Advanced Data Augmentation Methods in Neural Network for Functional Data Classification

Many real-world data have nonlinear characteristics, making it difficult for traditional linear models to fully explore the inherent laws of data. Functional data analysis methods, especially models based on deep learning, can effectively handle these nonlinear relationships and accurately capture trends in the data. To address this challenge, this paper proposes two innovative data augmentation methods based on functional neural networks: the Functional Basis Neural Network based on Derivatives (D-FBNN) and the Functional Basis Neural Network based on Additive Decomposition (AD-FBNN). First, D-FBNN extracts higher-order derivative information by leveraging the inherent properties of functional data. This method can not only use the derivative alone, but also introduce more abundant data features through the weighted linear combination of the original data and its derivatives. Second, AD-FBNN adopts the additive decomposition technique from time series analysis to decompose functional data into trend, seasonal and residual components, and analyzes their characteristics in different combinations. Numerical experiments on six benchmark functional datasets demonstrate the effectiveness of both methods in functional data classification tasks, highlighting their potential for improving classifier performance.