Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from such a multi-variate time series is of a fundamental importance for many monitoring and control tasks. For a periodic time series this is equivalent to determining its period length. In this work we present a persistent homology framework to estimate recurrence times in multi-variate time series with different generalizations of cyclic behavior (periodic, repetitive, and recurring). To this end, we provide three specialized methods within our framework that are provably stable and validate them using real-world data, including a new benchmark dataset from an injection molding machine.

Anomaly detection is a fundamental problem in domains such as healthcare, manufacturing, and cybersecurity. This thesis proposes new unsupervised methods for anomaly detection in both structured and streaming data settings. In the first part, we focus on structure-based anomaly detection, where normal data follows low-dimensional manifolds while anomalies deviate from them. We introduce Preference Isolation Forest (PIF), which embeds data into a high-dimensional preference space via manifold fitting, and isolates outliers using two variants: Voronoi-iForest, based on geometric distances, and RuzHash-iForest, leveraging Locality Sensitive Hashing for scalability. We also propose Sliding-PIF, which captures local manifold information for streaming scenarios. Our methods outperform existing techniques on synthetic and real datasets. We extend this to structure-based clustering with MultiLink, a novel method for recovering multiple geometric model families in noisy data. MultiLink merges clusters via a model-aware linkage strategy, enabling robust multi-class structure recovery. It offers key advantages over existing approaches, such as speed, reduced sensitivity to thresholds, and improved robustness to poor initial sampling. The second part of the thesis addresses online anomaly detection in evolving data streams. We propose Online Isolation Forest (Online-iForest), which uses adaptive, multi-resolution histograms and dynamically updates tree structures to track changes over time. It avoids retraining while achieving accuracy comparable to offline models, with superior efficiency for real-time applications. Finally, we tackle anomaly detection in cybersecurity via open-set recognition for malware classification. We enhance a Gradient Boosting classifier with MaxLogit to detect unseen malware families, a method now integrated into Cleafy's production system.

Large Language Models (LLMs) have become foundational in modern artificial intelligence, powering a wide range of applications from code generation and virtual assistants to scientific research and enterprise automation. However, concerns about data contamination--where test data overlaps with training data--have raised serious questions about the reliability of these applications. Despite awareness of this issue, existing methods fall short in effectively identifying or mitigating contamination. In this paper, we propose Residual-Noise Fingerprinting (RN-F), a novel framework for detecting contaminated data in LLMs. RN-F is a single-pass, gradient-free detection method that leverages residual signal patterns without introducing additional floating-point operations. Our approach is lightweight, model-agnostic, and efficient. We evaluate RN-F on multiple LLMs across various contaminated datasets and show that it consistently outperforms existing state-of-the-art methods, achieving performance improvements of up to 10.5% in contamination detection metrics.

The emerging paradigm of leveraging pretrained large language models (LLMs) for time series forecasting has predominantly employed linguistic-temporal modality alignment strategies through token-level or layer-wise feature mapping. However, these approaches fundamentally neglect a critical insight: the core competency of LLMs resides not merely in processing localized token features but in their inherent capacity to model holistic sequence structures. This paper posits that effective cross-modal alignment necessitates structural consistency at the sequence level. We propose the Structure-Guided Cross-Modal Alignment (SGCMA), a framework that fully exploits and aligns the state-transition graph structures shared by time-series and linguistic data as sequential modalities, thereby endowing time series with language-like properties and delivering stronger generalization after modality alignment. SGCMA consists of two key components, namely Structure Alignment and Semantic Alignment. In Structure Alignment, a state transition matrix is learned from text data through Hidden Markov Models (HMMs), and a shallow transformer-based Maximum Entropy Markov Model (MEMM) receives the hot-start transition matrix and annotates each temporal patch into state probability, ensuring that the temporal representation sequence inherits language-like sequential dynamics. In Semantic Alignment, cross-attention is applied between temporal patches and the top-k tokens within each state, and the ultimate temporal embeddings are derived by the expected value of these embeddings using a weighted average based on state probabilities. Experiments on multiple benchmarks demonstrate that SGCMA achieves state-of-the-art performance, offering a novel approach to cross-modal alignment in time series forecasting.

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.

