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difficulty 2/5

KNN

Definition

Classify a new point by looking at the k closest training examples and taking their majority vote — a model that stores the data instead of learning from it.

Formula
y^(x)=arg max⁡c∑i∈Nk(x)1[yi=c]\hat{y}(x) = \operatorname*{arg\,max}_{c} \sum_{i \in N_k(x)} \mathbb{1}[y_i = c]

Intuition

Ask the neighbours. To classify something new, find the k training examples closest to it and let them vote.

There is no fitting step worth the name — the model is the training set: "there is not even really a training stage or learning process" [1, §5.7.3]. That makes KNN the clearest illustration of a non-parametric method: it assumes nothing about the shape of the boundary, and so it is "often successful in classification situations where the decision boundary is very irregular" [3, §1.6].

Formal definition

How it works

Where it's used

Why & when

Worked example

Pitfalls

Check yourself

3 questions

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Sources

  1. Goodfellow, Bengio, Courville. Deep Learning (2016)book · retrieved 2026-10-07https://www.deeplearningbook.org/contents/ml.html
  2. scikit-learn — KNeighborsClassifierdocs · retrieved 2026-08-31https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html
  3. scikit-learn user guide — Nearest Neighborsdocs · retrieved 2026-10-07https://scikit-learn.org/stable/modules/neighbors.html
  4. scikit-learn — KNNImputerdocs · retrieved 2026-10-07https://scikit-learn.org/stable/modules/generated/sklearn.impute.KNNImputer.html

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