更改

b = \vec w \cdot \varphi(\vec x_i) - y_i &= \left[\sum_{k=1}^n c_ky_k\varphi(\vec x_k)\cdot\varphi(\vec x_i)\right] - y_i \\

b = \vec w \cdot \varphi(\vec x_i) - y_i &= \left[\sum_{k=1}^n c_ky_k\varphi(\vec x_k)\cdot\varphi(\vec x_i)\right] - y_i \\

   &= \left[\sum_{k=1}^n c_ky_kk(\vec x_k, \vec x_i)\right] - y_i.

   &= \left[\sum_{k=1}^n c_ky_kk(\vec x_k, \vec x_i)\right] - y_i.

\end{align}</math></blockquote>最后，可以通过计算下式来分类新点： <blockquote><math> \vec z \mapsto \sgn(\vec w \cdot \varphi(\vec z) + b) = \sgn\left(\left[\sum_{i=1}^n c_iy_ik(\vec x_i, \vec z)\right] + b\right).</math></blockquote>

\end{align}</math></blockquote>最后，可以通过计算下式来分类新点：

<math> \vec z \mapsto \sgn(\vec w \cdot \varphi(\vec z) + b) = \sgn\left(\left[\sum_{i=1}^n c_iy_ik(\vec x_i, \vec z)\right] + b\right).</math>

=== 现代方法 ===

=== 现代方法 ===