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K Selection Interactive Simulator

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Description

An interactive visualization demonstrating how the choice of k affects KNN decision boundaries and prediction behavior.

Learning Objectives

  • Analyze how k value affects the bias-variance tradeoff in KNN
  • Understand why k selection is critical for KNN performance
  • Observe how different k values create different decision boundaries
  • Recognize the relationship between k=1 and Voronoi diagrams

How to Use

  1. Adjust k: Use the slider to change the number of neighbors (1-25)
  2. Drag Test Point: Click and drag the red test point to see predictions change
  3. Show Voronoi: Toggle to visualize Voronoi cells when k=1
  4. Add Noise: Add outlier points to see how noise affects small k values
  5. Reset: Clear noise points and return to original data

Key Concepts

Small k (k=1)

  • High variance, low bias
  • Decision boundary follows training data closely
  • Sensitive to noise and outliers
  • Creates Voronoi diagram partitions

Large k (k>20)

  • Low variance, high bias
  • Smooth decision boundaries
  • May be too simple (underfit)
  • Less affected by individual points

Optimal k

  • Balances bias and variance
  • Often between 3-15 for many datasets
  • Should be determined by cross-validation

Interactive Features

  • Real-time Decision Boundaries: See how k affects class regions
  • Neighbor Connections: Lines show which points influence prediction
  • Vote Breakdown: See exact vote counts for each class
  • Distance Display: View distances to nearest neighbors
  • Warning Indicators: Alerts for extreme k values