svm-soft-margin-hinge-loss-slack-variables

IN premise — entries/2026/06/21/wiki-Support_vector_machine-chunk-2.md

Created 2026-06-21T09:55:54+00:00

Soft-margin SVM handles non-separable data by introducing slack variables zeta_i >= 0 and hinge loss max(0, 1 - y_i(w^T x_i - b)), minimizing ||w||² + C * sum(zeta_i).

Dependents

These beliefs depend on this one:

• IN svm-soft-margin-three-equivalent-views — The soft-margin SVM admits three equivalent mathematical formulations — slack variables with margin constraints, empirical risk minimization with hinge loss and Tikhonov regularization, and the C-parameter tradeoff between margin width and classification errors — all describing the same optimization from different theoretical perspectives.