Part of the learning process is the selection of these positions, the cancer-related loci, by applying a sparse regularization on the c i − s edges in Figure 1.
By applying a spectral graph theoretic regularization (Chung, 1997), we developed a method to transform the feature space based on the training examples so that regularized graph energy between data points of extremely different morphology is minimized.
The "generalized skyline plot" subsequently introduced by Strimmer and Pybus [ 17] reduces the over-fitting present in the classic skyline plot by applying a simple form of regularization: adjacent intervals that alone are likely to have high stochastic noise are pooled together (cf. Fig. 2b and 2d).
In Fig. 3, we demonstrate the impact of the regularization in the classical model, Eq. (20), in the top rows, and in the natural model, Eq. (21), in the bottom rows, by applying a different scaling in the regularization term, (B=0.06), 0.3, and 0.6, respectively.
Noise regularization is obtained by applying a penalty to the image resulting from the previous iteration following the one-step late method introduced by Green [17].
By applying a semi-smooth Newton method combined with a Moreau Yosida regularization technique for handling the control constraints we show superlinear convergence in function space.
Usually, Tikhonov regularization is carried out by applying an efficient solver1 to the equation bigl alpha I + A^{ast}Abigr) g = A^{ast} y, (42) which is equivalent to the spectral version of equation (39).
Finish by applying an overglaze.
Since Cauchy problems (2.2) and (2.3) are all severely ill posed, we should apply a regularization method to solve them.
In summary, our LPFS method can select feature and learn the classifier in a joint way and we can select a small set of features by applying strong regularization.
