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数据挖掘:支持向量机SVM

数据挖掘:支持向量机SVM

作者: Cache_wood | 来源:发表于2022-04-12 18:22 被阅读0次

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Support Vector Machines


We want to maximize: Margin = \frac{2}{||w||^2}

  • Which is equivalent to minimizing: L(w) = \frac{||w||^2}{2}

  • But subjected to the following constraints:
    f(z) = \left\{ \begin{array}{rcl} 1 & if& \vec{w}·\vec{x_i}+b\geq 1\\ -1 & if & \vec{w}·\vec{x_i}+b\leq -1\\ \end{array}\right. \\
    This is a constrained optimization problem

    • Numerical approaches to solve it.(e.g.,quadratic programming)

What if the problem is not linearly separable?

  • Introduce slack variables

    • Need to minimize
      L(w) = \frac{||w||^2}{2}+C(\sum_{i=1}^N \xi_i^k )

    • Subject to:
      f(z) = \left\{ \begin{array}{rcl} 1 & if& \vec{w}·\vec{x_i}+b\geq 1-\xi_i\\ -1 & if & \vec{w}·\vec{x_i}+b\leq -1+\xi_i\\ \end{array}\right. \\

    Nonlinear Support Vector Machines

    Transform data into higher dimensional space.

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