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CAKL: Commutative algebra k-mer learning of genomics
Faisal Suwayyid1,2, Yuta Hozumi2, Hongsong Feng3
1Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, KSA.
Arxiv
|August 20, 2025
Summary
We introduce commutative algebra k-mer learning (CAKL), a novel nonlinear algebraic framework for genomic sequence analysis. CAKL advances comparative genomics, outperforming existing methods in tasks like viral classification.
Area of Science:
- Genomics
- Computational Biology
- Algebraic Data Analysis
Background:
- Comparative genomic analysis faces challenges with existing sequence analysis models.
- Commutative algebra, a branch of mathematics, has been underexplored in biological data analysis.
Purpose of the Study:
- Introduce a novel nonlinear algebraic framework for analyzing genomic sequences.
- Establish a new mathematical paradigm for comparative genomic analysis by integrating commutative algebra, topology, combinatorics, and machine learning.
Main Methods:
- Developed commutative algebra k-mer learning (CAKL), a nonlinear algebraic framework.
- Applied CAKL to genetic variant identification, phylogenetic tree analysis, and viral genome classification.
Main Results:
- CAKL demonstrated superior performance compared to five state-of-the-art methods across eleven datasets.
- Achieved high accuracy in viral genome classification and showed stable predictive accuracy with increasing dataset size, indicating scalability and robustness.
Conclusions:
- CAKL represents a significant advancement in commutative algebraic data analysis and learning.
- This nonlinear algebraic approach offers a powerful new tool for comparative genomic analysis, addressing limitations of traditional methods.
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