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).
Therefore, it is possible to retrieve these spread values by minimizing the squared Frobenius norm of the difference between the model signal and the signal generated out of the image on the circular antenna.
Average residual errors for f, θ, and ϕ are obtained by considering the optimal values of ( {overset{frown }{h}}_fleft -0.821699right),{overset{frown }_fleft -0.821699right19399right),mathrm{overset{frownm {overset{frown }{h}}_{theta}left -0.919399right) in Table 3, which has been obtained by minimizing the squared residual errors of f, θ, and ϕ at the approximation m = 6 as shown in Table 2.
By minimizing the squared error ϵ between these p components and the predicted value x kc + 2τl), kc = M - 2τ + 1, M - 2τ + 2,…, M, l = 1, 2, …, L which is derived from Equation (7), the weight vector W composed of the weight coefficients w0(i), w1(i) and the constant C in Equation (7) can be estimated by the following cost function: ϵ = ∑ i = 1 p γ p - i θ i x k i - W T Z 2, (9).
In the global search, we randomly chose the initial values of these 5 variables within the range between 1/10 and 10-fold of their reference values, and optimized these values for the given ammonium concentration by minimizing the squared distance Z from the reference values.
For continuous functions, ordinary least squares (OLS) method is used which estimates model parameters by minimizing the square of the difference between actual and predicted outputs (error).
The optimal values of parameters c1, c2 and c3 are computed by minimizing the square residual error E m defined by Equation 19.
Finally, the reference signals are generated for both the coarse and fine actuators by minimizing the square integral of jerk during the transition.
