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We have tested 15 tuning methods on the case studies by comparing the regularization parameter selected by each tuning method with the optimal regularization parameter which minimizes the prediction error (i.e. the one with the best bias-variance trade-off).
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And by comparing with the traditional centralized regularization (CR), the necessity of respectively regularization for each inversing heat flux is confirmed by using different regularization parameters.
Comparing the three reconstructions for the orange flesh sample, the TV regularization shows the best reconstruction quality.
Firstly, we use Examples 1 and Examples 2 to compare the numerical effects among the truncate regularization method, the Tikhonov regularization method and quasi-boundary value regularization method under the a posteriori choice rule.
In this section we present and compare the results obtained using different regularization techniques.
A new metric is proposed to compare the distributions reconstructed from the different regularization methods with the true distributions.
We select optimal regularization parameters (α opt) by the DP, GCV, S-curve, L-curve, and the slope of L-curve methods, respectively, and compare the NMR T2 inversion results from different regularization parameter selection methods.
For both models, we fit the regularization parameters through cross-validation and compared the mean squared error on a common held-out set of 16 arrays selected by removing one array from each node with replicates.
The figure compares the true trace with the estimated ones obtained by CMMS, ℓ1, regularization, and BGMP.
By decreasing the regularization parameter, the weights of the features gradually increase, making the model more complex.
We also compared the prediction performance of the ts-RF model with linear kernel SVM, taken from LibSVM [ 2], the values of regularization parameter by factors C were 2-2 and 2-5, respectively.
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