Detecting null patterns in tensor data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914275823452160 |
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| author | Brooksbank, Peter A. Kassabov, Martin D. Wilson, James B. |
| author_facet | Brooksbank, Peter A. Kassabov, Martin D. Wilson, James B. |
| contents | This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor decompositions, and Tucker decompositions. It also includes a new family of null patterns -- not known to be detectable by current methods -- that can be thought of as continuous decompositions approximating curves and surfaces. We present a general algorithm to detect null patterns in each class using a parameter we call a \textit{chisel} that tunes the search to patterns of a prescribed shape. We also show that the patterns output by the algorithm are essentially unique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting null patterns in tensor data Brooksbank, Peter A. Kassabov, Martin D. Wilson, James B. Numerical Analysis Data Structures and Algorithms 15A69, 15A72 This article introduces a class of efficiently computable null patterns for tensor data. The class includes familiar patterns such as block-diagonal decompositions explored in statistics and signal processing, low-rank tensor decompositions, and Tucker decompositions. It also includes a new family of null patterns -- not known to be detectable by current methods -- that can be thought of as continuous decompositions approximating curves and surfaces. We present a general algorithm to detect null patterns in each class using a parameter we call a \textit{chisel} that tunes the search to patterns of a prescribed shape. We also show that the patterns output by the algorithm are essentially unique. |
| title | Detecting null patterns in tensor data |
| topic | Numerical Analysis Data Structures and Algorithms 15A69, 15A72 |
| url | https://arxiv.org/abs/2408.17425 |