Kernel Matrix Completion with Topological and Spectral Features for Multi-Modal Classification

Kernel methods offer a robust framework for integrating multi-modal datasets into a unified representation, thereby facilitating more comprehensive data interpretation. In the presence of incomplete datasets, multiple kernel learning is employed to enhance the efficiency of data completion and integration. We investigate kernel-based approaches to address the incomplete-data problem with applications to yeast protein data. Biological data such as yeast proteins can be represented through multiple modalities, including gene expression profiles, amino acid sequences, three-dimensional structures, and protein interaction networks. We introduce a computational pipeline based on kernel matrix completion, in which topological data analysis (TDA) and persistent spectral analysis are incorporated into the classification setting. TDA captures geometric structure across scales while spectral descriptors reflect connectivity patterns through Laplacian eigenvalues. Kernel, topological, and spectral descriptors are used with support vector machines to discriminate between membrane and non-membrane yeast proteins. Empirical results show that the combined pipeline improves both kernel completion accuracy and ROC performance relative to baseline kernel-only approaches. The best-performing configuration achieves an ROC score of 0.8632 using the average of three kernels augmented with TDA features. These results demonstrate competitive performance relative to strong kernel-based baselines under incomplete data conditions. The proposed approach provides a unified approach for learning from incomplete heterogeneous data while enriching kernel representations with geometric and spectral information.