Tensor approximate entropy: An entropy measure for sleep scoring

摘要

The tensor is a generalized data formation, and some tensor-based manipulation techniques are superior to time series or images in data processing. However, an effective measure of spatiotemporal regularity for tensors is still lacking. This study proposes an entropy measure for tensors, tensor approximate entropy (TensorApEn), to evaluate the regularity or complexity within tensors. TensorApEn is calculated by examining the conditional probabilities of the inherent similarities in tensors. Experiments are performed on general tensors and sleep tensors, where general tensors are formatted from common time series, and sleep tensors from electroencephalographs (EEG) and electrooculograms (EOG). Results demonstrate that TensorApEn has good consistency and discrimination abilities, and is statistically significant across six sleep stages (Wake, S1, S2, S3, S4, and REM) on 59481 sleep tensors from 61 subjects. In the sleep scoring task, compared to traditional entropy measures and existing works, TensorApEn shows higher classification accuracies of 96.45%, 91.87%, 85.43%, 83.76%, and 80.73% in 2- to 6-class classification modes, respectively, and the corresponding highest Kappa indices are 0.93, 0.88, 0.87, 0.83, and 0.82. It is concluded that TensorApEn is superior in evaluating complexity of tensors in both time and spatial dimensions, and this work also provides a valuable supplement to the research of tensors and the family of entropy measures.