Towards Measuring and Modeling Geometric Structures in Time Series Forecasting via Image Modality
This work addresses a gap in time series forecasting for domains like weather, finance, and traffic by improving structure evaluation and modeling, though it is incremental as it builds on existing methods with a new loss function.
The paper tackles the problem of evaluating and modeling geometric structures in time series forecasting by proposing TGSI, a novel metric that transforms time series into images, and SATL, a multi-component loss function to enhance structure modeling during training. Experiments show that models trained with SATL achieve superior performance in both MSE and TGSI metrics across multiple datasets, without increasing computational cost during inference.
Time Series forecasting is critical in diverse domains such as weather forecasting, financial investment, and traffic management. While traditional numerical metrics like mean squared error (MSE) can quantify point-wise accuracy, they fail to evaluate the geometric structure of time series data, which is essential to understand temporal dynamics. To address this issue, we propose the time series Geometric Structure Index (TGSI), a novel evaluation metric that transforms time series into images to leverage their inherent two-dimensional geometric representations. However, since the image transformation process is non-differentiable, TGSI cannot be directly integrated as a training loss. We further introduce the Shape-Aware Temporal Loss (SATL), a multi-component loss function operating in the time series modality to bridge this gap and enhance structure modeling during training. SATL combines three components: a first-order difference loss that measures structural consistency through the MSE between first-order differences, a frequency domain loss that captures essential periodic patterns using the Fast Fourier Transform while minimizing noise, and a perceptual feature loss that measures geometric structure difference in time-series by aligning temporal features with geometric structure features through a pre-trained temporal feature extractor and time-series image autoencoder. Experiments across multiple datasets demonstrate that models trained with SATL achieve superior performance in both MSE and the proposed TGSI metrics compared to baseline methods, without additional computational cost during inference.