Anomaly Detection #2

One-Class SVM

  • OC-SVM

Best for: Novelty detection on smaller datasets Aliases: OC-SVM

How it works

$$\min_{w,\rho}\ \tfrac{1}{2}\|w\|^2-\rho+\frac{1}{\nu n}\sum_{i=1}^{n}\max(0,\,\rho-w^\top\phi(x_i))$$

Maps the data into a high-dimensional feature space via $\phi$ and separates it from the origin by maximising the margin $\rho$ slackened by a hinge term, $\min_{w,\rho}\tfrac{1}{2}\|w\|^2-\rho+\frac{1}{\nu n}\sum_i\max(0,\rho-w^\top\phi(x_i))$. The hyperparameter $\nu\in(0,1]$ upper-bounds the training error fraction and lower-bounds the support fraction, trading false alarms for misses. A point is anomalous when $w^\top\phi(x)<\rho$, and the kernel trick makes the boundary nonlinear.

When to use

Novelty detection on smaller, well-behaved datasets where you can describe ’normal’ as a tight region.

Watch out

O(n^2+) training cost — doesn’t scale; nu and kernel choice matter; sensitive to feature scaling.

Common fields

Manufacturing · security · quality control