Image credit for formulas: Maarten Grootendorst [2]
Euclidean distance
Distance between two series.
Manhattan distance
Distance between two series.
Chebyshev distance
Distance between two series. Chebyshev distance has limited applicability.
Minkowski distance
This is the general formula that covers Euclidean, Manhattan and Chebyshev formulas for distance.
- p=1 — Manhattan distance
- p=2 — Euclidean distance
- p=∞ — Chebyshev distance
Cosine distance
Distance between two vectors
Jaccard distance
Jaccard index is the total number of similar entities between sets divided by the total number of entities. Jaccard distance is 1 minus Jaccard index.
Sorensen-Dice distance
Sørensen-Dice index is a measure of overlap between two sets
Haversine distance
Distance between two points on a sphere given their longitudes and latitudes.
Distance in flat space-time (“proper distance” in Special Relativity)
https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/spacetime/index.html
Distance in curved space-time (General Relativity)
Hamming distance
This is a measure of distance between two bit strings of equal length. Hamming distance is the number of values that are different between the two strings.
Log-Spectral distance
https://en.wikipedia.org/wiki/Log-spectral_distance
Chi-square distance
Chi-square distance is a measure of dissimilarity between two histograms and has been widely used in various applications such as image retrieval, texture and object classification, and shape classification.
https://stats.stackexchange.com/questions/184101/comparing-two-histograms-using-chi-square-distance
Pearson correlation coefficient
This is the most commonly used similarity measure, simply known as “correlation”
https://en.wikipedia.org/wiki/Pearson_correlation_coefficient
Mahalanobis distance
https://en.wikipedia.org/wiki/Mahalanobis_distance
Canberra distance
https://en.wikipedia.org/wiki/Canberra_distance
Bray-Curtis distance
https://en.wikipedia.org/wiki/Bray%E2%80%93Curtis_dissimilarity
Kullback–Leibler distance
https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence
Other correlation measures
Eisen cosine correlation distance, Spearman correlation distance, Kendall correlation distance [4]
Others
There is more, I am sure 🙂
References
[1] Jason Brownlee , “4 Distance Measures for Machine Learning“
[2] Maarten Grootendorst, “9 Distance Measures in Data Science“
[3] McCune and Grace, Chapter 6
[4] https://www.datanovia.com/en/lessons/clustering-distance-measures/
Suresh Emre
Renaissance Universal 