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60
Graph Kernels
, 2007
"... We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexit ..."
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Cited by 94 (9 self)
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n 6) to O(n 3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixedpoint methods that take O(dn 3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for ddimensional edge kernels, and O(n 4) in the infinitedimensional case; on sparse graphs these algorithms only take O(n 2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to Rconvolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semidefinite.
Efficient graphlet kernels for large graph comparison
, 2009
"... Stateoftheart graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting graphlets, i.e., subgraphs with k nodes where k ∈ {3, 4, 5}. Exhaustive enumeration of all graphlets being prohibitively expensive, we i ..."
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Cited by 50 (10 self)
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Stateoftheart graph kernels do not scale to large graphs with hundreds of nodes and thousands of edges. In this article we propose to compare graphs by counting graphlets, i.e., subgraphs with k nodes where k ∈ {3, 4, 5}. Exhaustive enumeration of all graphlets being prohibitively expensive, we introduce two theoretically grounded speedup schemes, one based on sampling and the second one specifically designed for bounded degree graphs. In our experimental evaluation, our novel kernels allow us to efficiently compare large graphs that cannot be tackled by existing graph kernels.
Proteinligand interaction prediction: an improved chemogenomics approach. Bioinformatics
, 2008
"... Motivation: Predicting interactions between small molecules and proteins is a crucial step to decipher many biological processes, and plays a critical role in drug discovery. When no detailed 3D structure of the protein target is available, ligandbased virtual screening allows the construction of ..."
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Cited by 42 (4 self)
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Motivation: Predicting interactions between small molecules and proteins is a crucial step to decipher many biological processes, and plays a critical role in drug discovery. When no detailed 3D structure of the protein target is available, ligandbased virtual screening allows the construction of predictive models by learning to discriminate known ligands from nonligands. However the accuracy of ligandbased models quickly degrades when the number of known ligands decreases, and in particular the approach is not applicable for orphan receptors with no known ligand. Results: We propose a systematic method to predict ligandprotein interactions, even for targets with no known 3D structure and few or no known ligands. Following the recent chemogenomics trend, we adopt a crosstarget view and attempt to screen the chemical space against whole families of proteins simultaneously. The lack of known ligand for a given target can then be compensated by the availability of known ligands for similar targets. We test this strategy on three important classes of drug targets, namely enzymes, Gprotein coupled receptors (GPCR) and ion channels, and report dramatic improvements in prediction accuracy over classical ligandbased virtual screening, in particular for targets with few or no known ligands. Availability: All data and algorithms are available as supplementary material. Contact:
Multiinstance learning by treating instances as nonI.I.D. samples
 In Proceedings of the 26th International Conference on Machine Learning
, 2009
"... Previous studies on multiinstance learning typically treated instances in the bags as independently and identically distributed. The instances in a bag, however, are rarely independent in real tasks, and a better performance can be expected if the instances are treated in an noni.i.d. way that exp ..."
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Cited by 41 (5 self)
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Previous studies on multiinstance learning typically treated instances in the bags as independently and identically distributed. The instances in a bag, however, are rarely independent in real tasks, and a better performance can be expected if the instances are treated in an noni.i.d. way that exploits relations among instances. In this paper, we propose two simple yet effective methods. In the first method, we explicitly map every bag to an undirected graph and design a graph kernel for distinguishing the positive and negative bags. In the second method, we implicitly construct graphs by deriving affinity matrices and propose an efficient graph kernel considering the clique information. The effectiveness of the proposed methods are validated by experiments. 1.
WeisfeilerLehman Graph Kernels
, 2011
"... In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the WeisfeilerLehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture ..."
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Cited by 32 (3 self)
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In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the WeisfeilerLehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can be defined based on this WeisfeilerLehman sequence of graphs, including a highly efficient kernel comparing subtreelike patterns. Its runtime scales only linearly in the number of edges of the graphs and the length of the WeisfeilerLehman graph sequence. In our experimental evaluation, our kernels outperform stateoftheart graph kernels on several graph classification benchmark data sets in terms of accuracy and runtime. Our kernels open the door to largescale applications of graph kernels in various disciplines such as computational biology and social network analysis.
Fast subtree kernels on graphs
"... In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & Gärtner scales as O(n 2 4 d h). Key to this efficiency is the ..."
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Cited by 28 (2 self)
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In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & Gärtner scales as O(n 2 4 d h). Key to this efficiency is the observation that the WeisfeilerLehman test of isomorphism from graph theory elegantly computes a subtree kernel as a byproduct. Our fast subtree kernels can deal with labeled graphs, scale up easily to large graphs and outperform stateoftheart graph kernels on several classification benchmark datasets in terms of accuracy and runtime. 1
A Survey of Frequent Subgraph Mining Algorithms
 THE KNOWLEDGE ENGINEERING REVIEW
, 2004
"... Graph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplica ..."
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Cited by 27 (1 self)
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Graph mining is an important research area within the domain of data mining. The field of study concentrates on the identification of frequent subgraphs within graph data sets. The research goals are directed at: (i) effective mechanisms for generating candidate subgraphs (without generating duplicates) and (ii) how best to process the generated candidate subgraphs so as to identify the desired frequent subgraphs in a way that is computationally efficient and procedurally effective. This paper presents a survey of current research in the field of frequent subgraph mining, and proposed solutions to address the main research issues.
Neighborhood based fast graph search in large networks
 in SIGMOD
, 2011
"... Complex social and information network search becomes important with a variety of applications. In the core of these applications, lies a common and critical problem: Given a labeled network and a query graph, how to efficiently search the query graph in the target network. The presence of noise a ..."
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Cited by 25 (1 self)
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Complex social and information network search becomes important with a variety of applications. In the core of these applications, lies a common and critical problem: Given a labeled network and a query graph, how to efficiently search the query graph in the target network. The presence of noise and the incomplete knowledge about the structure and content of the target network make it unrealistic to find an exact match. Rather, it is more appealing to find the topk approximate matches. In this paper, we propose a neighborhoodbased similarity measure that could avoid costly graph isomorphism and edit distance computation. Under this new measure, we prove that subgraph similarity search is NP hard, while graph similarity match is polynomial. By studying the principles behind this measure, we found an information propagation model that is able to convert a large net
Fast Neighborhood Subgraph Pairwise Distance Kernel
"... We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speedups in the Gram matrix co ..."
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Cited by 24 (10 self)
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We introduce a novel graph kernel called the Neighborhood Subgraph Pairwise Distance Kernel. The kernel decomposes a graph into all pairs of neighborhood subgraphs of small radius at increasing distances. We show that using a fast graph invariant we obtain significant speedups in the Gram matrix computation. Finally, we test the novel kernel on a wide range of chemoinformatics tasks, from antiviral to anticarcinogenic to toxicological activity prediction, and observe competitive performance when compared against several recent graph kernel methods. 1.
The Skew Spectrum of Graphs
, 2008
"... The central issue in representing graphstructured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on m ..."
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Cited by 19 (5 self)
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The central issue in representing graphstructured data instances in learning algorithms is designing features which are invariant to permuting the numbering of the vertices. We present a new system of invariant graph features which we call the skew spectrum of graphs. The skew spectrum is based on mapping the adjacency matrix of any (weigted, directed, unlabeled) graph to a function on the symmetric group and computing bispectral invariants. The reduced form of the skew spectrum is computable in O(n³) time, and experiments show that on several benchmark datasets it can outperform state of the art graph kernels.