Gaussian Beltrami-Klein Model for Protein Sequence Classification: A Hyperbolic Approach

Protein sequence classification is a crucial task in bioinformatics, enabling the understanding of protein functions and their roles in various biological processes. Several machine-learning approaches have been proposed to address the problems in the area. However, conventional machine learning approaches encounter limitations in capturing the intricate relationships and hierarchical structures inherent in genomic sequences due to the high-dimensional non-Euclidean spaces they operate within. To address this problem, we propose the utilization of the Beltrami-Klein model, a hyperbolic geometry-based approach, for protein sequence classification. Specifically, we integrate the Beltrami-Klein model with the Gaussian kernel to construct a Mercer kernel. The Gaussian-Beltrami-Klein distance captures the intrinsic hyperbolic geometry, representing a non-Euclidean space. Constructing a kernel matrix based on this distance allows for implicit mapping of the data into a higher-dimensional feature space, enabling the capture of intricate nonlinear relationships. This is especially advantageous when dealing with hierarchical or tree-like structures commonly found in biological sequences. Our experimental results demonstrate the effectiveness of the Beltrami-Klein model for protein sequence classification. The proposed approach achieves promising classification performance on the benchmark coronavirus host dataset, showcasing the advantages of utilizing hyperbolic geometry in bioinformatics tasks. The findings of this study contribute to the growing field of geometric deep learning and provide insights into the potential applications of hyperbolic representations in biological data analysis.