Hegselmann--Krause models are localized, distributed averaging dynamics on spatial data. A key aspect of these dynamics is that they lead to cluster formation, which has important applications in geographic information systems, dynamic clustering algorithms, opinion dynamics, and social networks. For these models, the key questions are whether a fixed point exists and, if so, characterizing it. In this work, we establish new results towards the "2R-Conjecture" for the Hegselmann--Krause model, for which no meaningful progress, or even any precise statement, has been made since its introduction in 2007. This conjecture relates to the structure of the fixed point when there are a large number of agents per unit space. We provide, among other results, a proof in expectation and a statement of a stronger result that is supported by simulation. The key methodological contribution is to consider the dynamics as an infinite-dimensional problem on the space of point processes, rather than on finitely many points. This enables us to leverage stationarity, shift invariance, and certain other symmetries to obtain the results. These techniques do not have finite-dimensional analogs.

Recent advances in machine learning have greatly expanded the repertoire of predictive methods for medical imaging. However, the interpretability of complex models remains a challenge, which limits their utility in medical applications. Recently, model-agnostic methods have been proposed to measure conditional variable importance and accommodate complex non-linear models. However, they often lack power when dealing with highly correlated data, a common problem in medical imaging. We introduce Hierarchical-CPI, a model-agnostic variable importance measure that frames the inference problem as the discovery of groups of variables that are jointly predictive of the outcome. By exploring subgroups along a hierarchical tree, it remains computationally tractable, yet also enjoys explicit family-wise error rate control. Moreover, we address the issue of vanishing conditional importance under high correlation with a tree-based importance allocation mechanism. We benchmarked Hierarchical-CPI against state-of-the-art variable importance methods. Its effectiveness is demonstrated in two neuroimaging datasets: classifying dementia diagnoses from MRI data (ADNI dataset) and analyzing the Berger effect on EEG data (TDBRAIN dataset), identifying biologically plausible variables.

Knowledge management (KM) is vital in the process industry for optimizing operations, ensuring safety, and enabling continuous improvement through effective use of operational data and past insights. A key challenge in this domain is the fragmented nature of event logs in shift books, where related records, e.g., entries documenting issues related to equipment or processes and the corresponding solutions, may remain disconnected. This fragmentation hinders the recommendation of previous solutions to the users. To address this problem, we investigate record linking (RL) as link prediction, commonly studied in graph-based machine learning, by framing it as a cross-document coreference resolution (CDCR) task enhanced with natural language inference (NLI) and semantic text similarity (STS) by shifting it into the causal inference (CI). We adapt CDCR, traditionally applied in the news domain, into an RL model to operate at the passage level, similar to NLI and STS, while accommodating the process industry's specific text formats, which contain unstructured text and structured record attributes. Our RL model outperformed the best versions of NLI- and STS-driven baselines by 28% (11.43 points) and 27% (11.21 points), respectively. Our work demonstrates how domain adaptation of the state-of-the-art CDCR models, enhanced with reasoning capabilities, can be effectively tailored to the process industry, improving data quality and connectivity in shift logs.

To improve the reading experience, many news sites organize news into topical collections, called stories. In this work, we present an approach for implementing real-time story identification for a news monitoring system that automatically collects news articles as they appear online and processes them in various ways. Story identification aims to assign each news article to a specific story that the article is covering. The process is similar to text clustering and topic modeling, but requires that articles be grouped based on particular events, places, and people, rather than general text similarity (as in clustering) or general (predefined) topics (as in topic modeling). We present an approach to story identification that is capable of functioning in real time, assigning articles to stories as they are published online. In the proposed approach, we combine text representation techniques, clustering algorithms, and online topic modeling methods. We combine various text representation methods to extract specific events and named entities necessary for story identification, showing that a mixture of online topic-modeling approaches such as BERTopic, DBStream, and TextClust can be adapted for story discovery. We evaluate our approach on a news dataset from Slovene media covering a period of 1 month. We show that our real-time approach produces sensible results as judged by human evaluators.

Clustering algorithms play a pivotal role in unsupervised learning by identifying and grouping similar objects based on shared characteristics. Although traditional clustering techniques, such as hard and fuzzy center-based clustering, have been widely used, they struggle with complex, high-dimensional, and non-Euclidean datasets. In particular, the fuzzy $C$-Means (FCM) algorithm, despite its efficiency and popularity, exhibits notable limitations in non-Euclidean spaces. Euclidean spaces assume linear separability and uniform distance scaling, limiting their effectiveness in capturing complex, hierarchical, or non-Euclidean structures in fuzzy clustering. To overcome these challenges, we introduce Filtration-based Hyperbolic Fuzzy C-Means (HypeFCM), a novel clustering algorithm tailored for better representation of data relationships in non-Euclidean spaces. HypeFCM integrates the principles of fuzzy clustering with hyperbolic geometry and employs a weight-based filtering mechanism to improve performance. The algorithm initializes weights using a Dirichlet distribution and iteratively refines cluster centroids and membership assignments based on a hyperbolic metric in the Poincaré Disc model. Extensive experimental evaluations on $6$ synthetic and $12$ real-world datasets demonstrate that HypeFCM significantly outperforms conventional fuzzy clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.

