Structural SVM is a variation of SVM, hereafter to be refered as SSVM

### Special prediction function of SSVM

Firstly let’s recall the normal SVM’s prediction function:

\[f(x)=sgn((ω\cdot x)+b)\]

ω is the weight vector，x is the input，b is the bias，\(sgn\) is sign function，\(f(x)\) is the prediction result.

On of SSVM’s specialties is its prediction function：

\[f_ω (x)=argmax_{y∈Υ} [ω\cdot Φ(x,y)]\]

y is the possible prediction result，Υ is y’s searching space，and Φ is some function of x and y.Φ will be a joint feature vector describes the relationship between x and y

Then for some given \(\omega\), different prediction will be made according to different x.