Enhancing Graph-based Machine Learning through Lyndon Partial Words

Objectives: This study integrates the combinatorial properties of Lyndon partial words with Graph-Based Machine Learning (GBML) to develop an innovative approach for sequence analysis. The research is particularly aimed at addressing challenges in fields like bioinformatics and natural language processing (NLP), where incomplete or fragmented data often hinder effective analysis. By leveraging the minimality and primitiveness inherent to Lyndon partial words, this study seeks to provide a robust framework for modeling and analyzing such data. Methods: Graphs were constructed from Lyndon partial words, where nodes represent unique partial words or their conjugates, and edges signify relationships such as lexicographical proximity or shared substrings. These graphs were subjected to advanced GBML techniques, including community detection algorithms to uncover clusters of related patterns, and similarity analysis to measure structural and semantic relationships. Data preprocessing ensured the accurate representation of partial words while maintaining their combinatorial integrity. Findings: The integration of Lyndon partial words into GBML demonstrates significant potential in pattern recognition and structural analysis, particularly for datasets characterized by fragmentation or incompleteness. The constructed graphs effectively capture underlying relationships and patterns, aiding in the discovery of meaningful insights in sequence data. This novel framework enables improved modeling of real-world scenarios, such as identifying recurring motifs in biological sequences or understanding linguistic variations in incomplete text datasets. Novelty: By combining the theoretical elegance of Lyndon partial words with the computational power of GBML, this study introduces a novel methodology for tackling incomplete data in sequence analysis. The approach highlights the adaptability of combinatorial constructs for solving practical problems, offering new avenues for research in data-intensive domains like bioinformatics and NLP. The framework also underscores the importance of interdisciplinary solutions in advancing machine learning applications for complex and fragmented datasets.