Linear Neural Network as a Fast Solver for Dictionary Learning Article Swipe
Rachana Sathish
,
Debdoot Sheet
,
Swanand Khare
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.36227/techrxiv.21988181.v1
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.36227/techrxiv.21988181.v1
Traditional numerical solvers for linear algebra problems such as dictionary learning (DictL) operating on large data face challenges because of super-linear computational complexity and massive memory requirement. This does not make it easily solvable on commonly available computers. A linear neural network (NN) is proposed to be employed as an alternate solver for such problems. Specifically, we demonstrate a linear fully-connected (FC) NN-based solver for DictL. It is employed to learn the dictionary atoms instead of the classically used k-singular value decomposition (K-SVD), while the sparse coefficients are learned using the classical orthogonal matching pursuit (OMP) approach. We compare the computational complexity of the classical vs our proposed FCNN-based approach implemented on both CPU and GPU using synthetically generated datasets with varying sizes. Further, we demonstrate practical utility in image denoising with DictL while comparing the equivalence of solution obtained from our FCNN-based solver with the traditional approach with K-SVD. We achieve a notable speedup compared to the traditional technique on both CPU and GPU implementations.
Related Topics
Concepts
Solver
Singular value decomposition
Computer science
Linear algebra
Speedup
Artificial neural network
Computational complexity theory
Matching pursuit
Equivalence (formal languages)
Parallel computing
Algorithm
Computational science
Artificial intelligence
Mathematics
Compressed sensing
Discrete mathematics
Geometry
Programming language
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.36227/techrxiv.21988181.v1
- OA Status
- gold
- References
- 12
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4319241289
All OpenAlex metadata
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https://openalex.org/W4319241289Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.36227/techrxiv.21988181.v1Digital Object Identifier
- Title
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Linear Neural Network as a Fast Solver for Dictionary LearningWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-02-05Full publication date if available
- Authors
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Rachana Sathish, Debdoot Sheet, Swanand KhareList of authors in order
- Landing page
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https://doi.org/10.36227/techrxiv.21988181.v1Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://doi.org/10.36227/techrxiv.21988181.v1Direct OA link when available
- Concepts
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Solver, Singular value decomposition, Computer science, Linear algebra, Speedup, Artificial neural network, Computational complexity theory, Matching pursuit, Equivalence (formal languages), Parallel computing, Algorithm, Computational science, Artificial intelligence, Mathematics, Compressed sensing, Discrete mathematics, Geometry, Programming languageTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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12Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.demonstrate | 57, 125 |
| abstract_inverted_index.equivalence | 136 |
| abstract_inverted_index.implemented | 110 |
| abstract_inverted_index.traditional | 146, 158 |
| abstract_inverted_index.coefficients | 86 |
| abstract_inverted_index.requirement. | 26 |
| abstract_inverted_index.super-linear | 20 |
| abstract_inverted_index.Specifically, | 55 |
| abstract_inverted_index.computational | 21, 100 |
| abstract_inverted_index.decomposition | 81 |
| abstract_inverted_index.synthetically | 117 |
| abstract_inverted_index.fully-connected | 60 |
| abstract_inverted_index.<p>Traditional | 0 |
| abstract_inverted_index.implementations.</p> | 165 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.00902674 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |