Towards Measuring and Modeling Geometric Structures in Time Series Forecasting via Image Modality

TL;DR

This paper introduces a novel evaluation metric (TGSI) and a shape-aware loss function (SATL) for time series forecasting, emphasizing geometric structure modeling to improve accuracy without extra inference costs.

Contribution

It proposes TGSI for geometric evaluation and SATL for structure-aware training, advancing time series forecasting by integrating geometric insights.

Findings

Models with SATL outperform baselines in MSE and TGSI metrics.

SATL enhances geometric structure modeling during training.

No additional inference cost is incurred by the proposed methods.

Abstract

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.