic relevance, a stochastic conformance metric based on directly-follows probabilities, to guide trace assignment. This allows clustering decisions to consider both structural alignment with a cluster's process model and the likelihood that a trace originates from a given stochastic process model. The method is computationally efficient, scales linearly with input size, and improves model interpretability by producing clusters with clearer control-flow patterns. Extensive experiments on public real-life datasets demonstrate that while our method yields superior stochastic coherence and graph simplicity, traditional fitness metrics reveal a trade-off, highlighting the specific utility of our approach for stochastic process analysis.

We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters are $\varepsilon$-far in total variation, the goal is to recover the partition. We establish upper and lower bounds on the sample complexity for two fundamental cases: (1) when one of the cluster's distributions is known, and (2) when both are unknown. Our upper and lower bounds characterize the sample complexity's dependence on the domain size $n$, number of distributions $k$, size $r$ of one of the clusters, and distance $\varepsilon$. In particular, we achieve tightness with respect to $(n,k,r,\varepsilon)$ (up to an $O(\log k)$ factor) for all regimes.

Federated Learning (FL) faces significant challenges in evolving environments, particularly regarding data heterogeneity and the rigidity of fixed network topologies. To address these issues, this paper proposes \textbf{SOFA-FL} (Self-Organizing Hierarchical Federated Learning with Adaptive Clustered Data Sharing), a novel framework that enables hierarchical federated systems to self-organize and adapt over time. The framework is built upon three core mechanisms: (1) \textbf{Dynamic Multi-branch Agglomerative Clustering (DMAC)}, which constructs an initial efficient hierarchical structure; (2) \textbf{Self-organizing Hierarchical Adaptive Propagation and Evolution (SHAPE)}, which allows the system to dynamically restructure its topology through atomic operations -- grafting, pruning, consolidation, and purification -- to adapt to changes in data distribution; and (3) \textbf{Adaptive Clustered Data Sharing}, which mitigates data heterogeneity by enabling controlled partial data exchange between clients and cluster nodes. By integrating these mechanisms, SOFA-FL effectively captures dynamic relationships among clients and enhances personalization capabilities without relying on predetermined cluster structures.

We propose an interpretable deep competing risks model called the Deep Kernel Aalen-Johansen (DKAJ) estimator, which generalizes the classical Aalen-Johansen nonparametric estimate of cumulative incidence functions (CIFs). Each data point (e.g., patient) is represented as a weighted combination of clusters. If a data point has nonzero weight only for one cluster, then its predicted CIFs correspond to those of the classical Aalen-Johansen estimator restricted to data points from that cluster. These weights come from an automatically learned kernel function that measures how similar any two data points are. On four standard competing risks datasets, we show that DKAJ is competitive with state-of-the-art baselines while being able to provide visualizations to assist model interpretation.

Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF (ONMF) variants further impose (approximate) orthogonality on the representation matrix so that its rows behave like soft cluster indicators. Existing algorithms, however, are typically derived from optimization viewpoints and do not explicitly exploit the conic geometry induced by NMF: data points lie in a convex cone whose extreme rays encode fundamental directions or "topics". In this work we revisit NMF from this geometric perspective and propose Cone Collapse, an algorithm that starts from the full nonnegative orthant and iteratively shrinks it toward the minimal cone generated by the data. We prove that, under mild assumptions on the data, Cone Collapse terminates in finitely many steps and recovers the minimal generating cone of $\mathbf{X}^\top$ . Building on this basis, we then derive a cone-aware orthogonal NMF model (CC-NMF) by applying uni-orthogonal NMF to the recovered extreme rays. Across 16 benchmark gene-expression, text, and image datasets, CC-NMF consistently matches or outperforms strong NMF baselines-including multiplicative updates, ANLS, projective NMF, ONMF, and sparse NMF-in terms of clustering purity. These results demonstrate that explicitly recovering the data cone can yield both theoretically grounded and empirically strong NMF-based clustering methods.

Agglomerative hierarchical clustering is one of the most widely used approaches for exploring how observations in a dataset relate to each other. However, its greedy nature makes it highly sensitive to small perturbations in the data, often producing different clustering results and making it difficult to separate genuine structure from spurious patterns. In this paper, we show how randomizing hierarchical clustering can be useful not just for measuring stability but also for designing valid hypothesis testing procedures based on the clustering results. We propose a simple randomization scheme together with a method for constructing a valid p-value at each node of the hierarchical clustering dendrogram that quantifies evidence against performing the greedy merge. Our test controls the Type I error rate, works with any hierarchical linkage without case-specific derivations, and simulations show it is substantially more powerful than existing selective inference approaches. To demonstrate the practical utility of our p-values, we develop an adaptive $α$-spending procedure that estimates the number of clusters, with a probabilistic guarantee on overestimation. Experiments on simulated and real data show that this estimate yields powerful clustering and can be used, for example, to assess clustering stability across multiple runs of the randomized algorithm.