Traditional approaches based on quantum mechanical computations or empirical models are often limited in scalability and accuracy. In recent years, machine learning (ML) has emerged as a promising alternative for property prediction across materials science domains [1-9]. Building on this momentum, several recent studies have proposed the use of ML models trained on curated magnetic datasets. In particular, the recent study [10] introduced the NE-MAD database, which aggregates experimentally measured magnetic transition temperatures and compositions. Similarly, the study by [11] utilized two of the largest available datasets of experimental Curie temperatures--comprising over 2,500 materials for training and more than 3,000 entries for validation--to compare machine learning strategies for predicting Curie temperature solely from chemical composition. Our work is inspired by these prior efforts and aims to improve the predictive accuracy and gain insights into model in-terpretability. We develop a pipeline that starts from the NE-MAD dataset, augments it with compositional and elemental features, and evaluates several ML models. A key contribution of our work is the integration of explainable AI (XAI) through SHAP (SHapley Additive exPlanations) analysis, which allows us to quantify how each input feature contributes to the model's prediction. Moreover, we benchmark our models on external datasets from literature to demonstrate generalization.

In this growing age of data and technology, large black-box models are becoming the norm due to their ability to handle vast amounts of data and learn incredibly complex input-output relationships. The deficiency of these methods, however, is their inability to explain the prediction process, making them untrustworthy and their use precarious in high-stakes situations. SHapley Additive exPlanations (SHAP) analysis is an explainable AI method growing in popularity for its ability to explain model predictions in terms of the original features. For each sample and feature in the data set, we associate a SHAP value that quantifies the contribution of that feature to the prediction of that sample. Clustering these SHAP values can provide insight into the data by grouping samples that not only received the same prediction, but received the same prediction for similar reasons. In doing so, we map the various pathways through which distinct samples arrive at the same prediction. To showcase this methodology, we present a simulated experiment in addition to a case study in Alzheimer's disease using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We also present a novel generalization of the waterfall plot for multi-classification.

Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time dependence structures for multivariate data of mixed kind. We introduce the Mixture of Mixed-Matrices (MMM) model: reorganizing the data in a three-way structure and assuming that the non-continuous variables are observations of underlying latent continuous variables, the model relies on a mixture of matrix-variate normal distributions to perform clustering in the latent dimension. The MMM model is thus able to handle continuous, ordinal, binary, nominal and count data and to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure in a parsimonious way and without assuming conditional independence. The inference is carried out through an MCMC-EM algorithm, which is detailed. An evaluation of the model through synthetic data shows its inference abilities. A real-world application on financial data is presented.

The flexibility of a power generation unit determines how quickly and often it can ramp up or down. In energy models, it depends on assumptions on the technical characteristics of the unit, such as its installed capacity or turbine technology. In this paper, we learn the empirical flexibility of gas units from their electricity generation, revealing how real-world limitations can lead to substantial differences between units with similar technical characteristics. Using a novel deep clustering approach, we transform 5 years (2019-2023) of unit-level hourly generation data for 49 German units from 100 MWp of installed capacity into low-dimensional embeddings. Our unsupervised approach identifies two clusters of peaker units (high flexibility) and two clusters of non-peaker units (low flexibility). The estimated ramp rates of non-peakers, which constitute half of the sample, display a low empirical flexibility, comparable to coal units. Non-peakers, predominantly owned by industry and municipal utilities, show limited response to low residual load and negative prices, generating on average 1.3 GWh during those hours. As the transition to renewables increases market variability, regulatory changes will be needed to unlock this flexibility potential.

Clustering patient subgroups is essential for personalized care and efficient resource use. Traditional clustering methods struggle with high-dimensional, heterogeneous healthcare data and lack contextual understanding. This study evaluates Large Language Model (LLM) based clustering against classical methods using a pediatric sepsis dataset from a low-income country (LIC), containing 2,686 records with 28 numerical and 119 categorical variables. Patient records were serialized into text with and without a clustering objective. Embeddings were generated using quantized LLAMA 3.1 8B, DeepSeek-R1-Distill-Llama-8B with low-rank adaptation(LoRA), and Stella-En-400M-V5 models. K-means clustering was applied to these embeddings. Classical comparisons included K-Medoids clustering on UMAP and FAMD-reduced mixed data. Silhouette scores and statistical tests evaluated cluster quality and distinctiveness. Stella-En-400M-V5 achieved the highest Silhouette Score (0.86). LLAMA 3.1 8B with the clustering objective performed better with higher number of clusters, identifying subgroups with distinct nutritional, clinical, and socioeconomic profiles. LLM-based methods outperformed classical techniques by capturing richer context and prioritizing key features. These results highlight potential of LLMs for contextual phenotyping and informed decision-making in resource-limited settings.

