On the Effect of Quantization on Extended Dynamic Mode Decomposition Article Swipe
Dilip Kumar Maity
,
Debdipta Goswami
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.02803
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2410.02803
Extended Dynamic Mode Decomposition (EDMD) is a widely used data-driven algorithm for estimating the Koopman Operator. EDMD extends Dynamic Mode Decomposition (DMD) by lifting the snapshot data using nonlinear dictionary functions before performing the estimation. This letter investigates how the estimation process is affected when the data is quantized. Specifically, we examine the fundamental connection between estimates of the operator obtained from unquantized data and those from quantized data via EDMD. Furthermore, using the law of large numbers, we demonstrate that, under a large data regime, the quantized estimate can be considered a regularized version of the unquantized estimate. We also explore the relationship between the two estimates in the finite data regime. We further analyze the effect of nonlinear lifting functions on this regularization due to quantization. The theory is validated through repeated numerical experiments conducted on two different dynamical systems.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2410.02803
- https://arxiv.org/pdf/2410.02803
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4403885278
All OpenAlex metadata
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https://openalex.org/W4403885278Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2410.02803Digital Object Identifier
- Title
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On the Effect of Quantization on Extended Dynamic Mode DecompositionWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-09-19Full publication date if available
- Authors
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Dilip Kumar Maity, Debdipta GoswamiList of authors in order
- Landing page
-
https://arxiv.org/abs/2410.02803Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2410.02803Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2410.02803Direct OA link when available
- Concepts
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Quantization (signal processing), Dynamic mode decomposition, Mode (computer interface), Decomposition, Computer science, Mathematics, Algorithm, Chemistry, Machine learning, Human–computer interaction, Organic chemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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