Classification Algorithms Arena

Classifier

k (neighbours) 5

Class separation 2.6

Decision threshold 0.50

Accuracy

–

AUC

–

TPR (recall)

–

FPR

–

ROC curve

FPR →AUC = –

How it works

Both algorithms answer the same question — "what's the probability this point is class 1?" — from opposite directions. k-NN looks locally: it finds the k closest training points to a query and returns the fraction that belong to class 1, with no training step at all. Logistic Regression looks globally: it fits one straight decision line by gradient descent, squashing a weighted sum of the coordinates through a sigmoid so the output always reads as a probability.

k-NN:      P(y=1|x) = (1/k) · Σ 1[yᵢ=1] over the k nearest xᵢ
LogReg:    P(y=1|x) = σ(w·x + b),  σ(z) = 1/(1+e⁻ᶻ)
           w,b updated by  w -= η·∇L(w,b)  each epoch

The terrain's height at every point in the plane is that predicted probability — a literal probability surface. The translucent plane is the decision threshold: wherever it slices through the terrain marks the boundary the classifier draws in feature space. Raise the threshold and fewer points get called positive (higher precision, lower recall); lower it and the opposite happens.

The ROC curve sweeps that threshold from 0 to 1 and plots the true-positive rate against the false-positive rate at each value — the diagonal is a coin flip, and the curve's area (AUC, computed here by trapezoidal integration over the real scores) is the probability a random positive point outscores a random negative one, independent of any single threshold choice.

k — larger k smooths the k-NN surface into gentler probability gradients; k=1 makes sharp, jagged, overfit boundaries around single points.
Class separation — pulls the two Gaussian blobs apart or together and retrains logistic regression on the new sample, changing how achievable a high AUC is.
Decision threshold — moves the sea-level plane and instantly recolours which spheres count as correctly classified (dimmed) versus misclassified (bright yellow ring).

True class 0 True class 1 Misclassified

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.