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Training minimizes the regularized cost function [38] (7).
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From the combination of these, the goal is to learn the kernel mapping of the instances and the kernelized prediction model as to minimize the regularized training losses in both domains.
The factor matrices (P) and (Q) are learned by minimizing the regularized squared error on the set of observed affinities (kappa): mathop {min}limits_{Q,P} mathop sum limits_{{(d_{i},t_{j} ) in kappa }}^ (m_{i,j} - q_{i}^{T} p_{j} )^{2} + lambda (||p||^{2} + ||q||^{2} ).
They can be assessed by minimizing the regularized risk function Rleft( w right) = frac{1}{2}left| {left| w right|} right|^{2} + Csumlimits_{i = 1}^{l} {L_{e} left( {y_{i},fleftt( {x_{i} } right)} right)} (20)Where (frac{1}{2}left| {left| w right|} right|^{2}) is used as a measurement of function flatness.
The proposed image enhancement method estimates the contrast enhanced image by minimizing the regularized retinex model as begin{array}{ll} argunderset{f_{R},f_{L}}min ; &left | f_{R}f_{L}-g right |^{2}_{2} +lambda_{1}left | nabla f_{L} right |^{2}_{2} &qquad +lambda_{2}left | nabla f_{R} right |_{1} +lambda_{3}left | f_{L}-hat{g}_{b} right |^{2}_{2}, end{array} (10).
In an empirical Bayesian framework, the "optimal" weights are those that maximize the conditional posterior density P(w| D, α, β, M), which is equivalent to minimizing the regularized objective function F in equation (5).
Maximizing the logarithm of a posteriori probability is equivalent to minimizing the ℓ1-regularized error function if Laplacian prior is applied.
We estimated parameters β0,…, β k from training data by minimizing the L2-regularized log-likelihood: 1 2 β T β + C ∑ i = 1 n log 1 + e − Rec i β T d i (4).
The regularized criterion is minimized with a hierarchical alternating least squares (HALS) scheme.
For robust eigenphone matrix estimation, the regularized objective function to be minimized is as following: Q′ ( V ) = Q ( V ) + J ( V ), (8).
To solve this problem, the proposed method simultaneously estimates the optimal illumination and reflectance components by minimizing the Retinex-based regularized energy functional to suppress noise amplification during brightness enhancement process.
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