2.4 Machine learning algorithms
2.4.1 Support vector
machine (SVM)
SVM has developed from the optimal classification surface in linearly
separable cases, and based on statistical learning theory, it has
excellent generalization ability in machine learning by replacing the
empirical risk minimization principle with the structural risk
minimization principle (Araghinejad, 2013) .By introducing appropriate
inner product kernel functions, the samples in the input space can be
mapped to high-dimensional spaces, thereby achieving linear
classification or regression after a certain nonlinear transformation
without increasing computational complexity (see Figure 5 (a)).
When SVM is applied to regression problems, its learning goal is to find
the best hyperplane closest to all data points at a given interval.
Given the dataset {(x1. y1),
(x2. y2), …, (xi,
yi)}, the problem can be converted into an optimization
problem under given objective functions and constraint which shows as
followed:
Where, and b are the weight coefficients and bias coefficients of the
optimal hyperplane respectively. C is the penalty factor, 、 are
introduced slack variables; is the given interval (ARNARI S, 1999;
Choubin et al., 2018; VAPNIK V, 1997) .