# A Unifying View of Explicit and Implicit Feature Maps of Graph Kernels

## TL;DR

This paper develops explicit feature maps for graph kernels, enabling faster large-scale graph classification with accuracy comparable to traditional kernel methods, through theoretical analysis and extensive experiments.

## Contribution

It introduces exact and approximate explicit feature maps for various graph kernels, improving computational efficiency while maintaining accuracy.

## Key findings

- Explicit feature maps often outperform kernel trick in speed.
- Approximate feature maps achieve near-accurate classification.
- Phase transition observed in runtime with label diversity and graph complexity.

## Abstract

Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for state-of-the-art kernels supporting real-valued attributes including the GraphHopper and graph invariant kernels. In extensive experiments we show that our approaches often achieve a classification accuracy close to the exact methods based on the kernel trick, but require only a fraction of their running time. Moreover, we propose and analyze algorithms for computing random walk, shortest-path and subgraph matching kernels by explicit and implicit feature maps. Our theoretical results are confirmed experimentally by observing a phase transition when comparing running time with respect to label diversity, walk lengths and subgraph size, respectively.