We introduce and address a novel distributed clustering problem where each participant has a private dataset containing only a subset of all available features, and some features are included in multiple datasets. This scenario occurs in many real-world applications, such as in healthcare, where different institutions have complementary data on similar patients. We propose two different algorithms suitable for solving distributed clustering problems that exhibit this type of feature space heterogeneity. The first is a federated algorithm in which participants collaboratively update a set of global centroids. The second is a one-shot algorithm in which participants share a statistical parametrization of their local clusters with the central server, who generates and merges synthetic proxy datasets. In both cases, participants perform local clustering using algorithms of their choice, which provides flexibility and personalized computational costs. Pretending that local datasets result from splitting and masking an initial centralized dataset, we identify some conditions under which the proposed algorithms are expected to converge to the optimal centralized solution. Finally, we test the practical performance of the algorithms on three public datasets.

Robotic Process Mining focuses on the identification of the routine types performed by human resources through a User Interface. The ultimate goal is to discover routine-type models to enable robotic process automation. The discovery of routine-type models requires the provision of a routine log. Unfortunately, the vast majority of existing works do not directly focus on enabling the model discovery, limiting themselves to extracting the set of actions that are part of the routines. They were also not evaluated in scenarios characterized by inconsistent routine execution, hereafter referred to as noise, which reflects natural variability and occasional errors in human performance. This paper presents a clustering-based technique that aims to extract routine logs. Experiments were conducted on nine UI logs from the literature with different levels of injected noise. Our technique was compared with existing techniques, most of which are not meant to discover routine logs but were adapted for the purpose. The results were evaluated through standard state-of-the-art metrics, showing that we can extract more accurate routine logs than what the state of the art could, especially in the presence of noise.

This paper introduces torchsom, an open-source Python library that provides a reference implementation of the Self-Organizing Map (SOM) in PyTorch. This package offers three main features: (i) dimensionality reduction, (ii) clustering, and (iii) friendly data visualization. It relies on a PyTorch backend, enabling (i) fast and efficient training of SOMs through GPU acceleration, and (ii) easy and scalable integrations with PyTorch ecosystem. Moreover, torchsom follows the scikit-learn API for ease of use and extensibility.

Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be performed to generate the clustering result after the procedure of feature extraction. More importantly, the connectivity of samples reflected by the clustering result is not utilized effectively. To overcome these defects, we propose Clustering Result re-Guided Incomplete Multi-view Spectral Clustering (CRG_IMSC). CRG_IMSC obtains the clustering result directly by imposing nonnegative constraint to the extracted feature. Furthermore, it constructs the connectivity matrix according to the result of spectral clustering, and minimizes the residual of self-representation based on the connectivity matrix. A novel iterative algorithm using multiplicative update is developed to solve the optimization problem of CRG_IMSC, and its convergence is proved rigorously. On benchmark datasets, for multi-view data, CRG_IMSC performs better than state-of-the-art clustering methods, and the experimental results also demonstrate the convergence of CRG_IMSC algorithm.

Dynamical systems in the life sciences are often composed of complex mixtures of overlapping behavioral regimes. Cellular subpopulations may shift from cycling to equilibrium dynamics or branch towards different developmental fates. The transitions between these regimes can appear noisy and irregular, posing a serious challenge to traditional, flow-based modeling techniques which assume locally smooth dynamics. To address this challenge, we propose MODE (Mixture Of Dynamical Experts), a graphical modeling framework whose neural gating mechanism decomposes complex dynamics into sparse, interpretable components, enabling both the unsupervised discovery of behavioral regimes and accurate long-term forecasting across regime transitions. Crucially, because agents in our framework can jump to different governing laws, MODE is especially tailored to the aforementioned noisy transitions. We evaluate our method on a battery of synthetic and real datasets from computational biology. First, we systematically benchmark MODE on an unsupervised classification task using synthetic dynamical snapshot data, including in noisy, few-sample settings. Next, we show how MODE succeeds on challenging forecasting tasks which simulate key cycling and branching processes in cell biology. Finally, we deploy our method on human, single-cell RNA sequencing data and show that it can not only distinguish proliferation from differentiation dynamics but also predict when cells will commit to their ultimate fate, a key outstanding challenge in computational biology.

