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Gu et al. computed fixed weights for kernels by projecting them in the maximum variance direction [20].
The first principal component (t[1]) best approximates the data in a least squares sense and represents the maximum variance direction in the data.
Thus, we relax the variability explanation ratio threshold ρ by only using the first PC to reconstruct each cD j matrix to catch the subtle data characteristics along the maximum variance direction.
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A PLS model will try to find the multidimensional direction in the X space that explains the maximum multidimensional variance direction in the Y space; that is, it will try to find the spectrum variables in X that can explain the result of burn or health in Y. PLS is particularly suited when the matrix of predictors has more variables than observations.
The essence of the analysis is to extract the information on the principal axis (or the maximum and minimum variance directions) using the spectral moments, and to interpret the spectra in the frame of random sweeping model.
The minimum variance direction provides the propagation direction of the wave.
For our simulations, we used two simple features: (i) the direction of maximum variance of the distribution of bone-contour points to extrapolate, and (ii) a characteristic point such as the farthest from the field of view border for,.
Two features were calculated on the bone-contour points: (i) the direction of maximum variance of the distribution, and (ii) the farthest point from the field of view border among the projections of the bone-contour point along the maximum variance axis.
Then, the PSD function of an equivalent normal stress is defined by considering a linear combination of the PSD functions of the normal stress and the projected shear stress along the direction of maximum variance, with such stresses acting on the critical plane.
Briefly, the aim is to determine the direction of maximum variance in the space of data points.
The first principal component points in the direction of maximum variance, the second component maximises the remaining variance and so on.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com