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difficulty 4/5

SVM

Definition

A classifier that places its boundary to leave the widest possible gap between the classes, with only the points on the edge of that gap deciding where it goes.

Formula
min⁡w,b  12∥w∥2s.t.yi(w⋅xi+b)≥1\min_{w,b} \; \tfrac{1}{2}\|w\|^2 \quad \text{s.t.} \quad y_i(w \cdot x_i + b) \ge 1

Intuition

If two classes can be separated by a straight line, there are infinitely many straight lines that do it. Logistic regression picks one by maximising likelihood. SVM asks a different question: which line leaves the widest gap?

The intuition is that a boundary squeezed against the data is fragile — nudge a point and it misclassifies. A boundary sitting in the middle of the widest possible corridor has the most room to be wrong about new data: "a slight error in measurement or a slight document variation will not cause a misclassification" [1, §15.1].

Formal definition

How it works

Where it's used

Why & when

Worked example

Pitfalls

Check yourself

3 questions

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Sources

  1. Manning, Raghavan, Schütze. Introduction to Information Retrieval — Support vector machines (2008)book · retrieved 2026-10-07https://nlp.stanford.edu/IR-book/html/htmledition/support-vector-machines-and-machine-learning-on-documents-1.html
  2. Goodfellow, Bengio, Courville. Deep Learning (2016)book · retrieved 2026-10-07https://www.deeplearningbook.org/contents/ml.html
  3. scikit-learn — SVCdocs · retrieved 2026-10-07https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html

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