A New Supervised Learning Approach: Statistical Adaptive Fourier Decomposition (SAFD)

Abstract

This paper proposes a new type of supervised learning approach - statistical adaptive Fourier decomposition (SAFD). SAFD uses the orthogonal rational systems, or Takenaka-Malmquist (TM) systems, to build up a learning model for the training set, based on which predictions of unknown data can be made. The approach focuses on the classification of signals or time series. AFD is a newly developed signal analysis method, which can adaptively decompose different signals into different TM systems that introduces the Fourier type but non-linear and non-negative time-frequency representation. SAFD fully integrates the learning process with the adaptability character of AFD, in which a small number of learned atoms are adequate to capture structures and features of the signals for classification. There are three advantages in SAFD. First, the features are automatically detected and extracted in the learning process. Secondly, all parameters are selected automatically by the algorithm. Finally, the learned features are mathematically represented and the characteristics can be further studied based on the induced instantaneous frequencies. The efficiency of the proposed method is verified by electrocardiography (ECG) signal classification. The experiments show promising results over other feature based learning approaches.