The continued rise of neural networks and large language models in the more recent past has altered the natural language processing landscape, enabling new approaches towards typical language tasks and achieving mainstream success. Despite the huge success of large language models, many disadvantages still remain and through this work we assess the state of the art in five application scenarios with a particular focus on the future perspectives and sensible application scenarios of traditional and older approaches and techniques. In this paper we survey recent publications in the application scenarios classification, information and relation extraction, text simplification as well as text summarization. After defining our terminology, i.e., which features are characteristic for traditional techniques in our interpretation for the five scenarios, we survey if such traditional approaches are still being used, and if so, in what way they are used. It turns out that all five application scenarios still exhibit traditional models in one way or another, as part of a processing pipeline, as a comparison/baseline to the core model of the respective paper, or as the main model(s) of the paper. For the complete statistics, see https://zenodo.org/records/13683801

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial kernels. Given $n$ training samples in $\mathbb{R}^d$ Tensor Sketch computes low-dimensional embeddings in $\mathbb{R}^D$ in time $\mathcal{O}\left( n(d+D \log{D}) \right)$ making it well-suited for high-dimensional and large-scale settings. We provide theoretical guarantees on the approximation error, ensuring the fidelity of the resulting kernel function estimates. We also discuss extensions and highlight applications where Tensor Sketch serves as a central computational tool.

The demand for high-quality medical imaging in clinical practice and assisted diagnosis has made 3D reconstruction in radiological imaging a key research focus. Artificial intelligence (AI) has emerged as a promising approach to enhancing reconstruction accuracy while reducing acquisition and processing time, thereby minimizing patient radiation exposure and discomfort and ultimately benefiting clinical diagnosis. This review explores state-of-the-art AI-based 3D reconstruction algorithms in radiological imaging, categorizing them into explicit and implicit approaches based on their underlying principles. Explicit methods include point-based, volume-based, and Gaussian representations, while implicit methods encompass implicit prior embedding and neural radiance fields. Additionally, we examine commonly used evaluation metrics and benchmark datasets. Finally, we discuss the current state of development, key challenges, and future research directions in this evolving field. Our project available on: https://github.com/Bean-Young/AI4Radiology.

Interactive visualization of embedding projections is a useful technique for understanding data and evaluating machine learning models. Labeling data within these visualizations is critical for interpretation, as labels provide an overview of the projection and guide user navigation. However, most methods for producing labels require clustering the points, which can be computationally expensive as the number of points grows. In this paper, we describe an efficient clustering approach using kernel density estimation in the projected 2D space instead of points. This algorithm can produce high-quality cluster regions from a 2D density map in a few hundred milliseconds, orders of magnitude faster than current approaches. We contribute the design of the algorithm, benchmarks, and applications that demonstrate the utility of the algorithm, including labeling and summarization.

This thesis delves into the forefront of wireless communication by exploring the synergistic integration of three transformative technologies: STAR-RIS, CoMP, and NOMA. Driven by the ever-increasing demand for higher data rates, improved spectral efficiency, and expanded coverage in the evolving landscape of 6G development, this research investigates the potential of these technologies to revolutionize future wireless networks. The thesis analyzes the performance gains achievable through strategic deployment of STAR-RIS, focusing on mitigating inter-cell interference, enhancing signal strength, and extending coverage to cell-edge users. Resource sharing strategies for STAR-RIS elements are explored, optimizing both transmission and reflection functionalities. Analytical frameworks are developed to quantify the benefits of STAR-RIS assisted CoMP-NOMA networks under realistic channel conditions, deriving key performance metrics such as ergodic rates and outage probabilities. Additionally, the research delves into energy-efficient design approaches for CoMP-NOMA networks incorporating RIS, proposing novel RIS configurations and optimization algorithms to achieve a balance between performance and energy consumption. Furthermore, the application of Deep Reinforcement Learning (DRL) techniques for intelligent and adaptive optimization in aerial RIS-assisted CoMP-NOMA networks is explored, aiming to maximize network sum rate while meeting user quality of service requirements. Through a comprehensive investigation of these technologies and their synergistic potential, this thesis contributes valuable insights into the future of wireless communication, paving the way for the development of more efficient, reliable, and sustainable networks capable of meeting the demands of our increasingly connected world.