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SVM—Linearly Separable

  • A separating hyperplane can be written as
      • WX + b = 0
    • where W={w1, w2, …, wn} is a weight vector and b a scalar (bias)
  • For 2-D it can be written as
      • w + w1 x1 + w2 x2 = 0
  • The hyperplane defining the sides of the margin:
      • H1: w + w1 x1 + w2 x2 ≥ 1 for yi = +1, and
      • H2: w + w1 x1 + w2 x2 ≤ – 1 for yi = –1
  • Any training tuples that fall on hyperplanes H1 or H2 (i.e., the sides defining the margin) are support vectors
  • This becomes a constrained (convex) quadratic optimization problem: Quadratic objective function and linear constraints → Quadratic Programming (QP) → Lagrangian multipliers

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