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Detecting Noise in Chaotic Signals through Principal Component Matrix Transformation

We study the reconstruction of continuous chaotic attractors from noisy time-series. A method of delays and principal component eigenbasis (defined by singular vectors) are used for state vectors reconstruction. We introduce a simple measure of trajectory vectors directional distribution for chosen principal component subspace, based on nonlinear transformation of principal component matrix. The value of such defined measure is dependent on the amount of noise in the data. For isotropically distributed noise (or close to isotropic), that allows us to set up window width boundaries for acceptable attractor reconstruction as a function of noise content in the data.

time series; chaotic signals; principal component analysis; PCA; singular value decomposition; SVD

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