Support Vector Machines (SVM) - Support Vector Classifier/Regression - Large/Maximal Margin Classifier/Regression
Support Vector Classifier
  • is a hyperplane that linearly separates data into 2 categories

SVM - Model Types

Linear SVM
(SVM Without Kernel)

  • when data are 1 dimensional then the Support Vector Classifier is a point (a flat affine of 0 dimensional subspace)
  • when data are 2 dimensional then the Support Vector Classifier is a line (a flat affine of 1 dimensional subspace)
  • when data are 3 dimensional then the Support Vector Classifier is a plane (a flat affine of 2 dimensional subspace)
  • when data are 𝑛 dimensional then the Support Vector Classifier is a hyperplane (a flat affine of 𝑛-1 dimensional subspace)

main idea:

  • start data at 𝑛 dimension
  • find a (hard-margin-classifier or soft-margin-classifier) that separates the 2 categories

Non-Linear SVM
(SVM With Kernel)

When there is no obvious linear classifier that separates data in a nice way Non-Linear SVM works by transforming data into a high dimensional space then finding the Support Vector Classifier

main idea:

  • start data at 𝑛 dimension
  • transform data into 𝑛+𝑘 dimension (using kernel functions)
  • find a (hard-margin-classifier or soft-margin-classifier) that separates the 2 categories

Hard-Margin SVM

  • super sensitive to outliers
  • does not work when groups overlap
  • considers only the edge between groups and computes the midpoint

Soft-Margin SVM

  • less sensitive to outliers
  • works when groups overlap

SVM - Model Examples

Hard Margin

Soft Margin

Linear

Non-Linear


transform data to higher dimension


transform data to higher dimension

SVM - Multi-class Classification

one-vs-all method - by training 𝑘 SVM problems (similar to multinomial logistic regression)

SVM - Other

Resources