Distance Metric Learning

Compilation of distance measures in Python.

Libraries

• Scikit-learn (Pairwise Metrics)
• SciPy (Distance Computations)
• NumPy (Linear Algebra)

List of Distances

• Sum of Absolute Difference
• Sum of Squared Difference
• Mean Absolute Error
• Mean Squared Error
• Euclidean Distance
• Chebyshev distance
• Minkowski Distance
• Canberra Distance
• Cosine Distance
• Pearson's Distance
• Hamming Distance

Distances

Sum of Absolute Differences (SAD)

• L1-norm
• Manhattan- or Taxicab-norm
• Minkowski distance with p=1
• Formula: ∑ |p_i - q_i|
• Code: SAD.py

Mean Absolute Error (MAE)

• 1/n * Sum of Absolute Difference
• Formula: ¹⁄_n * ∑ |p_i - q_i|
• Code: MAE.py

Sum of Squared Differences (SSD)

• Squared L2-norm
• Euclidean norm
• Squared Euclidean distance
• Formula: ∑ |p_i - q_i|²
• Code: SSD.py

Mean Squared Error (MSE)

• 1/n * Sum of Squared Difference
• Formula: ¹⁄_n * ∑ |p_i - q_i|²
• Code: MSE.py

Euclidean Distance

• L2-norm
• Natural distance in a geometric interpretation
• Formula: √ ∑ |p_i - q_i|²
• Code: Euclidean.py

Chebyshev Distance

• L-infinity norm
• Minkowski distance with p=infinity
• Formula: max |p_i - q_i|
• Code: Chebyshev.py

Minkowski Distance

• Lp-norm

Canberra Distance

• Weighted Manhattan distance

Cosine Distance

• Dot product scaled by product of Euclidean distances from the origin
• Represents angular distance of 2 vectors, ignoring scale

Pearson's Distance

• Correlation distance based on Pearson's product-momentum correlation coefficient of 2 sample vectors
• Measures linear relationship between 2 vectors

Hamming Distance

• No. of entries in 2 vectors which are different