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We introduce a new minimization that simultaneously minimizes the squared flows and the squared differences between flows.
Wu et al. in [10] suggested a new technique (FxlogLMS) based on fair M-estimator that minimizes the squared logarithmic transformations of error signal to achieve robustness.
Parameters of a linear model can be optimized in one step that minimizes the squared (and perhaps weighted) deviation, χ 2, but in nonlinear cases such as those arising in magnetic problems, the minimization equations are generally not analytically soluble.
To find a best match, the observed foundress numbers and the simulated foundress numbers are binned in ranges: 1 3, 4 6, >6, with the best match being that which minimizes the squared deviations between observed and simulated distributions.
In particular, the output y is modeled as a linear function of the input features X by estimating the coefficient vector that minimizes the squared residual error plus the (scaled) absolute value of the coefficient weights, inducing many of the weights to go to zero, and effectively eliminating the use of that feature in prediction.
Inversions of ecosystem flow networks currently use a constrained least-squares solution which at the same time minimizes the squared norm (the sum of squares) of the reconstructed flows.
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For nonlinearly separable classes linear classifiers were optimally designed, for example, by minimizing the squared error.
The optimal power distribution can be obtained by minimizing the squared η2 in (23) with respect to λ under the constraints that (28).
We therefore minimize the squared scaled error sum E tA, ΔTA2) = Σi ei2(1+αi2) which is a weighted least squares problem in the variables (tA, ΔTA2) [79] (Fig 13B).
The Jenks method minimized the squared deviations of the class means and set boundaries where relatively large spaces between exposure metric values occurred.
Landmark configurations are translated, scaled and rotated so as to minimize the squared, summed distances between the corresponding landmarks of each individual and the mean [ 26].
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