Marginalized Kernels Between Labeled Graphs

By Hisashi Kashima, Koji Tsuda, Akihiro Inokuchi. 2003

898 citations recorded by the source corpus.

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In Graph Learning

Citations in the corpus

Gated Graph Sequence Neural Networks (2015, methodology): “Standard approaches to the problem include engineering custom features of an input graph, graph kernels (Kashima et al., 2003; Shervashidze et al., 2011), and methods that deﬁne graph features in terms of random walks on graphs (Perozzi et al., 2014).”
The Graph Neural Network Model (2009, neutral): “For example, the diffusion kernel [33] is based on heat diffusion equation; the kernels proposed in [34] and [35] exploit the vectors produced by a graph random walker and those designed in [36]–[38] use a method of counting the number of common substructures of two trees.”
Position-aware Graph Neural Networks (2019, background): “G ¨ artner et al. (2003) and Kashima et al. (2003) also proposed graph kernels based on random walks, which count the number of walks two graphs have in common (Sugiyama & Borgwardt, 2015).”
Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks (2018, background): “Important early work in this area includes random-walk based kernels (G¨artner, Flach, and Wrobel 2003; Kashima, Tsuda, and Inokuchi 2003)) and kernels based on shortest paths (Borgwardt and Kriegel 2005).”
Text Categorization as a Graph Classification Problem (2015, background): “In parallel, the idea of marginalized kernels was extended to graphs by Kashima et al. (2003) and by Mahé et al. (2004).”
Kernel methods in machine learning (2007, neutral): “sign a kernel on vertices of them and also a kernel between them. In the former case, the graph itself becomes the object deﬁning the metric between the vertices. See Ga¨rtner [56] and Kashima et al. [82] for details on the latter. In the following we discuss kernels on graphs. Denote by W∈Rn×n the ”
DeepTox: Toxicity Prediction using Deep Learning (2016, background): “Graph-based compound and molecule representations led to the invention of graph and molecule kernels (Kashima et al., 2003, 2004; Ralaivola et al., 2005; Mahé et al., 2006; Mohr et al., 2008; Vishwanathan et al., 2010; Klambauer et al., 2015).”
Propagation kernels: efficient graph kernels from propagated information (2014, background): “Most of the existing graph kernels (Shervashidze et al. 2009, 2011; Hido and Kashima 2009; Kashima et al. 2003; Gärtner et al. 2003) are designed for unlabeled graphs or graphs with a complete set of discrete node labels.”
Extensions of marginalized graph kernels (2004, methodology): “We proposed two modifications of the graph kernel by Kashima et al. (2003).”
Learning Multi-Way Relations via Tensor Decomposition With Neural Networks (2018, background): “They count the co-occurrence of walks (Kashima, Tsuda, and Inokuchi 2003), paths (Borgwardt and Kriegel 2005), subgraphs called graphlets (Shervashidze et al. 2009), or subtrees (Shervashidze et al. 2011) in two graphs.”
Classification of small molecules by two- and three-dimensional decomposition kernels (2007, methodology): “In this article, we extend recent research in the area of kernel machines for defining similarity between small molecules (Horva´th et al., 2004; Kashima et al., 2003; Mahe et al., 2005; Menchetti et al., 2005; Swamidass et al., 2005) and propose new methods that combine 2D and 3D information.”
Fast Random Walk Graph Kernel (2012, methodology): “There are three major groups in graph kernels: kernels based on walks and paths [9, 20, 10, 3, 42, 43], kernels based on limited-size subgraphs [16, 36, 21], and kernels based on subtree patterns [25, 35, 15].”
Graph kernels for chemical informatics (2005, methodology): “In the next sections, we first review kernel methods and some of the existing graph kernels, including graph kernels for chemical applications, that have been developed in the literature [Gärtner, 2003, Gärtner et al., 2003, Kashima et al., 2003].”
Data clustering: 50 years beyond K-means (2008, neutral): “With the emergence of kernel learning, there have been growing efforts to develop kernel functions that are more suited for graph-based data (Kashima et al., 2003).”
Expected kernel for missing features in support vector machines (2011, methodology): “Expected kernels have been used to incorporate uncertainty due to additive and channel noise on test signals [3], and the same formulation has also been termed marginalized kernel and used to marginalize out hidden variables when computing kernels between graphs [4].”
Efficient Graph Kernels by Randomization (2012, background): “Unfortunately, existing graph kernels [4,6,10,18,19]”
Deep Graph Kernels (2015, background): “Then, we discuss three major graph kernel families, namely, graph kernels based on limited-sized subgraphs [13, 28], graph kernels based on subtree patterns [24, 27], and graph kernels based on walks [14, 33] and paths [3].”