Many real-world similarity measures are indefinite, violating the assumptions of kernel-based clustering methods.We propose a principled framework based on the polar decomposition of the similarity matrix, yielding a positive semi-definite component that preserves relational structure while enabling consistent out-of-sample extensions also for dissimilarities.The resulting polarized kernels support stable and interpretable clustering across synthetic and real datasets, demonstrating that polar decomposition provides a theoretically sound and practically effective bridge between indefinite similarity learning and kernel-based methods.

Federated learning enables privacy-preserving machine learning across distributed data sources, but real-world deployments face challenges that extend beyond standard protocols. This tutorial provides a structured overview of the field, addressing issues such as non-stationary data, client heterogeneity, resource constraints, and security threats. Beyond existing surveys, it incorporates hands-on insights and deployment experiences, including concrete war stories illustrating how federated learning methods perform under real-world conditions. The tutorial also outlines emerging directions, including federated graph learning, game-theoretic approaches, and sustainable AI concepts. It aims to provide both a conceptual framework and practical guidance for researchers and practitioners advancing federated learning in dynamic and evolving environments.

We present an extended formulation of our base framework FedT4T-Evo ; a Federated Learning approach that systematically evaluates utility-driven client strategies under resource limitations. To address challenges in distributed learning systems, including resource constraints and non- cooperative behaviors, we model client interactions through the Iterated Prisoner’s Dilemma. Our framework enables clients to adapt decision rules based on prior interactions and resource availability, optimizing both individual utility and contributions to the global optimization target. To further extend the natural perspective, we present a novel evolutionary selection algorithm that simulates ecological dynamics over populations of client strategies, providing a instinctive mechanism for the emergence and persistence of cooperation. Applied to benchmark tasks, our experimental results showed that the framework offers an effective approach for gaining insights into Federated Learning systems through the lens of cooperation theory. • A cooperation-theoretic FL framework is proposed to natively study and foster collaborative client behaviors. • Resource-aware mechanisms are introduced to adapt to heterogeneity and constraints in real-world FL environments. • Evolutionary dynamics are integrated to simulate ecological patterns of cooperation across FL clients.

We present a novel Federated Learning framework, FedT4T, that systematically evaluates utility-driven client strategies under resource constraints.Recognizing the significant challenges in practical distributed learning environments, such as limited resources and non-cooperative behaviors, we model client interactions using the Iterated Prisoner's Dilemma.Our framework enables clients to adapt their decision rules based on prior interactions and available resources, optimizing both individual utility and collective contribution to solve a global learning task.We apply FedT4T to a Federated Learning benchmark classification task and explore the dynamics of cooperation between clients driven by common strategies from cooperation theory under the impact of varying resource availability.The code is publicly available at https://github.com/cairo-thws/FedT4T.

We introduce an enhanced formulation of FedT4T-Pro, a Federated Learning framework designed to systematically assess utility-driven client strategies within resource-constrained environments. To address key challenges in practical distributed learning systems, such as resource limitations and non-cooperative behaviors, we model client interactions using the Iterated Prisoner’s Dilemma. Our framework empowers clients to refine their decision rules based on past interactions and available resources, optimizing both individual utility and overall contributions to a global learning objective. In addition, a novel sampling algorithm for client selection, drawing inspiration from evolutionary biology, is proposed as a natural incentive mechanism to encourage consistent cooperation and resource contributions. We apply FedT4T-Pro to a Federated Learning benchmark classification task and explore the dynamics of cooperation between clients driven by common strategies from Cooperation theory under the impact of varying resource availability. Furthermore, we experimentally show that the proposed sampling algorithm fosters collaborative behavior in FL training.

