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@INPROCEEDINGS{Ito:1009393,
      author       = {Ito, Junji and Gutzen, Robin and Krauße, Sven and Denker,
                      Michael and Grün, Sonja},
      title        = {{T}owards classification of spatio-temporal wave patterns
                      based on principal component analysis},
      reportid     = {FZJ-2023-02797},
      year         = {2023},
      abstract     = {Spatio-temporal oscillatory dynamics are found in a variety
                      of subjects in the natural sciences. [1]They are
                      mathematically described in terms of a complex-valued field
                      variable Z(r, t), from whichone can uniquely derive the
                      oscillation amplitude A(r, t) = |Z(r, t)| and oscillation
                      phase θ(r, t) = argZ(r, t), as functions of location r and
                      time t. In a wide class of systems, the phase variable
                      exhibitsspecific spatio-temporal patterns, such as planar
                      wave, radial wave, rotating wave, and so on.These patterns
                      have also been observed in the cerebral cortex of the brain
                      as spatio-temporal waves(STWs) of local field potential
                      (LFP) signals [2-5]. Previous studies have suggested that
                      specific phasepatterns, in particular planar waves, are
                      related to the coordination of spiking activity of
                      singleneurons, and therefore might play a fundamental role
                      in neuronal information processing [6-8].Studying the
                      implications of the STWs for brain function requires a
                      systematic classification methodto group given phase
                      patterns into distinct wave types (e.g. planar, radial, and
                      rotating). Thestrategies taken in previous studies rely on
                      defining a characteristic measure quantifying a feature
                      ofthe phase variable θ(r, t) for each wave type, and
                      setting a threshold on this measure to assign awave type to
                      an episode of data. An inherent shortcoming of this approach
                      is that it requires the adhoc and eventually arbitrary
                      selection of characteristic measures and thresholds.Here we
                      propose a method to quantify phase pattern characteristics
                      based on principal componentanalysis (PCA), which can be
                      used for a non-parametric classification of wave types. In
                      addition tothe standard PCA, we also employ the complex PCA,
                      which works on a complex-valued data matrixand decompose it
                      into components represented by complex-valued vectors (see
                      Figure). We showthat the principal components (PCs) obtained
                      via the complex PCA can naturally represent
                      phaserelationships among variables. We apply both methods to
                      Utah array recordings of LFPs from themacaque motor cortex,
                      which has been reported to exhibit various types of wave
                      patterns, anddiscuss the commonalities and differences
                      between the PCs obtained by the two methods.Furthermore, we
                      relate the time course of the obtained PCs to the time
                      course of the characteristicmeasures of wave types, which
                      were used in previous studies, and examine how individual
                      PCscorrespond to one or multiple of the characteristic
                      measures.We thereby employ the phase pattern quantification
                      with (the standard or complex) PCA as analternative method
                      of wave type classification. Further, decomposing the
                      cortical waves into“eigenmodes” and studying their
                      relations to neuronal and behavioral covariates would
                      provide apromising approach for investigating the functional
                      implications of the waves.References1. Winfree (1980) The
                      geometry of biological time. Vol. 2.2. Ermentrout et al.
                      (2001) Neuron 29(1):33–44. doi:
                      10.1016/S0896-6273(01)00178-73. Heitmann et al. (2012)
                      Front. Comput. Neurosci. 6:67. doi:
                      10.3389/fncom.2012.000674. Denker et al. (2018) Sci. Rep.
                      8(1):5200. doi: 10.1038/s41598-018-22990-75. Townsend et al.
                      (2018) PLoS CB 14(12):e1006643. doi:
                      10.1371/journal.pcbi.10066436. Takahashi et al. (2015) Nat.
                      Commun. 6(1):1–11. doi: 10.1038/ncomms81697. Vinck and
                      Bosman (2016) Front. Syst. Neurosci. 10:35. doi:
                      10.3389/fnsys.2016.000358. Davis et al. (2020) Nat. Commun.
                      12(1):6057. doi: 10.1038/s41467-021-26175-1},
      month         = {Jul},
      date          = {2023-07-15},
      organization  = {32nd Annual Computational Neuroscience
                       Meeting, Leipzig (Germany), 15 Jul 2023
                       - 19 Jul 2023},
      subtyp        = {After Call},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {5231 - Neuroscientific Foundations (POF4-523) / HBP SGA2 -
                      Human Brain Project Specific Grant Agreement 2 (785907) /
                      HBP SGA3 - Human Brain Project Specific Grant Agreement 3
                      (945539) / HAF - Helmholtz Analytics Framework (ZT-I-0003) /
                      JL SMHB - Joint Lab Supercomputing and Modeling for the
                      Human Brain (JL SMHB-2021-2027) / Algorithms of Adaptive
                      Behavior and their Neuronal Implementation in Health and
                      Disease (iBehave-20220812)},
      pid          = {G:(DE-HGF)POF4-5231 / G:(EU-Grant)785907 /
                      G:(EU-Grant)945539 / G:(DE-HGF)ZT-I-0003 / G:(DE-Juel1)JL
                      SMHB-2021-2027 / G:(DE-Juel-1)iBehave-20220812},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/1009393},
}