Abstract--Principal Component Analysis (PCA) and K-means constitute fundamental techniques in multivariate analysis. Although they are frequently applied independently or sequentially to cluster observations, the relationship between them, especially when K-means is used to cluster variables rather than observations, has been scarcely explored. This study seeks to address this gap by proposing an innovative method that analyzes the relationship between clusters of variables obtained by applying K-means on transposed data and the principal components of PCA. Our approach involves applying PCA to the original data and K-means to the transposed data set, where the original variables are converted into observations. The contribution of each variable cluster to each principal component is then quantified using measures based on variable loadings. This process provides a tool to explore and understand the clustering of variables and how such clusters contribute to the principal dimensions of variation identified by PCA. We analyze multiple data sets with varying variability structures (USArrests, Iris, Decathlon2) to show that the correspondence between clusters of variables and principal components depends on the data's inherent structure.

The development of the sixth generation of communication networks (6G) has been gaining momentum over the past years, with a target of being introduced by 2030. Several initiatives worldwide are developing innovative solutions and setting the direction for the key features of these networks. Some common emerging themes are the tight integration of AI, the convergence of multiple access technologies and sustainable operation, aiming to meet stringent performance and societal requirements. To that end, we are introducing REASON - Realising Enabling Architectures and Solutions for Open Networks. The REASON project aims to address technical challenges in future network deployments, such as E2E service orchestration, sustainability, security and trust management, and policy management, utilising AI-native principles, considering multiple access technologies and cloud-native solutions. This paper presents REASON's architecture and the identified requirements for future networks. The architecture is meticulously designed for modularity, interoperability, scalability, simplified troubleshooting, flexibility, and enhanced security, taking into consideration current and future standardisation efforts, and the ease of implementation and training. It is structured into four horizontal layers: Physical Infrastructure, Network Service, Knowledge, and End-User Application, complemented by two vertical layers: Management and Orchestration, and E2E Security. This layered approach ensures a robust, adaptable framework to support the diverse and evolving requirements of 6G networks, fostering innovation and facilitating seamless integration of advanced technologies.

Although machine learning (ML) has shown promise in numerous domains, there are concerns about generalizability to out-of-sample data. This is currently addressed by centrally sharing ample, and importantly diverse, data from multiple sites. However, such centralization is challenging to scale (or even not feasible) due to various limitations. Federated ML (FL) provides an alternative to train accurate and generalizable ML models, by only sharing numerical model updates. Here we present findings from the largest FL study to-date, involving data from 71 healthcare institutions across 6 continents, to generate an automatic tumor boundary detector for the rare disease of glioblastoma, utilizing the largest dataset of such patients ever used in the literature (25, 256 MRI scans from 6, 314 patients). We demonstrate a 33% improvement over a publicly trained model to delineate the surgically targetable tumor, and 23% improvement over the tumor's entire extent. We anticipate our study to: 1) enable more studies in healthcare informed by large and diverse data, ensuring meaningful results for rare diseases and underrepresented populations, 2) facilitate further quantitative analyses for glioblastoma via performance optimization of our consensus model for eventual public release, and 3) demonstrate the effectiveness of FL at such scale and task complexity as a paradigm shift for multi-site collaborations, alleviating the need for data sharing.