Support Vector Machine Learning notes (2) Hinge loss function

Hinge Loss function

For linear support vector machine learning, the model is to separate the hyperplane and the decision function,

The learning strategy is to maximize the soft interval, and the learning algorithm is convex two times programming.

The current support vector machine learning another explanation is to minimize the objective function:

The first item of the objective function is experience loss or empirical risk,

Functions are called hinge loss functions (hinge loss function).

Subscript "+" denotes a function that takes a positive value:

Theorem: The original optimization problem of linear support vector machines:

Equivalent to the optimization problem

Hinge loss function of the graph as follows, the horizontal axis is the function interval, the longitudinal axis is the loss