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How to choose the right distance metric in KNN?

Last Updated : 1 Nov, 2025

K-Nearest Neighbors (KNN) is a supervised learning algorithm that classifies new data points based on the closest existing labeled examples. To measure how “close” samples are, KNN relies on distance metrics that quantify similarity among feature values. Choosing an appropriate metric improves classification accuracy, robustness and generalization.

👁 types_of_distance_metric
Distance Metrics

Need for Right Distance Metric

Some common reasons distance metrics are important in KNN are:

  • Impacts how neighbors are selected and ranked.
  • Influences decision boundaries created by the classifier.
  • Improves handling of various data types like continuous, categorical.
  • Reduces misclassification in high-dimensional spaces.
  • Ensures fair comparison when features vary in scale.

Common Distance Metrics

👁 KNN_DISTANCES
Visualization

1. Euclidean Distance

Euclidean distance measures the straight-line distance between two points in continuous numerical space. It works best when all features are continuous and similarly scaled.

Formula:

Where, p and q are data points.

Properties

  • Sensitive to large differences in feature values.
  • Performs well on low-dimensional, normalized data.
  • Commonly used for geometric interpretation.

2. Manhattan Distance (L1 Norm)

Manhattan distance computes by summing absolute differences across dimensions. Useful when features represent directions, steps or grid-based movement.

Where p and q are data points.

Properties

  • Robust to outliers compared to Euclidean distance.
  • Preferred for high-dimensional data.
  • Works well in sparse feature environments.

3. Minkowski Distance

Minkowski Distance is generalized version of both Euclidean and Manhattan distances. Controlled by a parameter p.

Where,

  • p and q are data points,
  • When p=1: Manhattan distance,
  • When p=2: Euclidean distance.

4. Chebyshev Distance (Maximum Norm)

Chebyshev Distance measures the maximum absolute difference between two points across all features. It focuses on the largest deviation among dimensions.

Where p and q are data points.

Properties

  • Uses the maximum feature difference
  • Ignores smaller variations
  • Square-shaped distance boundary

5. Cosine Similarity

Cosine Similarity measures the angle between two vectors instead of magnitude, capturing how similar their direction is.

Formula

Where,

  • p⋅q is the dot product,
  • ∥p∥,∥q∥ are magnitudes of vectors.

Range: -1 to 1

  • 1: vectors point in the same direction (high similarity)
  • 0: vectors are orthogonal (no relation)
  • -1: vectors opposite direction (high dissimilarity)

Properties

  • Measures angle, not magnitude
  • Good for text or high-dimensional data
  • Scale-independent

Choosing the Right Distance Metric in KNN

Distance MetricWhen to Use

Not Ideal When

Use Case Scenario
Euclidean DistanceData is continuous and evenly scaled

Features vary greatly in scale

Image recognition, sensor data

Manhattan DistanceHigh-dimensional or grid-based data

Features are highly correlated

City-block routing, clustering
Minkowski DistanceNeed flexible distance tuning of parameter p

Unsure how to choose p

Generalized KNN experiments
Chebyshev DistanceMax difference matters across dimensions

Small variations are important

Chessboard moves, quality control
Cosine SimilarityAngle matters more than magnitude

Numerical size matters

Text similarity, embeddings, recommendations

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