stem/AI/Classification/Supervised/SVM.md

Towards Data Science: SVM Towards Data Science: SVM an overview

• Dividing line between two classes
  • Optimal hyperplane for a space
  • Margin maximising hyperplane
• Can be used for
  • Classification
    • SVC
  • Regression
    • SVR
• Alternative to Eigenmodels for supervised classification
• For smaller datasets
  • Hard to scale on larger sets

• Support vector points

  • Closest points to the hyperplane
  • Lines to hyperplane are support vectors

• Maximise margin between classes

• Take dot product of test point with vector perpendicular to support vector

• Sign determines class

Pros

• Linear or non-linear discrimination
• Effective in higher dimensions
• Effective when number of features higher than training examples
• Best for when classes are separable
• Outliers have less impact

Cons

• Long time for larger datasets
• Doesn’t do well when overlapping
• Selecting appropriate kernel

Parameters

• C
  • How smooth the decision boundary is
  • Larger C makes more curvy
  • 
• Gamma
  • Controls area of influence for data points
  • High gamma reduces influence of faraway points

Hyperplane

\beta_0+\beta_1X_1+\beta_2X_2+\cdot\cdot\cdot+\beta_pX_p=0

• $p$-dimensional space
• If $X$ satisfies equation
  • On plane
• Maximal margin hyperplane
• Perpendicular distance from each observation to given plane
  • Best plane has highest distance
• If support vector points shift
  • Plane shifts
  • Hyperplane only depends on the support vectors
    • Rest don't matter

Linearly Separable

• Not linearly separable
• Add another dimension
  • z=x^2+y^2
• Square of the distance of the point from the origin
• Now separable
• Let z=k
  • $k$ is a constant
• Project linear separator back to 2D
  • Get circle