# What is the Jaro-Winkler distance?

by Stephen M. Walker II, Co-Founder / CEO

## What is the Jaro-Winkler distance?

The Jaro-Winkler distance is a string metric used in computer science and statistics to measure the edit distance, or the difference, between two sequences. It's an extension of the Jaro distance metric, proposed by William E. Winkler in 1990, and is often used in the context of record linkage, data deduplication, and string matching.

The Jaro-Winkler distance computes a value between 0 and 1, where 0 indicates no similarity and 1 represents identical strings. It considers the number of matching characters, the number of transpositions (swapped characters), and a scaling factor for common prefix matches. The scaling factor in Jaro-Winkler gives higher weight to prefix similarities, making it especially effective for cases where slight misspellings or prefixes are common.

The calculation involves three main steps: computing the Jaro Distance, calculating the common prefix length, and applying the Jaro-Winkler formula. The formula takes into account the Jaro Distance, and the prefix scaling factor (usually 0.1 or 0.25), and adjusts the similarity score accordingly.

The Jaro-Winkler similarity (simw) is defined as:

``````\$\$simw = simj + lp(1 – simj)\$\$
``````

where:

• simj: The Jaro similarity between two strings, s1 and s2
• l: Length of the common prefix at the start of the string (max of 4 characters)
• p: Scaling factor for how much the score is adjusted upwards for having common prefixes. Typically this is defined as p = 0.1 and should not exceed p = 0.25.

The Jaro-Winkler distance would then be defined as `1 - simw`.

## How is the jaro-winkler distance calculated?

The Jaro-Winkler distance is a measure of similarity between two strings of text. It is used to compare the similarity of words or phrases by comparing their characters. The distance is calculated as follows:

1. First, calculate the number of matching characters in both strings. Two characters are considered matching if they are the same and are not more than 2 positions away from each other.
2. Next, calculate the number of transpositions, which are pairs of characters that are out of order in one string compared to the other.
3. Finally, calculate the Jaro distance as follows: `Jaro = (matches / length1 + matches / length2 + (matches - transpositions) / matches) / 3`.
4. The Winkler modification is then applied by adding a scaling factor to the Jaro distance if the strings have a prefix match of at least 4 characters. This scaling factor is calculated as `prefix_match * (1 - Jaro) / 2`.
5. The final Jaro-Winkler distance is calculated as `Jaro + Winkler_modification`. The Jaro-Winkler distance ranges from 0 to 1, with a value of 1 indicating that the two strings are identical and a value of 0 indicating that they have no characters in common.

## More terms

### What is error-driven learning?

Error-driven learning, also known as backpropagation or gradient descent, is a machine learning algorithm that adjusts the weights of a neural network based on the errors between its predicted output and the actual output. It works by iteratively calculating the gradients of the loss function with respect to each weight, then updating the weights in the opposite direction of the gradient to minimize the error. This process continues until the error is below a certain threshold or a maximum number of iterations is reached.

### What is KL-ONE in AI?

KL-ONE is a knowledge representation system used in artificial intelligence (AI). It was developed in the early 1980s by John McCarthy and Patrick J. Hayes, and it's based on the formalism of description logics. KL-ONE is a frame language, which means it's in the tradition of semantic networks and frames.