How to Kernelize the Ridge Regression Algorithm

The ridge regression algorithm learns a linear function to map input points to a real number by minimizing an objective function. The optimization problem in ridge regression is given by: $$ \min_{w \in \mathbb{R}^d} \frac{1}{n} \sum_{i=1}^{n} \left( Y_i - \langle w, \Phi(X_i) \rangle \right)^2 + \lambda \lVert w \rVert_2^2$$ Here, $\lambda$ denotes the tradeoff constant. The first term in the objective function is the training error (also called empirical risk of a predictor function) in terms of linear least squares error.