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It then solve the problem by finding a linear hyperplane.
The generalised ROC was formed by finding a linear combination of features which gives the largest area under the ROC curve.
The PCA model compresses or simplifies high-dimensional data by finding a linear combination of the original variables so the variance is maximized and new uncorrelated variables, principal components (PC) are created.
Canonical correlation analysis (CCA) captures the common features in the different sets, by finding a linear combination of all the variables in one set which correlates maximally with a linear combination of all the variables in the other set.
Another approach is to apply support vector machines (SVMs), which attempt to avoid overfitting by finding a linear discriminant function (or generalised linear discriminant) that maximises the margin (the minimum distance of any sample point to the decision boundary) (Vapnik, 1998).
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This transformation in geometry is performed by finding a suitable linear combination of the mentioned eigenvectors.
In essence, PCA seeks to reduce the dimension of the data by finding a few orthogonal linear combinations (the principal components) of the original variables with the largest variance.
Both these techniques reduce the dimensionality of the set of regression variables by finding a small number of linear combinations of the original predictors, but the strategy for finding the linear combinations differ between the two methods.
Support vector machines (SVM) [ 30] are machine learning algorithms which can approximate non-linear functions by mapping the inputs to a high-dimensional feature space using a kernel function and then, solving a linear problem by finding a maximum margin separating hyperplane.
By finding a barrier function related to the sub-Laplacian L, we prove that the Perron solutions for linear Dirichlet problems are continuous up to the boundary.
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