Sajini Anand - Academia.edu (original) (raw)
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Technische Hochschule Köln (Cologne University of Applied Sciences)
Jawaharlal Nehru Technological University Anantapur
Jawaharlal Nehru Technological University Anantapur
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Papers by Sajini Anand
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD with the help of data generated from nonlinear maps and flows (differential equations). The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper also demonstrates an application of nonlinear SVD to cryptanalysis where the encrypted signal is generated by a nonlinear transformation. A comparison of the method for both noise-free and noisy data along with their surrogate counterparts is included.
Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively ... more Singular Value Decomposition (SVD) is a powerful tool in linear algebra and has been extensively applied to Signal Processing, Statistical Analysis and Mathematical Modeling. We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD with the help of data generated from nonlinear maps and flows (differential equations). The method is to augment the embedding matrix with additional nonlinear columns derived from the initial embedding vectors and extract the nonlinear relationship using SVD. The paper also demonstrates an application of nonlinear SVD to cryptanalysis where the encrypted signal is generated by a nonlinear transformation. A comparison of the method for both noise-free and noisy data along with their surrogate counterparts is included.