Compare similarity algorithms

Question

I want to use string similarity functions to find corrupted data in my database.

I came upon several of them:

• Jaro,
• Jaro-Winkler,
• Levenshtein,
• Euclidean and
• Q-gram,

I wanted to know what is the difference between them and in what situations they work best?

Answer 1

Expanding on my wiki-walk comment in the errata and noting some of the ground-floor literature on the comparability of algorithms that apply to similar problem spaces, let's explore the applicability of these algorithms before we determine if they're numerically comparable.

From Wikipedia, Jaro-Winkler:

In computer science and statistics, the Jaro–Winkler distance (Winkler, 1990) is a measure of similarity between two strings. It is a variant of the Jaro distance metric (Jaro, 1989, 1995) and mainly[citation needed] used in the area of record linkage (duplicate detection). The higher the Jaro–Winkler distance for two strings is, the more similar the strings are. The Jaro–Winkler distance metric is designed and best suited for short strings such as person names. The score is normalized such that 0 equates to no similarity and 1 is an exact match.

Levenshtein distance:

In information theory and computer science, the Levenshtein distance is a string metric for measuring the amount of difference between two sequences. The term edit distance is often used to refer specifically to Levenshtein distance.

The Levenshtein distance between two strings is defined as the minimum number of edits needed to transform one string into the other, with the allowable edit operations being insertion, deletion, or substitution of a single character. It is named after Vladimir Levenshtein, who considered this distance in 1965.

Euclidean distance:

In mathematics, the Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, and is given by the Pythagorean formula. By using this formula as distance, Euclidean space (or even any inner product space) becomes a metric space. The associated norm is called the Euclidean norm. Older literature refers to the metric as Pythagorean metric.

And Q- or n-gram encoding:

In the fields of computational linguistics and probability, an n-gram is a contiguous sequence of n items from a given sequence of text or speech. The items in question can be phonemes, syllables, letters, words or base pairs according to the application. n-grams are collected from a text or speech corpus.

The two core advantages of n-gram models (and algorithms that use them) are relative simplicity and the ability to scale up – by simply increasing n a model can be used to store more context with a well-understood space–time tradeoff, enabling small experiments to scale up very efficiently.

The trouble is these algorithms solve different problems that have different applicability within the space of all possible algorithms to solve the longest common subsequence problem, in your data or in grafting a usable metric thereof. In fact, not all of these are even metrics, as some of them don't satisfy the triangle inequality.

Instead of going out of your way to define a dubious scheme to detect data corruption, do this properly: by using checksums and parity bits for your data. Don't try to solve a much harder problem when a simpler solution will do.