Investigating The Use of Higher-Order Spectral Features for Graph Analysis and Machine Learning Tasks - Sagar Satish Neve; Leena Patekar (Utilitas Mathematica, 2025)
Spectral approaches have been a key part of graph research for a long time, however most Graph Convolutional Networks (GCNs) use constrained Laplacian eigenvalue representations that don't provide higher-order structure information. This research looks at application of higher-order spectral features to improve machine learning tasks that use graphs. Based on the basic ideas of spectral graph theory. This research presents a spectral-feature-augmented GCN system that incorporates spectral entropy, wavelet signatures, heat kernel embeddings, and eigenvalue moment features to improve representation learning at both node and graph levels. This research looks at how well higher-order spectral characteristics may help with graph analysis and learning tasks. This system captures both local and global topological information by adding spectral features as spectral moments, entropy, wavelets, and heat kernel signatures to standard graph neural network (GNN) designs. The work uses the spectral graph theory to provide theoretical reasons and tests the actual advantages on benchmark datasets including Cora, MUTAG, and CiteSeer. The suggested spectral-feature-augmented GCN performs better than regular GCNs in node classification, graph classification, and link prediction, with significant gains in accuracy. These results show that there is a trade-off between the cost of computing and the performance of learning. They also show how important deep spectral information is in real-world graph learning pipelines.