elasticsearch fuzzy matching max_expansions & min_similarity

I'm using fuzzy matching in my project mainly to find misspellings and different spellings of the same names. I need to exactly understand how the fuzzy matching of elastic search works and how it uses the 2 parameters mentioned in the title.

As I understand the min_similarity is a percent by which the queried string matches the string in the database. I couldn't find an exact description of how this value is calculated.

The max_expansions as I understand is the Levenshtein distance by which a search should be executed. If this actually was Levenshtein distance it would have been the ideal so开发者_运维知识库lution for me. Anyway, it's not working for example i have the word "Samvel"

queryStr      max_expansions         matches?
samvel        0                      Should not be 0. error (but levenshtein distance   can be 0!)
samvel        1                      Yes
samvvel       1                      Yes
samvvell      1                      Yes (but it shouldn't have)
samvelll      1                      Yes (but it shouldn't have)
saamvelll     1                      No (but for some weird reason it matches with Samvelian)
saamvelll     anything bigger than 1 No

The documentation says something I actually do not understand:

Add max_expansions to the fuzzy query allowing to control the maximum number 
of terms to match. Default to unbounded (or bounded by the max clause count in 
boolean query).

So can please anyone explain to me how exactly these parameters affect the search results.

The min_similarity is a value between zero and one. From the Lucene docs:

For example, for a minimumSimilarity of 0.5 a term of the same length 
as the query term is considered similar to the query term if the edit 
distance between both terms is less than length(term)*0.5

The 'edit distance' that is referred to is the Levenshtein distance.

The way this query works internally is:

• it finds all terms that exist in the index that could match the search term, when taking the min_similarity into account
• then it searches for all of those terms.

You can imagine how heavy this query could be!

To combat this, you can set the max_expansions parameter to specify the maximum number of matching terms that should be considered.