https://arshadhs.github.io/tags/hinge-loss/Recent content in Hinge Loss on Arshad SiddiquiHugoen-usThu, 28 May 2026 00:00:00 +0000https://arshadhs.github.io/docs/ai/maths/010-linear-algebra/07-dimensionality-reduction/15-primal-dual-perspective-for-linear-svm/Thu, 28 May 2026 00:00:00 +0000https://arshadhs.github.io/docs/ai/maths/010-linear-algebra/07-dimensionality-reduction/15-primal-dual-perspective-for-linear-svm/<h1 id="primal-and-dual-perspective-for-linear-svm"> Primal and Dual Perspective for Linear SVM <a class="anchor" href="#primal-and-dual-perspective-for-linear-svm">#</a> </h1> <p>A linear Support Vector Machine finds a hyperplane that separates two classes with the maximum possible margin.</p> <p>The primal view gives the direct geometric optimisation problem. The dual view rewrites the problem using Lagrange multipliers and reveals why only support vectors matter.</p> <blockquote class="book-hint info"> <p><strong>Key takeaway:</strong> Linear SVM maximises the margin by minimising <span> ( \frac{1}{2}|w|^2 ) </span></p> <p>subject to correct-classification constraints. The dual solution expresses <span> ( w ) </span></p>