001041480 001__ 1041480
001041480 005__ 20250416202206.0
001041480 0247_ $$2doi$$a10.48550/ARXIV.2403.17687
001041480 0247_ $$2doi$$a10.48550/arXiv.2403.17687
001041480 037__ $$aFZJ-2025-02266
001041480 1001_ $$0P:(DE-Juel1)180539$$aAlbers, Jasper$$b0$$eCorresponding author
001041480 245__ $$aAssessing the similarity of real matrices with arbitrary shape
001041480 260__ $$barXiv$$c2024
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001041480 520__ $$aAssessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis. Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. Here, we propose singular angle similarity (SAS), a measure for evaluating the structural similarity between two arbitrary, real matrices of the same shape based on singular value decomposition. After introducing the measure, we compare SAS with standard measures for matrix comparison and show that only SAS captures the two-dimensional structure of matrices. Further, we characterize the behavior of SAS in the presence of noise and as a function of matrix dimensionality. Finally, we apply SAS to two use cases: square non-symmetric matrices of probabilistic network connectivity, and non-square matrices representing neural brain activity. For synthetic data of network connectivity, SAS matches intuitive expectations and allows for a robust assessment of similarities and differences. For experimental data of brain activity, SAS captures differences in the structure of high-dimensional responses to different stimuli. We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape.
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001041480 536__ $$0G:(EU-Grant)945539$$aHBP SGA3 - Human Brain Project Specific Grant Agreement 3 (945539)$$c945539$$fH2020-SGA-FETFLAG-HBP-2019$$x3
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001041480 650_7 $$2Other$$aNeurons and Cognition (q-bio.NC)
001041480 650_7 $$2Other$$aData Analysis, Statistics and Probability (physics.data-an)
001041480 650_7 $$2Other$$aQuantitative Methods (q-bio.QM)
001041480 650_7 $$2Other$$aFOS: Biological sciences
001041480 650_7 $$2Other$$aFOS: Physical sciences
001041480 7001_ $$0P:(DE-Juel1)176776$$aKurth, Anno$$b1
001041480 7001_ $$0P:(DE-Juel1)171572$$aGutzen, Robin$$b2
001041480 7001_ $$0P:(DE-Juel1)176593$$aMorales-Gregorio, Aitor$$b3
001041480 7001_ $$0P:(DE-Juel1)144168$$aGrün, Sonja$$b4
001041480 7001_ $$0P:(DE-Juel1)144174$$aDiesmann, Markus$$b5
001041480 773__ $$a10.48550/arXiv.2403.17687
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001041480 9201_ $$0I:(DE-Juel1)IAS-6-20130828$$kIAS-6$$lComputational and Systems Neuroscience$$x0
001041480 9201_ $$0I:(DE-Juel1)INM-10-20170113$$kINM-10$$lJara-Institut Brain structure-function relationships$$x1
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