Representation and Processing of Time Series Data with Hyperdimensional Computing

Temporal structure is crucial in fields like healthcare, autonomous driving, and robotics, where both event content and order matter. Time series classification assigns labels to sequences by exploiting temporal dependencies, but many state-of-the-art methods either ignore this information or require high computational costs to model it explicitly. Therefore, compact representations that preserve temporal order while reducing complexity are essential. This thesis investigates Hyperdimensional Computing (HDC) as a framework for classifying time series. HDC encodes data into high-dimensional vector spaces using algebraic operations such as superposition and binding, allowing for compositional and similarity-preserving representations. The work focuses on four main contributions: (1) analyzing existing HDC models regarding their algebraic properties and superposition capacity, (2) developing efficient sequence encodings based on Fractional Power Encoding (FPE) with real-valued Hadamard binding that preserve equivariance, (3) integrating HDC-based temporal encodings into state-of-the-art classifiers like ROCKET models, and (4) extending superposition through importance-weighted inputs to address capacity limits. The proposed methods are validated on synthetic and real-world benchmarks, achieving competitive results, including a winning solution in a seizure prediction challenge.:1. Introduction 2. Basics on Time Series Classification and HDC 3. A Comparison of VSAs 4. HDC for Temporal Sequence Encoding 5. Point-wise Data Encoding and Temporal Representation in HDC 6. Locally-based Data Encoding and Temporal Representation in HDC 7. Weighted Superposition for Data Channel Selection 8. Conclusion