《統計學習方法》學習之三：SVM

阿新 • • 發佈：2018-12-23

一、SVM原理

線性可分支援向量機

$\begin{aligned} (37) & min_{α} & \frac{1}{2} \sum_{i = 1}^{N} \sum_{j = 1}^{N} α_{i} α_{j} y_{i} y_{j} (x_{i} \cdot x_{j}) - \sum_{i = 1}^{N} α_{i} \\ (38) & s . t . & \sum_{i = 1}^{N} α_{i} y_{i} = 0 \\ (39) & 0 \leq α_{i}, i = 1, 2, \dots, N \end{aligned}$
線性支援向量機

$\begin{aligned} (40) & min_{α} & \frac{1}{2} \sum_{i = 1}^{N} \sum_{j = 1}^{N} α_{i} α_{j} y_{i} y_{j} (x_{i} \cdot x_{j}) - \sum_{i = 1}^{N} α_{i} \\ (41) & s . t . & \sum_{i = 1}^{N} α_{i} y_{i} = 0 \\ (42) & 0 \leq α_{i} \leq C, i = 1, 2, \dots, N \end{aligned}$
非線性支援向量機

$\begin{aligned} (43) & min_{α} & \frac{1}{2} \sum_{i = 1}^{N} \sum_{j = 1}^{N} α_{i} α_{j} y_{i} y_{j} K (x_{i}, x_{j}) - \sum_{i = 1}^{N} α_{i} \\ (44) & s . t . & \sum_{i = 1}^{N} α_{i} y_{i} = 0 \\ (45) & 0 \leq α_{i} \leq C, i = 1, 2, \dots, N \end{aligned}$