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You searched for subject:(matrix nonlinearity). Showing records 1 – 2 of 2 total matches.

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University of Minnesota

1. Yang, Bo. Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements.

Degree: PhD, Electrical Engineering, 2019, University of Minnesota

The past few decades have seen a rapid expansion of our digital world. While early dwellers of the Internet exchanged simple text messages via email, modern citizens of the digital world conduct a much richer set of activities online: entertainment, banking, booking for restaurants and hotels, just to name a few. In our digitally enriched lives, we not only enjoy great convenience and efficiency, but also leave behind massive amounts of data that offer ample opportunities for improving these digital services, and creating new ones. Meanwhile, technical advancements have facilitated the emergence of new sensors and networks, that can measure, exchange and log data about real world events. These technologies have been applied to many different scenarios, including environmental monitoring, advanced manufacturing, healthcare, and scientific research in physics, chemistry, bio-technology and social science, to name a few. Leveraging the abundant data, learning-based and data-driven methods have become a dominating paradigm across different areas, with data analytics driving many of the recent developments. However, the massive amount of data also bring considerable challenges for analytics. Among them, the collected data are often high-dimensional, with the true knowledge and signal of interest hidden underneath. It is of great importance to reduce data dimension, and transform the data into the right space. In some cases, the data are generated from certain generative models that are identifiable, making it possible to reduce the data back to the original space. In addition, we are often interested in performing some analysis on the data after dimensionality reduction (DR), and it would be helpful to be mindful about these subsequent analysis steps when performing DR, as latent structures can serve as a valuable prior. Based on this reasoning, we develop two methods, one for the linear generative model case, and the other one for the nonlinear case. In a related setting, we study parameter estimation under unknown nonlinear distortion. In this case, the unknown nonlinearity in measurements poses a severe challenge. In practice, various mechanisms can introduce nonlinearity in the measured data. To combat this challenge, we put forth a nonlinear mixture model, which is well-grounded in real world applications. We show that this model is in fact identifiable up to some trivial indeterminancy. We develop an efficient algorithm to recover latent parameters of this model, and confirm the effectiveness of our theory and algorithm via numerical experiments.

Subjects/Keywords: clustering; dimensionality reduction; identifiability; matrix factorization; nonlinearity; unsupervised learning

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Yang, B. (2019). Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/206423

Chicago Manual of Style (16th Edition):

Yang, Bo. “Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements.” 2019. Doctoral Dissertation, University of Minnesota. Accessed January 17, 2020. http://hdl.handle.net/11299/206423.

MLA Handbook (7th Edition):

Yang, Bo. “Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements.” 2019. Web. 17 Jan 2020.

Vancouver:

Yang B. Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements. [Internet] [Doctoral dissertation]. University of Minnesota; 2019. [cited 2020 Jan 17]. Available from: http://hdl.handle.net/11299/206423.

Council of Science Editors:

Yang B. Unsupervised Learning of Latent Structure from Linear and Nonlinear Measurements. [Doctoral Dissertation]. University of Minnesota; 2019. Available from: http://hdl.handle.net/11299/206423


University of Lund

2. Jönsson, Ulf. Robustness Analysis of Uncertain and Nonlinear Systems.

Degree: 1996, University of Lund

Control design is often done based on simplified models. After design it is necessary to verify that the real closed loop system behaves well. This is mostly done by experiments and simulations. Theoretical analysis is an important complement to this that can help to verify critical cases. Structural information about uncertainties, time-variations, nonlinearities, and signals can be described by integral quadratic constraints. The information provided by these constraints can be used to reduce conservatism in analysis of robust stability and robust performance. This thesis treats several aspects of this method for robustness analysis. It is shown how the Popov criterion can be used in combination with other integral quadratic constraints. A new Popov criterion for systems with slowly time-varying polytopic uncertainty is obtained as a result of this. A corresponding result for systems with parametric uncertainty is also derived. The robustness analysis is in practice a problem of finding the most appropriate integral quadratic constraint. This can be formulated as a convex but infinite-dimensional optimization problem. The thesis introduces a flexible format for computations over finite-dimensional subspaces. The restricted optimization problem can generally be formulated in terms of linear matrix inequalities. Duality theory is used to obtain bounds on the computational conservatism. A class of problems is identified for which the dual is particularly attractive.

Subjects/Keywords: Reglerteknik; LInear matrix inequalities; Control systems; Nonlinearity; Uncertainty; Popov criterion; Duality; Convex optimization; Multipliers; Robust stability; Robust performance; Automation; robotics; control engineering; Automatiska system; robotteknik; reglerteknik

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Jönsson, U. (1996). Robustness Analysis of Uncertain and Nonlinear Systems. (Doctoral Dissertation). University of Lund. Retrieved from http://lup.lub.lu.se/record/17770 ; http://portal.research.lu.se/ws/files/4661414/8840257.pdf

Chicago Manual of Style (16th Edition):

Jönsson, Ulf. “Robustness Analysis of Uncertain and Nonlinear Systems.” 1996. Doctoral Dissertation, University of Lund. Accessed January 17, 2020. http://lup.lub.lu.se/record/17770 ; http://portal.research.lu.se/ws/files/4661414/8840257.pdf.

MLA Handbook (7th Edition):

Jönsson, Ulf. “Robustness Analysis of Uncertain and Nonlinear Systems.” 1996. Web. 17 Jan 2020.

Vancouver:

Jönsson U. Robustness Analysis of Uncertain and Nonlinear Systems. [Internet] [Doctoral dissertation]. University of Lund; 1996. [cited 2020 Jan 17]. Available from: http://lup.lub.lu.se/record/17770 ; http://portal.research.lu.se/ws/files/4661414/8840257.pdf.

Council of Science Editors:

Jönsson U. Robustness Analysis of Uncertain and Nonlinear Systems. [Doctoral Dissertation]. University of Lund; 1996. Available from: http://lup.lub.lu.se/record/17770 ; http://portal.research.lu.se/ws/files/4661414/8840257.pdf

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