Supervised Learning: k-NN Decision Surface Sandbox

Add Labeled Examples

Click anywhere on the grid to drop a labeled point of the selected class. The model retrains instantly on every example you add.

Model: k-Nearest Neighbors

Neighbors k 3

Live Metrics

Labeled points

LOOCV accuracy

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Class A / B

0 / 0

Surface cells

How it works

Supervised learning fits a rule to labeled examples (x, y) so it can predict the label of a new x it has never seen. Here x is a point's 2D position in the feature grid and y is its class (A or B).

The model is k-Nearest Neighbors: to classify any point p, find the k training points closest to p by Euclidean distance and take a majority vote of their labels.

distance(p, xi) = √[(px−xi)² + (pz−zi)²]
ŷ(p) = majority label among the k nearest xi
confidence(p) = (votes for winning class) / k

The colored landscape is this rule evaluated on a dense grid: height and color intensity show the model's confidence, the sharp ridge between blue and red is the decision boundary. Small k gives a jagged boundary that memorizes noise (overfitting); large k smooths it into a simpler rule (underfitting if too large).

LOOCV accuracy (leave-one-out cross-validation) removes each point in turn, predicts its label from the rest, and reports the fraction correctly recovered — a genuine measure of how well the model generalizes to unseen data, not just how well it memorizes the training set.

Class A Class B

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