"how numbers are stored and used in computers"

Overlap Coefficient

The Overlap coefficient is a similarity measure between two strings that compares the size of their intersection to the size of the smaller set. It is particularly useful when comparing strings of different lengths, as it normalizes the similarity score based on the smaller string.

O(m·n)

space

O(1)

O(n)·O(n)

Cosine distance

O(n)·O(1)

Hamming distance

O(m+n)·O(m+n)

Jaccard distance

Sorensen-Dice coefficient

Overlap coefficient

O(m·n)·O(m·n)

Levenshtein distance

Damerau-Levenshtein distance

O(m·n)·O(1)

Jaro-Winkler distance

O(n)

time

O(m·n)

Mathematical Definition

The Overlap coefficient between two strings and is defined as:

where:

and are the sets created from strings and
and are the cardinalities of sets and
denotes set intersection
denotes the minimum function

The distance version is defined as:

Properties

The Overlap coefficient exhibits several important mathematical characteristics. It produces a value ranging from 0 to 1, where 0 indicates identical strings. While the coefficient is symmetric, meaning the similarity between string A and B is the same as between B and A, it does not satisfy the triangle inequality, making it a non-metric measure. The coefficient is always non-negative, and it has the unique property of being normalized by the smaller set size, making it particularly useful for comparing strings of different lengths.

Applications

The Overlap coefficient has become a fundamental tool in various text processing and information retrieval applications. In document similarity analysis, it helps identify similar documents by comparing their word or character sets, regardless of their length. For text classification tasks, it provides an effective way to categorize documents based on their content. In information retrieval systems, it helps rank search results by relevance. The coefficient is also valuable in plagiarism detection, where it can identify similar text passages across different documents. Additionally, it plays a crucial role in search engines, helping to match user queries with relevant documents in the index.

Implementation

code.ts
1function overlapDistance(s1: string, s2: string): number {
2    // Implementation coming soon
3}

References

Overlap coefficient. (n.d.). In Wikipedia. Retrieved from https://en.wikipedia.org/wiki/Overlap_coefficient
Tan, P. N., Steinbach, M., & Kumar, V. (2005). Introduction to Data Mining. Pearson Education.