We consider generating post-hoc explanations of clusters generated from various datasets using auxiliary information which was not used by clustering algorithms. Following terminology used in previous work, we refer to the auxiliary information as tags. Our focus is on two forms of explanations, namely disjunctive form (where the explanation for a cluster consists of a set of tags) and a two-clause conjunctive normal form (CNF) explanation (where the explanation consists of two sets of tags, combined through the AND operator). We use integer linear programming (ILP) as well as heuristic methods to generate these explanations. We experiment with a variety of datasets and discuss the insights obtained from our explanations. We also present experimental results regarding the scalability of our explanation methods.

Co-clustering exploits the duality of instances and features to simultaneously uncover meaningful groups in both dimensions, often outperforming traditional clustering in high-dimensional or sparse data settings. Although recent deep learning approaches successfully integrate feature learning and cluster assignment, they remain susceptible to noise and can suffer from posterior collapse within standard autoencoders. In this paper, we present the first fully variational Co-clustering framework that directly learns row and column clusters in the latent space, leveraging a doubly reparameterized ELBO to improve gradient signal-to-noise separation. Our unsupervised model integrates a Variational Deep Embedding with a Gaussian Mixture Model (GMM) prior for both instances and features, providing a built-in clustering mechanism that naturally aligns latent modes with row and column clusters. Furthermore, our regularized end-to-end noise learning Compositional ELBO architecture jointly reconstructs the data while regularizing against noise through the KL divergence, thus gracefully handling corrupted or missing inputs in a single training pipeline. To counteract posterior collapse, we introduce a scale modification that increases the encoder's latent means only in the reconstruction pathway, preserving richer latent representations without inflating the KL term. Finally, a mutual information-based cross-loss ensures coherent co-clustering of rows and columns. Empirical results on diverse real-world datasets from multiple modalities, numerical, textual, and image-based, demonstrate that our method not only preserves the advantages of prior Co-clustering approaches but also exceeds them in accuracy and robustness, particularly in high-dimensional or noisy settings.

Public transportation is a major source of greenhouse gas emissions, highlighting the need to improve bus fuel efficiency. Clustering algorithms assist in analyzing fuel efficiency by grouping data into clusters, but irrelevant features may complicate the analysis and choosing the optimal number of clusters remains a challenging task. Therefore, this paper employs the Gaussian mixture models to cluster the solo fuel-efficiency dataset. Moreover, an integration method that combines the Silhouette index, Calinski-Harabasz index, and Davies-Bouldin index is developed to select the optimal cluster numbers. A dataset with 4006 bus trips in North Jutland, Denmark is utilized as the case study. Trips are first split into three groups, then one group is divided further, resulting in four categories: extreme, normal, low, and extremely low fuel efficiency. A preliminary study using visualization analysis is conducted to investigate how driving behaviors and route conditions affect fuel efficiency. The results indicate that both individual driving habits and route characteristics have a significant influence on fuel efficiency.

Multi-objective reinforcement learning (MORL) is used to solve problems involving multiple objectives. An MORL agent must make decisions based on the diverse signals provided by distinct reward functions. Training an MORL agent yields a set of solutions (policies), each presenting distinct trade-offs among the objectives (expected returns). MORL enhances explainability by enabling fine-grained comparisons of policies in the solution set based on their trade-offs as opposed to having a single policy. However, the solution set is typically large and multi-dimensional, where each policy (e.g., a neural network) is represented by its objective values. We propose an approach for clustering the solution set generated by MORL. By considering both policy behavior and objective values, our clustering method can reveal the relationship between policy behaviors and regions in the objective space. This approach can enable decision makers (DMs) to identify overarching trends and insights in the solution set rather than examining each policy individually. We tested our method in four multi-objective environments and found it outperformed traditional k-medoids clustering. Additionally, we include a case study that demonstrates its real-world application.

Structure in the data distribution has long been recognized as central to the development of internal structure in artificial and biological neural networks (Rumelhart et al., 1986; Olshausen & Field, 1996; Rogers & McClelland, 2004). Recent observations have renewed interest in this topic: language models progress through distinct stages of development during training, acquiring increasingly sophisticated linguistic and reasoning abilities in ways that seem to reflect the structure of the data distribution (Olsson et al., 2022; Chen et al., 2024; Belrose et al., 2024; Tigges et al., 2024; Edelman et al., 2024; Hoogland et al., 2024). A deeper understanding of how structure in the data determines internal structure in trained models requires tools that provide information about which components of a model are being shaped in response to what structure in the data distribution. Our foundation for the study of such questions begins with the local learning coefficient (LLC; Lau et al. 2023) from singular learning theory (SLT; Watanabe 2009), which is a measure of model complexity. In this paper, we introduce the refined local learning coefficient (rLLC), which measures the complexity of a component of the model with respect to an arbitrary data distribution. We focus mainly on the rLLCs of individual attention heads and demonstrate the utility of these metrics in studying the progressive differentiation and specialization of heads. The diversity of attention heads at the end of training has been established in recent years through mechanistic interpretability, which has provided numerous examples of attention heads that appear to have specialized functions, including previous-token heads (Voita et al., 2019; Clark et al., 2019) and induction heads (Olsson et al., 2022) among other kinds (Wang et al., 2023; Gould et al., 2024).