Kernelizing Protein Interaction Languages: Spectral Approximations and Random Fourier Features

Abstract

Protein-peptide interactions play an important role in many biological phenomena, spanning adaptive immunity to disease pathology. In the Sliding Window Interaction Grammar (SWING) framework, interactions are represented as sequences of biochemical tokens embedded using Doc2Vec, allowing robust generalisation to unobserved MHC alleles. However, classification remains limited to a single Euclidean feature space that is incapable of resolving binding landscapes. This dissertation develops SWING for four distinct kernel types: Gaussian, Laplacian, anisotropic (ARD), and the Spectral Mixture (SM) kernel, each approximated using scalable Random Fourier Features. The SM kernel incorporates prior knowledge about secondary structure into its spectral density as biological priors through optimisation by kernel target alignment, and the ARD kernel learns dimension-specific scales to downweight noise. Late-fusion ensembling is achieved through stacked meta-classification across diverse feature spaces. Evaluating the proposed method across five peptide-MHC binding datasets reveals that the SM kernel attains the highest AUROC in all settings, capturing 39% to 80% of the remaining headroom in each towards perfect predictions, including 80% in a mixed class dataset on which other kernels saturate. These results show that directly encoding secondary structure periodicity into the kernel leads to consistent and generalising improvements compared to the SWING approach.