Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis
Analyzing signals arising from dynamical systems typically requires many modeling assumptions. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality." In this paper, we propose a method for building an intrinsic representation of such signals in a...
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| Format: | Article |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/132143 |
| _version_ | 1811084663196745728 |
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| author | Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques |
| author_facet | Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques |
| author_sort | Shnitzer, Tal |
| collection | MIT |
| description | Analyzing signals arising from dynamical systems typically requires many modeling assumptions. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality." In this paper, we propose a method for building an intrinsic representation of such signals in a purely data-driven manner. First, we apply a manifold learning technique, diffusion maps, to learn the intrinsic model of the latent variables of the dynamical system, solely from the measurements. Second, we use concepts and tools from control theory and build a linear contracting observer to estimate the latent variables in a sequential manner from new incoming measurements. The effectiveness of the presented framework is demonstrated by applying it to a toy problem and to a music analysis application. In these examples, we show that our method reveals the intrinsic variables of the analyzed dynamical systems. |
| first_indexed | 2024-09-23T12:55:05Z |
| format | Article |
| id | mit-1721.1/132143 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:55:05Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1321432022-04-01T16:27:10Z Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques Analyzing signals arising from dynamical systems typically requires many modeling assumptions. In high dimensions, this modeling is particularly difficult due to the "curse of dimensionality." In this paper, we propose a method for building an intrinsic representation of such signals in a purely data-driven manner. First, we apply a manifold learning technique, diffusion maps, to learn the intrinsic model of the latent variables of the dynamical system, solely from the measurements. Second, we use concepts and tools from control theory and build a linear contracting observer to estimate the latent variables in a sequential manner from new incoming measurements. The effectiveness of the presented framework is demonstrated by applying it to a toy problem and to a music analysis application. In these examples, we show that our method reveals the intrinsic variables of the analyzed dynamical systems. 2021-09-20T18:21:09Z 2021-09-20T18:21:09Z 2019-01-03T14:23:46Z Article http://purl.org/eprint/type/JournalArticle 1053-587X 1941-0476 https://hdl.handle.net/1721.1/132143 Shnitzer, Tal, Ronen Talmon, and Jean-Jacques Slotine. “Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis.” IEEE Transactions on Signal Processing 65, no. 4 (February 15, 2017): 904–918. doi:10.1109/tsp.2016.2616334. http://dx.doi.org/10.1109/TSP.2016.2616334 IEEE Transactions on Signal Processing Creative Commons Attribution-Noncommercial-Share Alike Attribution-NonCommercial-ShareAlike 4.0 International http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Shnitzer, Tal Talmon, Ronen Slotine, Jean-Jacques Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title | Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title_full | Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title_fullStr | Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title_full_unstemmed | Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title_short | Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis |
| title_sort | manifold learning with contracting observers for data driven time series analysis |
| url | https://hdl.handle.net/1721.1/132143 |
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