We present a numerically robust, computationally efficient approach for non-I.I.D. data stream sampling in federated client systems, where resources are limited and labeled data for local model adaptation is sparse and expensive.The proposed method identifies relevant stream observations to optimize the underlying client model, given a local labeling budget, and performs instantaneous labeling decisions without relying on any memory buffering strategies.Our experiments show enhanced training batch diversity and an improved numerical robustness of the proposal compared to existing strategies over large-scale data streams, making our approach an effective and convenient solution in FL environments.* MR is supported through the Bavarian HighTech Agenda, specifically by the Würzburg Center for Artificial Intelligence and Robotics (CAIRO) and the ProPere THWS scholarship.57

Federated Learning has gained significant attention as a data protecting paradigm for decentralized, clientside learning in the era of interconnected, sensor-equipped edge devices. However, practical applications of Federated Learning face three major challenges: First, the expensive data labeling process required for target adaptation involves human participation. Second, the data collection process on client devices suffers from covariate shift due to environmental impact on attached sensors, leading to a discrepancy between source and target samples. Third, in resource-limited environments, both continuous or regular model updates are often infeasible due to limited data transmission capabilities or technical constraints on channel availability and energy efficiency. To address these challenges, we propose FedAcross, an efficient and scalable Federated Learning framework designed specifically for real-world client adaptation in industrial environments. It is based on a pre-trained source model that includes a deep backbone, an adaptation module, and a classifier running on a powerful server. By freezing the backbone and the classifier during client adaptation on resourceconstrained devices, we enable the domain adaptive linear layer to solely handle target domain adaptation and minimize the overall computational overhead. Our extensive experimental results validate the effectiveness of FedAcross in achieving competitive adaptation on low-end client devices with limited target samples, effectively addressing the challenge of domain shift. Our framework effectively handles sporadic model updates within resource-limited environments, ensuring practical and seamless deployment.

Kernel functions are a key element in many machine learning methods to capture the similarity between data points. However, a considerable number of these functions do not meet all mathematical requirements to be a valid positive semi-definite kernel, a crucial precondition for kernel-based classifiers such as Support Vector Machines or Kernel Fisher Discriminant classifiers. In this paper, we propose a novel strategy employing a polar decomposition to effectively transform invalid kernel matrices to positive semi-definite matrices, while preserving the topological structure inherent to the data points. Utilizing polar decomposition allows the effective transformation of indefinite kernel matrices from Krein space to positive semi-definite matrices in Hilbert space, thereby providing an efficient out-of-sample extension for new unseen data and enhancing kernel method applicability across diverse classification tasks. We evaluate our approach on a variety of benchmark datasets and demonstrate its superiority over competitive methods.

Heterogeneous data is common in many real-world machine learning applications, such as healthcare, market analysis, environmental sciences, and social media analysis. In these domains, data is often represented in different modalities and, most of the time, in non-vectorial formats, like text, images, and video. Traditional machine learning algorithms are often limited in their ability to effectively analyze and learn from such diverse data types. In this paper, we propose two approaches for such heterogeneous data analysis: static and adaptive subspace kernel fusion. The first approach is a kernel-based method extracting the essential parts of the subspace of each input modality and creating one single fused representation of the data. The second approach utilizes an adaptation step by integrating the weighting of spectral properties into the fusion process in order to improve the data’s representation with respect to a given classification task. Our proposed methods are evaluated on several multi-modal, heterogeneous data sets and demonstrate significant performance improvement compared to other methods in the field. Our results highlight the importance of fusing the underlying subspace information of heterogeneous data for achieving superior performance in machine learning tasks.

Data and information are nowadays frequently available in multiple modalities like different sensor signals, textual descriptions, graph structures, and other formats.The maximum information from these heterogeneous representations can be obtained by fusing the various modalities by specific embeddings or proximity measures.Current approaches are widely limited in the fusion model and the applied measures, especially when the given data is non-vectorial.We propose a model to learn the spectral properties of the different inner product representations in a joined optimization problem.The approach is evaluated on various multimodal data and compared to modern multiple-kernel learning and baseline techniques.* MM and MR are supported by the Bavarian HighTech agenda and the Würzburg Center for Artificial Intelligence and Robotics (CAIRO).Additionally, we thank Dr. Benjamin Paaßen for the invaluable discussions about this research topic during a fantastic boating trip.