Table 1 Summary of selected graph kernels: Computation by explicit (EX) and implicit (IM) feature mapping and support for attributed graphs
Graph kernel | Computation | Labels | Attributes |
|---|---|---|---|
Shortest-Path (Borgwardt and Kriegel 2005) | IM | + †| + †|
Generalized Shortest-Path (Hermansson et al. 2015) | IM | + | + †|
Graphlet (Shervashidze et al. 2009) | EX | – | – |
Cycles and Trees (Horváth et al. 2004) | EX | + ⋆ | – |
Tree Pattern Kernel (Ramon and Gärtner 2003; Mahé and Vert 2009) | IM | + | + ⋆ |
Ordered Directed Acyclic Graphs (Da San Martino et al. 2012a; 2012b) | EX | + | – |
GraphHopper (Feragen et al. 2013) | IM | + †| + |
Graph Invariant (Orsini et al. 2015) | IM | + | + |
Subgraph Matching (Kriege and Mutzel 2012) | IM | + | + |
Weisfeiler-Lehman Subtree (Shervashidze et al. 2011) | EX | + | – |
Weisfeiler-Lehman Edge (Shervashidze et al. 2011) | EX | + | – |
Weisfeiler-Lehman Shortest-Path (Shervashidze et al. 2011) | EX | + | – |
k-dim. Local Weisfeiler-Lehman Subtree (Morris et al. 2017) | EX | + | – |
Neighborhood Hash Kernel (Hido and Kashima 2009) | EX | + | – |
Propagation Kernel (Neumann et al. 2016) | EX | + | + |
Neighborhood Subgraph Pairwise Distance Kernel (Costa and De Grave 2010) | EX | + | – |
Random Walk (Gärtner et al. 2003; Kashima et al. 2003; Mahé et al. 2004; Vishwanathan et al. 2010; Sugiyama and Borgwardt 2015; Kang et al. 2012) | IM | + | + |
Optimal Assignment Kernel (Fröhlich et al. 2005) | IM | + | + |
Weisfeiler-Lehman Optimal Assignment (Kriege et al. 2016) | IM | + | – |
Pyramid Match (Nikolentzos et al. 2017b) | IM | + | – |
Matchings of Geometric Embeddings (Johansson and Dubhashi 2015) | IM | + | + ⋆ |
Descriptor Matching Kernel (Su et al. 2016) | IM | + | + †|
Graphlet Spectrum (Kondor et al. 2009) | EX | + | – |
Multiscale Laplacian Graph Kernel (Kondor and Pan 2016) | IM | + | + ⋆†|
Global Graph Kernel (Johansson et al. 2014) | EX | – | – |
Deep Graph Kernels (Yanardag and Vishwanathan 2015a) | IM | + | – |
Smoothed Graph Kernels (Yanardag and Vishwanathan 2015b) | IM | + ⋆ | – |
Hash Graph Kernel (Morris et al. 2016) | EX | + | + |
Depth-based Representation Kernel (Bai et al. 2014) | IM | – | – |
Aligned Subtree Kernel (Bai et al. 2015) | IM | + | – |