← Mathematics for Machine Learning

Learn / Mathematics for Machine Learning

12 - Classification with Support Vector Machines

Advanced mastery of Chapter 12, covering every named section and exercise-style synthesis across book pages 370-392.

Learning path

0%

0 of 4 sections marked complete · about 42 minutes

Learning objectives

What you will be able to explain

  • Separating hyperplanes
  • Point-to-hyperplane distance
  • Hard-margin primal
  • Soft-margin SVM
  • Primal components
  • Dual SVM anatomy

Section 01

Separating hyperplanes to Hard-margin primal

01

Separating hyperplanes

Joint positive scaling preserves the boundary but changes functional margins.

Guided checkpoint

For wTx+b=0w^Tx+b=0.

Source: Sec. 12.1, pp. 372-374

02

Point-to-hyperplane distance

Distance is ∣−5∣/5=1|-5|/5=1.

Guided checkpoint

For w=[3,4]Tw=[3,4]^T, b=−5b=-5, and x=[0,0]Tx=[0,0]^T, compute distance to the hyperplane.

Source: Sec. 12.1, pp. 372-374

03

Hard-margin primal

Minimizing weight norm maximizes geometric margin under canonical scaling.

Guided checkpoint

The canonical hard-margin objective is:

Source: Sec. 12.2, pp. 374-383

Section 02

Soft-margin SVM to Dual SVM anatomy

01

Soft-margin SVM

Soft margin handles overlap and outliers.

Guided checkpoint

Judge each claim.

Source: Sec. 12.2, pp. 374-383

02

Primal components

Only points with active constraints affect the boundary directly.

Guided checkpoint

Match object.

Source: Sec. 12.2, pp. 374-383

03

Dual SVM anatomy

The dual depends on data only through inner products and sparse multipliers.

Guided checkpoint

Match dual feature.

Source: Sec. 12.3, pp. 383-388

Section 03

Support vectors and KKT to Kernel validity and effect

01

Support vectors and KKT

KKT conditions explain sparsity of the dual representation.

Guided checkpoint

Judge each statement.

Source: Sec. 12.3, pp. 383-388

02

Kernel trick

The dual permits implicit feature-space inner products.

Guided checkpoint

A valid kernel replaces which quantity?

Source: Sec. 12.4, pp. 388-390

03

Kernel validity and effect

Kernels define geometry without explicit high-dimensional features.

Guided checkpoint

Check each claim.

Source: Sec. 12.4, pp. 388-390

Section 04

Numerical solution to Exercise-style hinge loss

01

Numerical solution

Practical SVM training exploits convexity, sparsity, and decomposition.

Guided checkpoint

Match method concern.

Source: Sec. 12.5, pp. 390-392

02

Further-reading bridge

RKHS theory formalizes kernels as inner products over functions.

Guided checkpoint

Which theory studies kernel-induced function spaces?

Source: Sec. 12.6, p. 392

03

Exercise-style hinge loss

max(0,1−yf)=max(0,1.25)=1.25max(0,1-yf)=max(0,1.25)=1.25.

Guided checkpoint

For label y=−1y=-1 and score f(x)=0.25f(x)=0.25, compute hinge loss.

Source: Chapter 12 synthesis, pp. 370-392

Knowledge check

Turn understanding into recall.

The quiz now follows the same concepts in scored form. You can return to this lesson from the quiz whenever a gap appears.

Start the quiz →Back to course