Non-Linear Kernel-based Support Vector Machine Algorithm

A Non-Linear Kernel-based Support Vector Machine Algorithm is an SVM training algorithm that can be implemented by a non-linear SVM training system to solve a non-linear SVM training task (to produce a non-linear SVM based on a non-linear kernel).

• Context:
  • It can be interpreted as maximizing the margin of a Non-Linear Kernel (so that the distance to the closest misclassified entity is the widest)
• Example(s):
  • ...
• Counter-Example(s):
  • Linear SVM Algorithm.
  • Logistic Regression Algorithm.
• See: Kernel-based SVM Algorithm, Discriminative Non-Linear Classifier Learning Algorithm, Linearly Separable, Quadratic Programming, Lagrange Multiplier, Karush–Kuhn–Tucker Conditions, Bias of an Estimator, Dual Problem, Maximum-Margin Hyperplane.

---

---

References

2016

• https://www.quora.com/Why-is-kernelized-SVM-much-slower-than-linear-SVM
  • QUOTE: Basically, a kernel-based SVM requires on the order of n^2 computation for training and order of nd computation for classification, where n is the number of training examples and d the input dimension (and assuming that the number of support vectors ends up being a fraction of n, which is shown to be expected in theory and in practice). Instead, a 2-class linear SVM requires on the order of nd computation for training (times the number of training iterations, which remains small even for large n) and on the order of d computations for classification.

---