How to resolve the algorithm Jaro similarity step by step in the Julia programming language

Published on 22 June 2024 08:30 PM
#Julia

How to resolve the algorithm Jaro similarity step by step in the Julia programming language

Table of Contents

Problem Statement

The Jaro distance is a measure of edit distance between two strings; its inverse, called the Jaro similarity, is a measure of two strings' similarity: the higher the value, the more similar the strings are. The score is normalized such that   0   equates to no similarities and   1   is an exact match.

The Jaro similarity

d

j

{\displaystyle d_{j}}

of two given strings

s

1

{\displaystyle s_{1}}

and

s

2

{\displaystyle s_{2}}

is Where:

Two characters from

s

1

{\displaystyle s_{1}}

and

s

2

{\displaystyle s_{2}}

respectively, are considered matching only if they are the same and not farther apart than

⌊

max (

|

s

1

|

,

|

s

2

|

)

2

⌋

− 1

{\displaystyle \left\lfloor {\frac {\max(|s_{1}|,|s_{2}|)}{2}}\right\rfloor -1}

characters. Each character of

s

1

{\displaystyle s_{1}}

is compared with all its matching characters in

s

2

{\displaystyle s_{2}}

. Each difference in position is half a transposition; that is, the number of transpositions is half the number of characters which are common to the two strings but occupy different positions in each one.

Given the strings

s

1

{\displaystyle s_{1}}

DWAYNE   and

s

2

{\displaystyle s_{2}}

DUANE   we find:

We find a Jaro score of:

Implement the Jaro algorithm and show the similarity scores for each of the following pairs:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Jaro similarity step by step in the Julia programming language

Function Definition:

  • The code defines a function named jarodistance that calculates the Jaro-Winkler distance between two strings, s1 and s2.
  • The Jaro-Winkler distance is a measure of string similarity that weights common prefixes and transpositions more heavily than other mismatches.

Function Implementation:

  • Initialization: The function initializes three variables: m (number of matches), t (number of transpositions), and p (number of matching prefixes).
  • Match Search: It iterates over each character in s1 and s2. For each pair of characters, it checks if they match and if the difference in their positions is within a predefined "match standard" (matchstd).
    • If both conditions are met, it increments m to count a match.
    • If the characters match and their positions are the same, it increments p to count a matching prefix.
  • Transposition Calculation: It calculates t as half the difference between m and p. This counts the number of transpositions, where characters are swapped in position.
  • Distance Calculation: Finally, it calculates the Jaro-Winkler distance as follows:
    • (m / length(s1) + m / length(s2) + (m - t) / m) / 3: This formula incorporates the match count, string lengths, and transposition count to produce a distance value between 0 (exact match) and 1 (no match).

Testing the Function:

  • The code includes three @show statements that demonstrate the usage of the jarodistance function with different string pairs:
    • "MARTHA", "MARHTA": High similarity, small distance
    • "DIXON", "DICKSONX": Moderate similarity, larger distance
    • "JELLYFISH", "SMELLYFISH": Low similarity, large distance

Source code in the julia programming language

function jarodistance(s1, s2)
    m = t = p = 0
    matchstd = max(length(s1), length(s2)) / 2 - 1
    for (i1, c1) in enumerate(s1)
        for (i2, c2) in enumerate(s2)
            (c1 == c2) && (abs(i2 - i1) ≤ matchstd) && (m += 1)
            (c1 == c2) && (i2 == i1) && (p += 1)
        end
    end
    t = (m - p) / 2
    1 / 3 * (m / length(s1) + m / length(s2) + (m - t) / m)
end

@show jarodistance("MARTHA", "MARHTA")
@show jarodistance("DIXON", "DICKSONX")
@show jarodistance("JELLYFISH", "SMELLYFISH")

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