K‑Nearest Neighbors (3‑class)

Visualize how K‑NN classifies a query point among three clusters using distance weighting.

Interactive simulation

Vote by nearest neighbors

k neighbors3.00

Query x0.52

Query y0.48

Step animation speed (ms)550.00

Active neighbors

0/3

Predicted class

Score class 0

—

Score class 1

—

Score class 2

—

Chart

Mathematical intuition

d_{euclid}(x, x_i)=\sqrt{\sum_j (x_j-x_{ij})^2}

d_{manhattan}(x, x_i)=\sum_j |x_j-x_{ij}|

\hat{y}=\arg\max_c\sum_{i\in N_k(x)} w_i\,\mathbf{1}[y_i=c]

with optional weighted votes $w_i=1/(d_i+\epsilon)$ .

Step-by-step workflow

Input → Processing → Learning → Prediction → Output

Input

Feature vector x

Processing

Compute distance to all points

Learning

Store training set (lazy)

Prediction

k‑neighbor vote

Output

Class / regression value

Loading Lab...