Normalised measure

Measure is normalised if it’s values are in the range from 0 to 1 e.g.

• $0 \leq sim(x, y) \leq 1$
• $0 \leq dis(x, y) \leq 1$

If measure is normalised it is easy to convert from one to another:

• $sim(x,y) = 1 - dis(x,y)$
• $dis(x,y) = 1 - sim(x,y)$

Normalisation

There are a lot of normalisation approaches including:

• Higuera, Mico (normalisation)
• Levy et al. (normalisation)
• Li, Bo (normalisation)

Reading

• Muhammad Marwan Muhammad Fuad. “Parameter-Free Extended Edit Distance”. In: International Conference on Data Warehousing and Knowledge Discovery. Springer, 2014, pp. 465–475.
• Elzinga, Cees H. and Matthias Studer. “Normalization of Distance and Similarity in Sequence Analysis.” Sociological Methods & Research 48 (2019): 877 - 904.
• de la Higuera, Colin & Mico, Luisa. (2008). A Contextual Normalised Edit Distance. 354-361. 10.1109/ICDEW.2008.4498345.
• Moalla, Zied, Lina Fatima Soualmia, Élise Prieur-Gaston, Thierry Lecroq and Stéfan Jacques Darmoni. “Spell-checking queries by combining Levenshtein and Stoilos distances.” F1000Research 2 (2011): n. pag.
• Elzinga, Cees H.. “Distance, Similarity and Sequence Comparison.” (2014).
• Kim H. A k-mismatch string matching for generalized edit distance using diagonal skipping method. PLoS One. 2021 May 4;16(5):e0251047 . doi: 10.1371/journal.pone.0251047. PMID: 33945564; PMCID: PMC8096107.