We introduce ClustRecNet - a novel deep learning (DL)-based recommendation framework for determining the most suitable clustering algorithms for a given dataset, addressing the long-standing challenge of clustering algorithm selection in unsupervised learning. To enable supervised learning in this context, we construct a comprehensive data repository comprising 34,000 synthetic datasets with diverse structural properties. Each of them was processed using 10 popular clustering algorithms. The resulting clusterings were assessed via the Adjusted Rand Index (ARI) to establish ground truth labels, used for training and evaluation of our DL model. The proposed network architecture integrates convolutional, residual, and attention mechanisms to capture both local and global structural patterns from the input data. This design supports end-to-end training to learn compact representations of datasets and enables direct recommendation of the most suitable clustering algorithm, reducing reliance on handcrafted meta-features and traditional Cluster Validity Indices (CVIs). Comprehensive experiments across synthetic and real-world benchmarks demonstrate that our DL model consistently outperforms conventional CVIs (e.g. Silhouette, Calinski-Harabasz, Davies-Bouldin, and Dunn) as well as state-of-the-art AutoML clustering recommendation approaches (e.g. ML2DAC, AutoCluster, and AutoML4Clust). Notably, the proposed model achieves a 0.497 ARI improvement over the Calinski-Harabasz index on synthetic data and a 15.3% ARI gain over the best-performing AutoML approach on real-world data.

Accurate recognition and re-identification of individual animals is essential for successful wildlife population monitoring. Traditional methods, such as leg banding of birds, are time consuming and invasive. Recent progress in artificial intelligence, particularly computer vision, offers encouraging solutions for smart conservation and efficient automation. This study presents a unique pipeline for extracting high-quality key frames from videos of kākā (Nestor meridionalis), a threatened forest-dwelling parrot in New Zealand. Key frame extraction is well-studied in person re-identification, however, its application to wildlife is limited. Using video recordings at a custom-built feeder, we extract key frames and evaluate the re-identification performance of our pipeline. Our unsupervised methodology combines object detection using YOLO and Grounding DINO, optical flow blur detection, image encoding with DINOv2, and clustering methods to identify representative key frames. The results indicate that our proposed key frame selection methods yield image collections which achieve high accuracy in kākā re-identification, providing a foundation for future research using media collected in more diverse and challenging environments. Through the use of artificial intelligence and computer vision, our non-invasive and efficient approach provides a valuable alternative to traditional physical tagging methods for recognising kākā individuals and therefore improving the monitoring of populations. This research contributes to developing fresh approaches in wildlife monitoring, with applications in ecology and conservation biology.

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

A central question in artificial intelligence is the extent to which machine learning models comprehend mathematics. To address this, we propose a novel framework for measuring mathematical reasoning that moves beyond standard benchmarks to diagnose specific failure points. Our method first generates structured, step-by-step reasoning from gpt-3.5-turbo on the GSM8K dataset. We then use a more capable analyst model, gpt-4o-mini, to categorize errors and, crucially, perform an unsupervised clustering of every reasoning sentence to identify emergent "reasoning modes." This analysis reveals a cognitive profile with a stark, nonhuman-like brittleness: while the model achieves near-perfect accuracy on procedural modes like sequential calculation, its performance on modes requiring combinatorial reasoning with restrictions plummets. By identifying and quantifying the reliability of these distinct reasoning skills, our work provides a more granular method to evaluate mathematical comprehension and offers a precise roadmap for developing new capabilities and more reliable future applications.

Large Language Models (LLMs) have demonstrated impressive capabilities across various tasks, but fine-tuning them for domain-specific applications often requires substantial domain-specific data that may be distributed across multiple organizations. Federated Learning (FL) offers a privacy-preserving solution, but faces challenges with computational constraints when applied to LLMs. Low-Rank Adaptation (LoRA) has emerged as a parameter-efficient fine-tuning approach, though a single LoRA module often struggles with heterogeneous data across diverse domains. This paper addresses two critical challenges in federated LoRA fine-tuning: 1. determining the optimal number and allocation of LoRA experts across heterogeneous clients, and 2. enabling clients to selectively utilize these experts based on their specific data characteristics. We propose FedLEASE (Federated adaptive LoRA Expert Allocation and SElection), a novel framework that adaptively clusters clients based on representation similarity to allocate and train domain-specific LoRA experts. It also introduces an adaptive top-$M$ Mixture-of-Experts mechanism that allows each client to select the optimal number of utilized experts. Our extensive experiments on diverse benchmark datasets demonstrate that FedLEASE significantly outperforms existing federated fine-tuning approaches in heterogeneous client settings while maintaining communication efficiency.