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35
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 54 (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.
Hash Kernels for Structured Data
, 2009
"... We propose hashing to facilitate efficient kernels. This generalizes previous work using sampling and we show a principled way to compute the kernel matrix for data streams and sparse feature spaces. Moreover, we give deviation bounds from the exact kernel matrix. This has applications to estimation ..."
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Cited by 50 (4 self)
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We propose hashing to facilitate efficient kernels. This generalizes previous work using sampling and we show a principled way to compute the kernel matrix for data streams and sparse feature spaces. Moreover, we give deviation bounds from the exact kernel matrix. This has applications to estimation on strings and graphs.
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 36 (4 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.
Hash kernels
 Proc. Intl. Workshop on Artificial Intelligence and Statistics. Society for Artificial Intelligence and Statistics
, 2009
"... We propose hashing to facilitate efficient kernels. This generalizes previous work using sampling and we show a principled way to compute the kernel matrix for data streams and sparse feature spaces. Moreover, we give deviation bounds from the exact kernel matrix. This has applications to estimation ..."
Abstract

Cited by 34 (7 self)
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We propose hashing to facilitate efficient kernels. This generalizes previous work using sampling and we show a principled way to compute the kernel matrix for data streams and sparse feature spaces. Moreover, we give deviation bounds from the exact kernel matrix. This has applications to estimation on strings and graphs. 1
Predicting enzyme class from protein structure without alignments
 J Mol Biol
, 2005
"... Methods for predicting protein function from structure are becoming more important as the rate at which structures are solved increases more rapidly than experimental knowledge. As a result, protein structures now frequently lack functional annotations. The majority of methods for predicting protein ..."
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Cited by 31 (0 self)
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Methods for predicting protein function from structure are becoming more important as the rate at which structures are solved increases more rapidly than experimental knowledge. As a result, protein structures now frequently lack functional annotations. The majority of methods for predicting protein function are reliant upon identifying a similar protein and transferring its annotations to the query protein. This method fails when a similar protein cannot be identified, or when any similar proteins identified also lack reliable annotations. Here, we describe a method that can assign function from structure without the use of algorithms reliant upon alignments. Using simple attributes that can be calculated from any crystal structure, such as secondary structure content, amino acid propensities, surface properties and ligands, we describe each enzyme in a nonredundant set. The set is split according to Enzyme Classification (EC) number. We combine the predictions of oneclass versus oneclass support vector machine models to make overall assignments of EC number to an accuracy of 35 % with the topranked prediction, rising to 60% accuracy with the top two ranks. In doing so we demonstrate the utility of simple structural attributes in protein function prediction and shed light on the link between structure and function. We apply our methods to predict the function of every currently unclassified protein in the Protein Data Bank.
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 30 (3 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
Discriminative Clustering by Regularized Information Maximization
"... Is there a principled way to learn a probabilistic discriminative classifier from an unlabeled data set? We present a framework that simultaneously clusters the data and trains a discriminative classifier. We call it Regularized Information Maximization (RIM). RIM optimizes an intuitive information ..."
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Cited by 27 (1 self)
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Is there a principled way to learn a probabilistic discriminative classifier from an unlabeled data set? We present a framework that simultaneously clusters the data and trains a discriminative classifier. We call it Regularized Information Maximization (RIM). RIM optimizes an intuitive informationtheoretic objective function which balances class separation, class balance and classifier complexity. The approach can flexibly incorporate different likelihood functions, express prior assumptions about the relative size of different classes and incorporate partial labels for semisupervised learning. In particular, we instantiate the framework to unsupervised, multiclass kernelized logistic regression. Our empirical evaluation indicates that RIM outperforms existing methods on several real data sets, and demonstrates that RIM is an effective model selection method. 1
Metropolis algorithms for representative subgraph sampling
 In Data Mining, 2008. ICDM’08. Eighth IEEE International Conference on
, 2008
"... While data mining in chemoinformatics studied graph data with dozens of nodes, systems biology and the Internet are now generating graph data with thousands and millions of nodes. Hence data mining faces the algorithmic challenge of coping with this significant increase in graph size: Classic algori ..."
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Cited by 26 (0 self)
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While data mining in chemoinformatics studied graph data with dozens of nodes, systems biology and the Internet are now generating graph data with thousands and millions of nodes. Hence data mining faces the algorithmic challenge of coping with this significant increase in graph size: Classic algorithms for data analysis are often too expensive and too slow on large graphs. While one strategy to overcome this problem is to design novel efficient algorithms, the other is to ’reduce ’ the size of the large graph by sampling. This is the scope of this paper: We will present novel Metropolis algorithms for sampling a ’representative ’ small subgraph from the original large graph, with ’representative ’ describing the requirement that the sample shall preserve crucial graph properties of the original graph. In our experiments, we improve over the pioneering work of Leskovec and Faloutsos (KDD 2006), by producing representative subgraph samples that are both smaller and of higher quality than those produced by other methods from the literature. 1
Nearoptimal supervised feature selection among frequent subgraphs
 IN SIAM INT’L CONF. ON DATA MINING
, 2009
"... Graph classification is an increasingly important step in numerous application domains, such as function prediction of molecules and proteins, computerised scene analysis, and anomaly detection in program flows. Among the various approaches proposed in the literature, graph classification based on f ..."
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Cited by 23 (10 self)
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Graph classification is an increasingly important step in numerous application domains, such as function prediction of molecules and proteins, computerised scene analysis, and anomaly detection in program flows. Among the various approaches proposed in the literature, graph classification based on frequent subgraphs is a popular branch: Graphs are represented as (usually binary) vectors, with components indicating whether a graph contains a particular subgraph that is frequent across the dataset. On large graphs, however, one faces the enormous problem that the number of these frequent subgraphs may grow exponentially with the size of the graphs, but only few of them possess enough discriminative power to make them