Time series image coding classification theory based on Lagrange multiplier method

Time series classification is a crucial area of research within data analysis. Recent advancements in convolutional neural networks (CNNs) for image recognition and classification have inspired innovative approaches in this field. Researchers have begun transforming one-dimensional time series (TS) into visual representations, harnessing the capabilities of image classification paradigms to improve TS classification accuracy. Despite extensive research on the classification of time series images (TSI), the underlying classification principles have not been fully established.To address this gap, our paper integrates time series image encoding with algebraic techniques, utilizing Gramian Angular Summation Fields (GASF) and Gramian Angle Difference Fields (GADF) as effective encoding methods. We provide a theoretical justification for the advantages of CNNs in TSI classification by employing the Lagrange multiplier method and the Karush-Kuhn-Tucker (KKT) conditions. This rigorous proof framework enhances the theoretical foundation for TSI classification based on image encoding.To validate our theoretical assertions, we conduct experiments using the benchmark UCR dataset, with empirical findings largely corroborating our theoretical proofs. In summary, our work not only advances the theoretical understanding of TSI classification but also demonstrates its practical effectiveness.