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@INPROCEEDINGS{Albers:1028773,
      author       = {Albers, Jasper and Kurth, Anno and Gutzen, Robin and
                      Morales-Gregorio, Aitor and Denker, Michael and Grün, Sonja
                      and van Albada, Sacha and Diesmann, Markus},
      title        = {{Q}uantifying shared structure between real matrices of
                      arbitrary shape},
      reportid     = {FZJ-2024-04819},
      year         = {2024},
      abstract     = {Assessing the similarity of matrices is valuable for
                      analyzing the extent to which data sets exhibit common
                      features in tasks such as data clustering, dimensionality
                      reduction, pattern recognition, group comparisons, and graph
                      analysis. Methods proposed for comparing vectors, such as
                      the cosine similarity, can be readily generalized to
                      matrices. However, these approaches usually neglect the
                      inherent two-dimensional structure of matrices. Existing
                      methods that take this structure into account are only
                      well-defined on square, symmetric, positive- definite
                      matrices, limiting the range of applicability. Here, we
                      propose Singular Angle Similarity (SAS), a measure for
                      evaluating the structural similarity between two arbitrary,
                      real matrices of the same shape based on singular value
                      decomposition. By taking the two-dimensional structure of
                      matrices explicitly into account, SAS is able to capture
                      structural features that cannot be identified by traditional
                      methods such as Euclidean distance or the cosine
                      similarity.After introducing and characterizing the measure,
                      we apply SAS to two neuroscientific use cases: adjacency
                      matrices of probabilistic network connectivity, and state
                      evolution matrices representing neural brain activity. We
                      demonstrate that SAS can distinguish between network models
                      based on their adjacency matrices. Furthermore, SAS captures
                      differences in high-dimensional responses to different
                      stimuli in MUAe data from macaque V1, which can be related
                      to the underlying response properties of the neurons.
                      Thereby, SAS allows for a quantification of closeness of
                      related response patterns in a network of neurons. We
                      conclude that SAS is a suitable measure for quantifying the
                      shared structure of matrices with arbitrary shape in
                      neuroscience and beyond.},
      month         = {Jun},
      date          = {2024-06-25},
      organization  = {FENS Forum, Wien (Austria), 25 Jun
                       2024 - 29 Jun 2024},
      subtyp        = {After Call},
      cin          = {IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)IAS-6-20130828 / I:(DE-Juel1)INM-10-20170113},
      pnm          = {5231 - Neuroscientific Foundations (POF4-523) / BMBF
                      03ZU1106CB - NeuroSys: Algorithm-Hardware Co-Design (Projekt
                      C) - B (BMBF-03ZU1106CB) / DFG project 313856816 - SPP 2041:
                      Computational Connectomics (313856816) / EBRAINS 2.0 -
                      EBRAINS 2.0: A Research Infrastructure to Advance
                      Neuroscience and Brain Health (101147319) / JL SMHB - Joint
                      Lab Supercomputing and Modeling for the Human Brain (JL
                      SMHB-2021-2027)},
      pid          = {G:(DE-HGF)POF4-5231 / G:(DE-Juel1)BMBF-03ZU1106CB /
                      G:(GEPRIS)313856816 / G:(EU-Grant)101147319 / G:(DE-Juel1)JL
                      SMHB-2021-2027},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/1028773},
}