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Hung et al. developed a very large scale integration (VLSI) setup of wavelet-based seizure prediction algorithm using the correlation dimension (Dc) and its correlation coefficient[48].
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The analysis was performed using the correlation matrix, and the observations were visualized with the first three principal components in two and three dimensions.
The Grassberger-Procaccia algorithm and least squares regression were used to calculate the correlation dimension for the model order estimate.
Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics.
The Kolmogorov entropy, K, and the correlation dimension, D2, are used to compute the invariant properties of the corresponding attractor.
The Kolmogorov entropy, K, and the correlation dimension, D2, are used for monitoring slugging dynamics from the resulting bubble, particle and bulk time scales.
Then, the correlation dimension estimation D can be attained using least square regression.
Substitute the form of um,n into (23), we finally have R λ ≤ π − σ m, n · F − 1 1 − α 4 π sin π m − n M sin θ H (24). Therefore, in order to use the correlation interferometer algorithm based on dimension separation, the radius to wavelength ratio must satisfy (24).
Dimension D0 is usually called the fractal dimension, dimension D1 is the information dimension, while dimension D2 is called the correlation dimension.
The correlation dimension can be determined correspondingly, D = 1.7643.
The correlation dimension and correlation coefficient are estimated in the phase space as seizure prediction features.
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