The phrase "as a regularized" is not correct in English as it is incomplete and lacks context.
It could potentially be used in a context discussing a process or method that has been standardized or made regular.
Example: "The data was analyzed as a regularized approach to ensure consistency in the results."
Alternatives: "in a standardized manner" or "as a standardized process".
Gradient theories, as a regularized continuum mechanics approach, have found wide applications for modeling strain localization failure process.
In such settings, a general approach to estimation is to solve a regularized convex program (known as a regularized $M$-estimator) which combines a loss function (measuring how well the model fits the data) with some regularization function that encourages the assumed structure.
The corrector update can be derived as a regularized LS criterion, which will also be useful to account for the sparsity attribute.
For any (alpha>0), the unique solution (f_{alpha}^{delta,n}) of (47) is considered as a regularized solution of (f^{dagger,n,delta}). Without loss of generality, we can assume that (operatorname {dim}(mathcal{R}( K_{n}^) ) =n+1).
In this section by using an approach due to Fukushima [8], we construct another gap function associated with problem SVMQVIP (1.1), which can be viewed as a regularized gap function.
This distance metric learning problem is posed as a regularized optimization problem (see Materials and Methods).
As regards numerical stability, a regularized adaptation is necessary to simulate high Reynolds number flows.
As a further application, a regularized trace for the operators π(f) can be defined, yielding a distribution on G which can be interpreted as a global character of π, and is given by a fixed point formula analogous to the Atiyah Bott character formula for an induced representation of G.
Signal recovery problem in compressed sensing can be mathematically modeled as a ℓ0 regularized problem, which aims at searching a sparse solution.
In contrast, by using an overcomplete dictionary approach we effectively linearize the forward model and solve the moving target problem as a larger, regularized inversion problem subject to sparsity constraints.
As a sparsely regularized model for comparison, we used L p -regularized LR(L p LR) (Liu et al., 2007) whose effectiveness has been demonstrated on expression microarray data.
