Objective: The recently-introduced hypnodensity graph provides a probability distribution over sleep stages per data window (i.e. an epoch). This work explored whether this representation reveals continuities that can only be attributed to intra-and inter-rater disagreement of expert scorings, or also to co-occurrence of sleep stage-dependent features within one epoch.

Approach: We proposed a simplified model for time series like the ones measured during sleep, and a second model to describe the annotation process by an expert. Generating data according to these models, enabled controlled experiments to investigate the interpretation of the hypnodensity graph. Moreover, the influence of both the supervised training strategy, and the used softmax non-linearity were investigated. Polysomnography recordings of 96 health sleepers (of which 11 were used as independent test set), were subsequently used to transfer conclusions to real data.
Main results: A hypnodensity graph, predicted by a

supervised neural classifier, represents the probability with which the sleep expert(s) assigned a label to an epoch. It thus reflects annotator behavior, and is thereby only indirectly linked to the ratio of sleep stage-dependent features in the epoch. Unsupervised training was shown to result in hypnodensity graph that were slightly less dependent on this annotation process, resulting in, on average, higher-entropy distributions over sleep stages (Hunsupervised = 0.41 vs Hsupervised = 0.29). Moreover, pre-softmax predictions were, for both training strategies, found to better reflect the ratio of sleep stage-dependent characteristics in an epoch, as compared to the postsoftmax counterparts (i.e. the hypnodensity graph). In real data, this was observed from the linear relation between pre-softmax N3 predictions and the amount of delta power.

Significance: This study provides insights in, and proposes new, representations of sleep that may enhance our comprehension about sleep and sleep disorders.