Abstract Time series classification poses significant challenges due to the inherent temporal order of the data points and the existence of sequential dependencies between them. The ROCKET family, featuring methods like MiniROCKET, MultiROCKET, and HYDRA, is currently a leading approach in this domain, leveraging convolution kernels to aggregate temporal features into encodings for linear classifiers. However, these models encode temporal features over short temporal windows and then aggregate them as an unordered set of encodings over the longer temporal window of the entire data sequence. This prevents these models from capturing any longer sequence structure. To address this design drawback, we propose integrating hyperdimensional computing into ROCKET methods to explicitly incorporate temporal order of the short-term features within the entire time series. This approach enhances the discriminative power of encodings generated by MiniROCKET, MultiROCKET, and HYDRA where longer-term structure exists in the data, leading to increased classification performance with minimal computational overhead. More specifically, we introduce a method to represent time series as high-dimensional vectors through multiplicative binding of ROCKET encodings with encodings representing temporal order, applying this approach across various ROCKET methods. Additionally, we explore different high-dimensional vector representations of temporal order, yielding diverse similarity kernels that enhance classification accuracy. Through experiments on synthetic datasets, we highlight the limitations of ROCKET methods in handling temporal dependencies and show how the methods based on hyperdimensional computing overcome these limitations. Furthermore, our extensive experimental evaluation with real-world datasets included in the recent UCR archive, validates the advantages of our approach, consistently achieving classification improvements across all ROCKET methods that integrate hyperdimensional computing. Notably, our best model achieves a relative error rate reduction of over 50% compared to the best ROCKET model on several UCR datasets.

Abstract Tensor factorizations have been widely used for the task of uncovering patterns in various domains. Often, the input is time-evolving, shifting the goal to tracking the evolution of the underlying patterns instead. To adapt to this more complex setting, existing methods incorporate temporal regularization but they either have overly constrained structural requirements or lack uniqueness which is crucial for interpretation. In this paper, in order to capture the underlying evolving patterns, we introduce t(emporal)PARAFAC2, which utilizes temporal smoothness regularization on the evolving factors. Previously, Alternating Optimization and Alternating Direction Method of Multipliers-based algorithmic approach has been introduced to fit the PARAFAC2 model to fully observed data. In this paper, we extend this algorithmic framework to the case of partially observed data and use it to fit the tPARAFAC2 model to complete and incomplete datasets with the goal of revealing evolving patterns. Our numerical experiments on simulated datasets demonstrate that tPARAFAC2 can extract the underlying evolving patterns more accurately compared to the state-of-the-art in the presence of high amounts of noise and missing data. Using two real datasets, we also demonstrate the effectiveness of the algorithmic approach in terms of handling missing data and tPARAFAC2 model in terms of revealing evolving patterns. The paper provides an extensive comparison of different approaches for handling missing data within the proposed framework, and discusses both the advantages and limitations of tPARAFAC2 model.