Distance Functions

Comprehensive collection of distance and similarity measures for various application areas

Geometric Distances

Euclidean Distance
Standard distance in 2D/3D space, L₂-norm for geometric calculations
Manhattan Distance
Taxicab distance, L₁-norm for grid-based navigation and robust statistics
Minkowski Distance
Generalized Lₚ-norm, encompasses Manhattan, Euclidean and Chebyshev
Maximum Norm (Chebyshev)
L∞-norm, chessboard distance for worst-case scenarios

Statistical Distances

Correlation Coefficient
Pearson correlation for linear relationships between variables
Bray-Curtis Distance
Ecological distance for species abundance and biodiversity analysis
Canberra Distance
Weighted distance for positive values with relative scaling

Similarity Measures

Cosine Similarity
Angle-based similarity for vectors, independent of magnitude

Text and String Distances

Levenshtein Distance
Edit distance for texts, spell checking and DNA sequences

About Distance Functions

Distance functions are mathematical tools for measuring similarity or dissimilarity between objects, points or datasets. They form the foundation for many algorithms in:

  • Machine Learning - k-NN, Clustering
  • Data Analysis - Similarity search
  • Bioinformatics - Sequence comparisons
  • Image Processing - Feature matching
  • Text Analysis - Document similarity
  • Geometry - Spatial calculations
Tip: The choice of the right distance function depends on your data and the desired application. Euclidean distance for geometric problems, Manhattan for robust statistics, cosine similarity for high-dimensional data.