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The vector x i,2 and the matrix of regularized coefficients (bar {boldsymbol {Gamma }}=(bar {boldsymbol {gamma }}_{1},dots,bar {boldsymbol {gamma }}_{g})) represent the daily variation and are present only if g > 0. The discussion of model (1b) is essentially identical, and hence this appendix focuses exclusively on Eq. 1a.
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For the within-class scatter matrix, a regularized version of that in [27] is used: (18).
The regularized covariance matrix of k th class is (12).
Here, we computed the partial correlations using the shrinkage estimation method, a form of regularized estimator of the covariance matrix and its inverse (Schafer and Strimmer, 2005 ).
First, the solutions of regularized ELM (RELM) and kernelized ELM (KELM) using the matrix Cholesky factorization are introduced; then the recursive method for calculating Cholesky factor of involved matrix in RELM and KELM is designed when RELM and KELM are applied to train SLFN online; consequently, the CF-FORELM and CF-FOKELM are obtained.
The coupling to the fluid is accomplished by the use of the method of regularized Stokeslets for the force and regularized rotlets for the torque.
The first algorithm is based on a tensor product of regularized one-dimensional delta functions.
A symmetric version of regularized long wave equation (SRLWE), (1.1).
Moreover, the accuracy of regularized solution is estimated.
The results of regularized estimation are given in Table 3.
Fig. 4 Jackknife of regularized training gain for Adinandra griffithii.
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