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Explore Intrinsic Geometry of Sleep Dynamics and Predict Sleep Stage by Unsupervised Learning Techniques

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Harmonic Analysis and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 168))

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Abstract

We propose a novel unsupervised approach for sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools. Specifically, we apply diffusion-based algorithms, diffusion map (DM), and alternating diffusion (AD) algorithms, to reconstruct the intrinsic geometry of sleep dynamics by reorganizing the spectral information of an electroencephalogram (EEG) extracted from a nonlinear-type time frequency analysis tool, the synchrosqueezing transform (SST). The visualization is achieved by the nonlinear dimension reduction properties of DM and AD. Moreover, the reconstructed nonlinear geometric structure of the sleep dynamics allows us to achieve the automatic annotation purpose. The hidden Markov model is trained to predict the sleep stage. The prediction performance is validated on a publicly available benchmark database, Physionet Sleep-EDF [extended] SC∗ and ST∗, with the leave-one-subject-out cross-validation. The overall accuracy and macro F1 achieve 82.57% and 76% in Sleep-EDF SC∗ and 77.01% and 71.53% in Sleep-EDF ST∗, which is compatible with the state-of-the-art results by supervised learning-based algorithms. The results suggest the potential of the proposed algorithm for clinical applications.

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Notes

  1. 1.

    According to the noise analysis in [38], when the signal-to-noise ratio is small, it is beneficial to set the diagonal terms of the affinity matrix to 0; that is, set W ii = 0.

  2. 2.

    Note that ϕ l is a n-dim vector while f l is a smooth function defined on M. To properly state the convergence, we need to convert ϕ l into a continuous function defined on M. Also, when μ l has a non-trivial multiplicity, the convergence should be stated using the eigenprojection operator. We refer these technical details to [31].

  3. 3.

    Its multiway clustering is supported by the recently developed theory for the multiway spectral clustering algorithm [51].

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Authors and Affiliations

  1. Department of Mathematics, National Chen-Kung University, Tainan, Taiwan

    Gi-Ren Liu

  2. Department of Thoracic Medicine, Healthcare Center, Chang Gung Memorial Hospital, Chang Gung University, School of Medicine, New Taipei, Taiwan

    Yu-Lun Lo

  3. Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

    Yuan-Chung Sheu

  4. Department of Mathematics and Department of Statistical Science, Duke University, Durham, NC, USA

    Hau-Tieng Wu

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  1. Gi-Ren Liu
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  2. Yu-Lun Lo
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  3. Yuan-Chung Sheu
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  4. Hau-Tieng Wu
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Correspondence to Hau-Tieng Wu .

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  1. Institute of Mathematics, University of Zurich, Zurich, Switzerland

    Michael Th. Rassias

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Liu, GR., Lo, YL., Sheu, YC., Wu, HT. (2021). Explore Intrinsic Geometry of Sleep Dynamics and Predict Sleep Stage by Unsupervised Learning Techniques. In: Rassias, M.T. (eds) Harmonic Analysis and Applications. Springer Optimization and Its Applications, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-030-61887-2_11

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