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| 001 | 1041480 | ||
| 005 | 20250416202206.0 | ||
| 024 | 7 | _ | |a 10.48550/ARXIV.2403.17687 |2 doi |
| 024 | 7 | _ | |a 10.48550/arXiv.2403.17687 |2 doi |
| 037 | _ | _ | |a FZJ-2025-02266 |
| 100 | 1 | _ | |a Albers, Jasper |0 P:(DE-Juel1)180539 |b 0 |e Corresponding author |
| 245 | _ | _ | |a Assessing the similarity of real matrices with arbitrary shape |
| 260 | _ | _ | |c 2024 |b arXiv |
| 336 | 7 | _ | |a Preprint |b preprint |m preprint |0 PUB:(DE-HGF)25 |s 1744789488_15481 |2 PUB:(DE-HGF) |
| 336 | 7 | _ | |a WORKING_PAPER |2 ORCID |
| 336 | 7 | _ | |a Electronic Article |0 28 |2 EndNote |
| 336 | 7 | _ | |a preprint |2 DRIVER |
| 336 | 7 | _ | |a ARTICLE |2 BibTeX |
| 336 | 7 | _ | |a Output Types/Working Paper |2 DataCite |
| 520 | _ | _ | |a 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 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. |
| 536 | _ | _ | |a 5231 - Neuroscientific Foundations (POF4-523) |0 G:(DE-HGF)POF4-5231 |c POF4-523 |f POF IV |x 0 |
| 536 | _ | _ | |a BMBF 03ZU1106CB - NeuroSys: Algorithm-Hardware Co-Design (Projekt C) - B (BMBF-03ZU1106CB) |0 G:(DE-Juel1)BMBF-03ZU1106CB |c BMBF-03ZU1106CB |x 1 |
| 536 | _ | _ | |a DFG project G:(GEPRIS)313856816 - SPP 2041: Computational Connectomics (313856816) |0 G:(GEPRIS)313856816 |c 313856816 |x 2 |
| 536 | _ | _ | |a HBP SGA3 - Human Brain Project Specific Grant Agreement 3 (945539) |0 G:(EU-Grant)945539 |c 945539 |f H2020-SGA-FETFLAG-HBP-2019 |x 3 |
| 536 | _ | _ | |a EBRAINS 2.0 - EBRAINS 2.0: A Research Infrastructure to Advance Neuroscience and Brain Health (101147319) |0 G:(EU-Grant)101147319 |c 101147319 |f HORIZON-INFRA-2022-SERV-B-01 |x 4 |
| 536 | _ | _ | |a JL SMHB - Joint Lab Supercomputing and Modeling for the Human Brain (JL SMHB-2021-2027) |0 G:(DE-Juel1)JL SMHB-2021-2027 |c JL SMHB-2021-2027 |x 5 |
| 588 | _ | _ | |a Dataset connected to DataCite |
| 650 | _ | 7 | |a Neurons and Cognition (q-bio.NC) |2 Other |
| 650 | _ | 7 | |a Data Analysis, Statistics and Probability (physics.data-an) |2 Other |
| 650 | _ | 7 | |a Quantitative Methods (q-bio.QM) |2 Other |
| 650 | _ | 7 | |a FOS: Biological sciences |2 Other |
| 650 | _ | 7 | |a FOS: Physical sciences |2 Other |
| 700 | 1 | _ | |a Kurth, Anno |0 P:(DE-Juel1)176776 |b 1 |
| 700 | 1 | _ | |a Gutzen, Robin |0 P:(DE-Juel1)171572 |b 2 |
| 700 | 1 | _ | |a Morales-Gregorio, Aitor |0 P:(DE-Juel1)176593 |b 3 |
| 700 | 1 | _ | |a Grün, Sonja |0 P:(DE-Juel1)144168 |b 4 |
| 700 | 1 | _ | |a Diesmann, Markus |0 P:(DE-Juel1)144174 |b 5 |
| 773 | _ | _ | |a 10.48550/arXiv.2403.17687 |
| 909 | C | O | |o oai:juser.fz-juelich.de:1041480 |p openaire |p VDB |p ec_fundedresources |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 0 |6 P:(DE-Juel1)180539 |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 1 |6 P:(DE-Juel1)176776 |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 3 |6 P:(DE-Juel1)176593 |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 4 |6 P:(DE-Juel1)144168 |
| 910 | 1 | _ | |a Forschungszentrum Jülich |0 I:(DE-588b)5008462-8 |k FZJ |b 5 |6 P:(DE-Juel1)144174 |
| 913 | 1 | _ | |a DE-HGF |b Key Technologies |l Natural, Artificial and Cognitive Information Processing |1 G:(DE-HGF)POF4-520 |0 G:(DE-HGF)POF4-523 |3 G:(DE-HGF)POF4 |2 G:(DE-HGF)POF4-500 |4 G:(DE-HGF)POF |v Neuromorphic Computing and Network Dynamics |9 G:(DE-HGF)POF4-5231 |x 0 |
| 920 | 1 | _ | |0 I:(DE-Juel1)IAS-6-20130828 |k IAS-6 |l Computational and Systems Neuroscience |x 0 |
| 920 | 1 | _ | |0 I:(DE-Juel1)INM-10-20170113 |k INM-10 |l Jara-Institut Brain structure-function relationships |x 1 |
| 980 | _ | _ | |a preprint |
| 980 | _ | _ | |a VDB |
| 980 | _ | _ | |a I:(DE-Juel1)IAS-6-20130828 |
| 980 | _ | _ | |a I:(DE-Juel1)INM-10-20170113 |
| 980 | _ | _ | |a UNRESTRICTED |
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