Manifold Learning With Contracting Observers for Data-Driven Time-Series Analysis
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1604.04492.pdf
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2.39 MB
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Author(s)
Shnitzer, Tal
Talmon, Ronen
Slotine, Jean-Jacques E
Date Issued
2016
Journal
IEEE Transactions on Signal Processing
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
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.
Version
Original manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Nonlinear Systems Laboratory
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
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DOI of Published Version
https://doi.org/10.1109/TSP.2016.2616334
