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| Home > Publications database > Quantifying shared structure between real matrices of arbitrary shape |
| Poster (After Call) | FZJ-2024-04819 |
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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.
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