  Randomizing the Fourier-transform (FT) phases of temporal-spatial data
generates surrogates that approximate examples from the data-generating
distribution. We propose such FT surrogates as a novel tool to augment and
analyze training of neural networks and explore the approach in the example of
sleep-stage classification. By computing FT surrogates of raw EEG, EOG, and EMG
signals of under-represented sleep stages, we balanced the CAPSLPDB sleep
database. We then trained and tested a convolutional neural network for sleep
stage classification, and found that our surrogate-based augmentation improved
the mean F1-score by 7%. As another application of FT surrogates, we formulated
an approach to compute saliency maps for individual sleep epochs. The
visualization is based on the response of inferred class probabilities under
replacement of short data segments by partial surrogates. To quantify how well
the distributions of the surrogates and the original data match, we evaluated a
trained classifier on surrogates of correctly classified examples, and
summarized these conditional predictions in a confusion matrix. We show how
such conditional confusion matrices can qualitatively explain the performance
of surrogates in class balancing. The FT-surrogate augmentation approach may
improve classification on noisy signals if carefully adapted to the data
distribution under analysis.
