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In order to find robust and sparse solution for classification problem by using Least Square methods, we propose a novel regularized Weighted Least Square Support Vector Classifier in this paper.
Motivated by the simplicity and the applicability of the L-curve to automatically determine a regularization parameter in regularized (weighted) least-squares solutions [24,34,35], in this section, we propose to use the L-curve to automatically determine the reshaping filter length (L^{text {auto}}_{g}) in acoustic multi-channel equalization techniques.
In order to control the sparsity of solution, we further propose a regularized Weighted Least Square Support Vector Classifier model.
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The basis of the algorithm is a regularized MLR model that is solved using a penalized negative log likelihood function using iteratively regularized re-weighted least squares.
In addition, Ramirez et al. develop an iterative algorithm to solve a Lorentzian ℓ 0-regularized cost function using iterative weighted myriad filters [43].
The original sparse representation problem is regularized with a properly designed weighted ℓ1 minimization and effectively solved with existing solver.
This was achieved by low-dimensional subspace tracking through the minimization of a weighted least squares regression, regularized with a nuclear norm.
Once the spatial weights are regularized, we revert the orthogonal transform and obtain a spatial grid of regularized patterns.
Further, the TSSG tracker is novel in exploiting the sparsity present in the grid-based state vector, which allows one to leverage efficient solvers of (weighted) least-squares (LS) minimization problems regularized by the ℓ1-norm of the desired state estimate.
The weighted likelihood in the M-step is regularized by introducing a penalty term K based on the spline basis used to generate U and the roughness penalty desired by the analyst.
The right hand side of (36) was chosen by He et al. [9] to regularize the matting based on the DCP and to enforce smoothing weighted by λ.
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