Similarity measures between strings extended to sets of strings.

Area of Science:

• Computer Science
• Information Theory
• Data Analysis

Background:

• Traditional similarity measures often focus on individual strings.
• Extending these measures to sets of strings presents challenges in maintaining intuitive properties.
• Handling large or continuous alphabets requires robust computational methods.

Purpose of the Study:

• To generalize existing string similarity measures for application to sets of strings.
• To develop and demonstrate novel similarity measures suitable for diverse applications.
• To explore the applicability of these measures with nondenumerable alphabets, such as the unit interval.

Main Methods:

• Extension of established string similarity metrics to handle collections of strings.
• Development of two distinct similarity measures: one for pointwise comparisons, another for substring analysis.
• Application of measures to examples using the unit interval [0, 1] as a continuous alphabet.

Main Results:

• The proposed extensions maintain desirable properties of the original similarity measures.
• Two novel measures demonstrate effectiveness for different application needs (pointwise vs. substring).
• Successful application of measures to sets of strings over a continuous alphabet.

Conclusions:

• The generalized similarity measures provide an intuitive and mathematically sound approach for sets of strings.
• The developed measures offer flexibility for applications requiring precise numerical or substring-based comparisons.
• The framework accommodates complex alphabets, broadening the scope of string similarity analysis.