The geometric margin

ProofFoundation⏱ 15 minClassical MLsvmmargingeometrydistance

Theory: Support Vector Machines — Complete Derivation →

Problem

Derive the distance from a point $x_0$ to the hyperplane $\{x:\langle w,x\rangle+b=0\}$ , and explain why the objective $\min_i y_i(\langle w,x_i\rangle+b)/\|w\|_2$ is invariant under $(w,b)\mapsto(cw,cb)$ while the numerator alone is not.

Write a complete argument. Every inequality you use should be one you could state precisely.

Solution

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

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