Drift2Matrix: Kernel-Induced Self Representation for Concept Drift Adaptation in Co-evolving Time Series

In the realm of time series analysis, tackling the phenomenon of concept drift poses a significant challenge. Concept drift - characterized by the evolving statistical properties of time series data, affects the reliability and accuracy of conventional analysis models. This is particularly evident in co-evolving scenarios where interactions among variables are crucial. This paper presents Drift2Matrix, a novel framework that leverages kernel-induced self-representation for adaptive responses to concept drift in time series. Drift2Matrix employs a kernel-based learning mechanism to generate a representation matrix, encapsulating the inherent dynamics of co-evolving time series. This matrix serves as a key tool for identification and adaptation to concept drift by observing its temporal variations. Furthermore, Drift2Matrix effectively identifies prevailing patterns and offers insights into emerging trends through pattern evolution analysis. Our empirical evaluation of Drift2Matrix across various datasets demonstrates its effectiveness in handling the complexities of concept drift. This approach introduces a novel perspective in the theoretical domain of co-evolving time series analysis, enhancing adaptability and accuracy in the face of dynamic data environments. Co-evolving time series data analysis plays a crucial role in diverse sectors including finance, healthcare, and meteorology. Within these areas, multiple time series evolve simultaneously and interact with one another, forming complex, dynamic systems. A particularly pervasive issue is concept drift Lu et al. (2018b); Yu et al. (2024), which refers to shifts in the underlying data distribution over time, thereby undermining the effectiveness of static models. Traditional time series approaches commonly rely on the assumptions of stationarity and linear relationships. Methods such as ARIMA and VAR Box (2013), for instance, perform well in circumstances with stable and predictable dynamics. Conversely, machine learning methodologies Li et al. (2022); Wen et al. (2020), such as diverse neural network architectures Ho et al. (2022); Li et al. (2023); Yang et al. (2024), offer more flexibility but often require large amounts of data and face difficulties in terms of interpretability and adaptability, especially in dynamic contexts. The evolving study has steered the field towards more adaptive and dynamic models.