ALGORITHM - String similarity score/hash

Question

Is there a method to calculate something like general \"similarity score\" of a string? In a way that I am not comparing two strings together but rather I get some number/scores

Answer 1

TL;DR: Python BK-tree

Interesting question. I have limited experience within this field, but since the Levenshtein distance fulfills the triangle inequality, I figured that there must be a way of computing some sort of absolute distance to an origin in order to find strings in the vicinity of each other without performing direct comparisons against all entries in the entire database.

While googling on some terms related to this, I found one particularly interesting thesis: Aspects of Metric Spaces in Computation by Matthew Adam Skala.

At page 26 he discusses similarity measures based on kd-trees and others, but concludes:

However, general metric spaces do not provide the geometry required by those techniques. For a general metric space with no other assumptions, it is necessary distance-based to use a distance-based approach that indexes points solely on the basis of their distance from each other. Burkhard and Keller [35] offered one of the first such index structures, now known as a BK-tree for their initials, in 1973. In a BK-tree, the metric is assumed to have a few discrete return values, each internal node contains a vantage point, and the subtrees correspond to the different values of the metric.

A blog entry about how BK-trees work can be found here.

In the thesis, Skala goes on describing other solutions to this problem, including VP-trees and GH-trees. Chapter 6 analyses distances based on the Levenshtein edit distance. He also presents some other interesting distance metrics for strings.

I also found Foundations of Multidimensional and Metric Data Structures, which seems relevant to your question.