Developers insert logging statements in source code to capture relevant runtime information essential for maintenance and debugging activities. Log level choice is an integral, yet tricky part of the logging activity as it controls log verbosity and therefore influences systems' observability and performance. Recent advances in ML-based log level prediction have leveraged large language models (LLMs) to propose log level predictors (LLPs) that demonstrated promising performance improvements (AUC between 0.64 and 0.8). Nevertheless, current LLM-based LLPs rely on randomly selected in-context examples, overlooking the structure and the diverse logging practices within modern software projects. In this paper, we propose OmniLLP, a novel LLP enhancement framework that clusters source files based on (1) semantic similarity reflecting the code's functional purpose, and (2) developer ownership cohesion. By retrieving in-context learning examples exclusively from these semantic and ownership aware clusters, we aim to provide more coherent prompts to LLPs leveraging LLMs, thereby improving their predictive accuracy. Our results show that both semantic and ownership-aware clusterings statistically significantly improve the accuracy (by up to 8\% AUC) of the evaluated LLM-based LLPs compared to random predictors (i.e., leveraging randomly selected in-context examples from the whole project). Additionally, our approach that combines the semantic and ownership signal for in-context prediction achieves an impressive 0.88 to 0.96 AUC across our evaluated projects. Our findings highlight the value of integrating software engineering-specific context, such as code semantic and developer ownership signals into LLM-LLPs, offering developers a more accurate, contextually-aware approach to logging and therefore, enhancing system maintainability and observability.

Clustering large data is a fundamental problem with a vast number of applications. Due to the increasing size of data, practitioners interested in clustering have turned to distributed computation methods. In this work, we consider the widely used k-center clustering problem and its variant used to handle noisy data, k-center with outliers. In the noise-free setting we demonstrate how a previously-proposed distributed method is actually an O(1)-approximation algorithm, which accurately explains its strong empirical performance. Additionally, in the noisy setting, we develop a novel distributed algorithm that is also an O(1)-approximation. These algorithms are highly parallel and lend themselves to virtually any distributed computing framework. We compare both empirically against the best known noisy sequential clustering methods and show that both distributed algorithms are consistently close to their sequential versions. The algorithms are all one can hope for in distributed settings: they are fast, memory efficient and they match their sequential counterparts.

Clustering algorithms often assume all features contribute equally to the data structure, an assumption that usually fails in high-dimensional or noisy settings. Feature weighting methods can address this, but most require additional parameter tuning. We propose SHARK (Shapley Reweighted $k$-means), a feature-weighted clustering algorithm motivated by the use of Shapley values from cooperative game theory to quantify feature relevance, which requires no additional parameters beyond those in $k$-means. We prove that the $k$-means objective can be decomposed into a sum of per-feature Shapley values, providing an axiomatic foundation for unsupervised feature relevance and reducing Shapley computation from exponential to polynomial time. SHARK iteratively re-weights features by the inverse of their Shapley contribution, emphasising informative dimensions and down-weighting irrelevant ones. Experiments on synthetic and real-world data sets show that SHARK consistently matches or outperforms existing methods, achieving superior robustness and accuracy, particularly in scenarios where noise may be present. Software: https://github.com/rickfawley/shark.

Modern software systems are increasingly shifting from monolithic architectures to microservices to enhance scalability, maintainability, and deployment flexibility. Existing microservice extraction methods typically rely on hard clustering, assigning each software component to a single microservice. This approach often increases inter-service coupling and reduces intra-service cohesion. We propose Mo2oM (Monolithic to Overlapping Microservices), a framework that formulates microservice extraction as a soft clustering problem, allowing components to belong probabilistically to multiple microservices. This approach is inspired by expert-driven decompositions, where practitioners intentionally replicate certain software components across services to reduce communication overhead. Mo2oM combines deep semantic embeddings with structural dependencies extracted from methodcall graphs to capture both functional and architectural relationships. A graph neural network-based soft clustering algorithm then generates the final set of microservices. We evaluate Mo2oM on four open-source monolithic benchmarks and compare it against eight state-of-the-art baselines. Our results demonstrate that Mo2oM achieves improvements of up to 40.97% in structural modularity (balancing cohesion and coupling), 58% in inter-service call percentage (communication overhead), 26.16% in interface number (modularity and decoupling), and 38.96% in non-extreme distribution (service size balance) across all benchmarks.

We propose a novel segmentation-based explainable artificial intelligence (XAI) method for neural networks working on point cloud classification. As one building block of this method, we propose a novel point-shifting mechanism to introduce perturbations in point cloud data. Recently, AI has seen an exponential growth. Hence, it is important to understand the decision-making process of AI algorithms when they are applied in critical areas. Our work focuses on explaining AI algorithms that classify point cloud data. An important aspect of the methods used for explaining AI algorithms is their ability to produce explanations that are easy for humans to understand. This allows them to analyze the AI algorithms better and make appropriate decisions based on that analysis. Therefore, in this work, we intend to generate meaningful explanations that can be easily interpreted by humans. The point cloud data we consider represents 3D objects such as cars, guitars, and laptops. We make use of point cloud segmentation models to generate explanations for the working of classification models. The segments are used to introduce perturbations into the input point cloud data and generate saliency maps. The perturbations are introduced using the novel point-shifting mechanism proposed in this work which ensures that the shifted points no longer influence the output of the classification algorithm. In contrast to previous methods, the segments used by our method are meaningful, i.e. humans can easily interpret the meaning of the segments. Thus, the benefit of our method over other methods is its ability to produce more meaningful saliency maps. We compare our method with the use of classical clustering algorithms to generate explanations. We also analyze the saliency maps generated for example inputs using our method to demonstrate the usefulness of the method in generating meaningful explanations.