K-Nearest Neighbors

Updated 02 Oct 2026

•
What it is
- •
  predicts from the labeled training observations closest to a query point
•
Classification
- •
  choose $k$ , compute distances, select the $k$ nearest observations, and combine their labels, often by majority vote.
- •
  distance weighting is an alternative to equal voting.
•
Checked example
- •
  query $(6,4)$ ; training points are $P_1=(4,2)$ on time, $P_2=(8,5)$ late, $P_3=(5,3)$ on time, and $P_4=(7,4)$ late.
- •
  distances are $\sqrt8,\sqrt5,\sqrt2,1$ respectively.
- •
  for $k=3$ , neighbors are $P_4,P_3,P_2$ : two “late” votes, so predict “late.”
•
Limitations
- •
  sensitive to feature scaling, distance choise, irrelevant features, and the choice of $k$
•
Related
- •
  Euclidean Distance
- •
  Unavailable reference

Linked references 1