Support Vector Machine
An SVM finds the maximum-margin hyperplane for classification, achieving nonlinearity via the kernel trick; the solution is determined by the support vectors.
Purpose
To provide a strong method for small-sample, high-dimensional, nonlinear classification with generalization guarantees.
Mechanism
Maximize the margin 2/||w||, equivalent to minimizing ||w||^2/2 subject to y_i(w·x_i+b)≥1. The kernel trick K(x,z)=φ(x)·φ(z) implicitly maps to high dimensions. The soft-margin parameter C balances margin and misclassification.
Use cases
- Classification problems
- Small samples, high dimensions
- Nonlinear classification
Related terms
Vector
A vector is a quantity with magnitude and direction, represented as an ordered array of numbers, supporting addition, scalar multiplication, dot products, and cross products; it is the foundation of physics and geometry. GLOSSARY
Cosine Similarity
Cosine similarity measures the cosine of the angle between two vectors, ignoring vector length; it is widely used for text-vector similarity computation. GLOSSARY