We introduce and investigate the iterated application of Generalized Matrix Learning Vector Quantizaton for the analysis of feature relevances in classification problems, as well as for the construction of class-discriminative subspaces. The suggested Iterated Relevance Matrix Analysis (IRMA) identifies a linear subspace representing the classification specific information of the considered data sets using Generalized Matrix Learning Vector Quantization (GMLVQ). By iteratively determining a new discriminative subspace while projecting out all previously identified ones, a combined subspace carrying all class-specific information can be found. This facilitates a detailed analysis of feature relevances, and enables improved low-dimensional representations and visualizations of labeled data sets. Additionally, the IRMA-based class-discriminative subspace can be used for dimensionality reduction and the training of robust classifiers with potentially improved performance.

In machine learning, data often comes from different sources, but combining them can introduce extraneous variation that affects both generalization and interpretability. For example, we investigate the classification of neurodegenerative diseases using FDG-PET data collected from multiple neuroimaging centers. However, data collected at different centers introduces unwanted variation due to differences in scanners, scanning protocols, and processing methods. To address this issue, we propose a two-step approach to limit the influence of center-dependent variation on the classification of healthy controls and early vs. late-stage Parkinson’s disease patients. First, we train a Generalized Matrix Learning Vector Quantization (GMLVQ) model on healthy control data to identify a “relevance space” that distinguishes between centers. Second, we use this space to construct a correction matrix that restricts a second GMLVQ system’s training on the diagnostic problem. We evaluate the effectiveness of this approach on the real-world multi-center datasets and simulated artificial dataset. Our results demonstrate that the approach produces machine learning systems with reduced bias - being more specific due to eliminating information related to center differences during the training process - and more informative relevance profiles that can be interpreted by medical experts. This method can be adapted to similar problems outside the neuroimaging domain, as long as an appropriate “relevance space” can be identified to construct the correction matrix.

The debris from past merger events is expected and, to some extent, known to populate the stellar halo near the Sun. We aim to identify and characterise such merger debris using Gaia DR3 data supplemented by metallicity and chemical abundance information from LAMOST LRS and APOGEE for halo stars within 2.5 kpc from the Sun. We utilise a single linkage-based clustering algorithm to identify over-densities in Integrals of Motion space that could be due to merger debris. Combined with metallicity information and chemical abundances, we characterise these statistically significant over-densities. We find that the local stellar halo contains 7 main dynamical groups, some of in-situ and some of accreted origin, most of which are already known. We report the discovery of a new substructure, which we name ED-1. In addition, we find evidence for 11 independent smaller clumps, 5 of which are new: ED-2, 3, 4, 5 and 6 are typically rather tight dynamically, depict a small range of metallicities, and their abundances when available, as well as their location in Integrals of Motion space, suggest an accreted origin. The local halo contains an important amount of substructure, of both in-situ and accreted origin.

Context.Merger debris is expected to populate the stellar haloes of galaxies. In the case of the Milky Way, this debris should be apparent as clumps in a space defined by the orbital integrals of motion of the stars.Aims.Our aim is to develop a data-driven and statistics-based method for finding these clumps in integrals-of-motion space for nearby halo stars and to evaluate their significance robustly.Methods.We used data fromGaiaEDR3, extended with radial velocities from ground-based spectroscopic surveys, to construct a sample of halo stars within 2.5 kpc from the Sun. We applied a hierarchical clustering method that makes exhaustive use of the single linkage algorithm in three-dimensional space defined by the commonly used integrals of motion energyE, together with two components of the angular momentum,LzandL⊥. To evaluate the statistical significance of the clusters, we compared the density within an ellipsoidal region centred on the cluster to that of random sets with similar global dynamical properties. By selecting the signal at the location of their maximum statistical significance in the hierarchical tree, we extracted a set of significant unique clusters. By describing these clusters with ellipsoids, we estimated the proximity of a star to the cluster centre using the Mahalanobis distance. Additionally, we applied the HDBSCAN clustering algorithm in velocity space to each cluster to extract subgroups representing debris with different orbital phases.Results.Our procedure identifies 67 highly significant clusters (> 3σ), containing 12% of the sources in our halo set, and 232 subgroups or individual streams in velocity space. In total, 13.8% of the stars in our data set can be confidently associated with a significant cluster based on their Mahalanobis distance. Inspection of the hierarchical tree describing our data set reveals a complex web of relations between the significant clusters, suggesting that they can be tentatively grouped into at least six main large structures, many of which can be associated with previously identified halo substructures, and a number of independent substructures. This preliminary conclusion is further explored in a companion paper, in which we also characterise the substructures in terms of their stellar populations.Conclusions.Our method allows us to systematically detect kinematic substructures in the Galactic stellar halo with a data-driven and interpretable algorithm. The list of the clusters and the associated star catalogue are provided in two tables available at the CDS.

PURPOSE Staying injury free is a major factor for success in sports. Although injuries are difficult to forecast, novel technologies and data-science applications could provide important insights. Our purpose was to use machine learning for the prediction of injuries in runners, based on detailed training logs. METHODS Prediction of injuries was evaluated on a new data set of 74 high-level middle- and long-distance runners, over a period of 7 years. Two analytic approaches were applied. First, the training load from the previous 7 days was expressed as a time series, with each day's training being described by 10 features. These features were a combination of objective data from a global positioning system watch (eg, duration, distance), together with subjective data about the exertion and success of the training. Second, a training week was summarized by 22 aggregate features, and a time window of 3 weeks before the injury was considered. RESULTS A predictive system based on bagged XGBoost machine-learning models resulted in receiver operating characteristic curves with average areas under the curves of 0.724 and 0.678 for the day and week approaches, respectively. The results of the day approach especially reflect a reasonably high probability that our system makes correct injury predictions. CONCLUSIONS Our machine-learning-based approach predicts a sizable portion of the injuries, in particular when the model is based on training-load data in the days preceding an injury. Overall, these results demonstrate the possible merits of using machine learning to predict injuries and tailor training programs for athletes.