Refer to 6.2.2 Kernel Ridge Regression, An Introduction to Support Vector Machines and Other Kernel-based Learning Methods, Nello Cristianini and John Shawe-Taylor
Refer to 7.3.2 Kernel Methods for Pattern Analysis, John Shawe-Taylor University of Southampton, Nello Cristianini University of California at Davis
Kernel ridge regression (KRR) combines Ridge Regression (linear least squares with l2-norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For non-linear kernels, this corresponds to a non-linear function in the original space.
The form of the model learned by Kernel Ridge is identical to support vector regression (SVR). However, different loss functions are used: KRR uses squared error loss while support vector regression uses ε-insensitive loss, both combined with l2 regularization. In contrast to SVR, fitting KernelRidge can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus slower than SVR, which learns a sparse model for ε > 0, at prediction-time. [http://scikit-learn.org/stable/modules/kernel_ridge.html]
Reference: (for SVR) https://in.mathworks.com/matlabcentral/fileexchange/63060-support-vector-regression