Random Wavelet Features for Graph Kernel Machines
This work addresses the scalability issue in graph representation learning for tasks like node classification and link prediction, offering a principled and efficient solution, though it is incremental as it builds on random feature methods for kernel approximation.
The paper tackled the problem of designing scalable node embeddings for graph kernels, which are computationally prohibitive for large networks, by introducing randomized spectral node embeddings that estimate low-rank kernel approximations, achieving more accurate results than existing methods, especially for spectrally localized kernels.
Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design node embeddings whose dot products capture meaningful notions of node similarity induced by the graph. Graph kernels offer a principled way to define such similarities, but their direct computation is often prohibitive for large networks. Inspired by random feature methods for kernel approximation in Euclidean spaces, we introduce randomized spectral node embeddings whose dot products estimate a low-rank approximation of any specific graph kernel. We provide theoretical and empirical results showing that our embeddings achieve more accurate kernel approximations than existing methods, particularly for spectrally localized kernels. These results demonstrate the effectiveness of randomized spectral constructions for scalable and principled graph representation learning.