Results 1  10
of
73
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 ..."
Abstract

Cited by 101 (9 self)
 Add to MetaCart
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.
ShortestPath Kernels on Graphs
 In Proceedings of the 2005 International Conference on Data Mining
, 2005
"... Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have bee ..."
Abstract

Cited by 62 (5 self)
 Add to MetaCart
(Show Context)
Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have been proposed so far. As a general problem, these kernels are either computationally expensive or limited in their expressiveness. We try to overcome this problem by defining expressive graph kernels which are based on paths. As the computation of all paths and longest paths in a graph is NPhard, we propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortestpath kernels show significantly higher classification accuracy than walkbased kernels. 1
Graph Kernels for Chemical Informatics
, 2005
"... Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their cova ..."
Abstract

Cited by 59 (7 self)
 Add to MetaCart
Increased availability of large repositories of chemical compounds is creating new challenges and opportunities for the application of machine learning methods to problems in computational chemistry and chemical informatics. Because chemical compounds are often represented by the graph of their covalent bonds, machine learning methods in this domain must be capable of processing graphical structures with variable size. Here we first briefly review the literature on graph kernels and then introduce three new kernels (Tanimoto, MinMax, Hybrid) based on the idea of molecular fingerprints and counting labeled paths of depth up to d using depthfirst search from each possible vertex. The kernels are applied to three classification problems to predict mutagenicity, toxicity, and anticancer activity on three publicly available data sets. The kernels achieve performances at least comparable, and most often superior, to those previously reported in the literature reaching accuracies of 91.5 % on the Mutag dataset, 6567 % on the PTC (Predictive Toxicology Challenge) dataset, and 72 % on the NCI (National Cancer Institute) dataset. Properties and tradeoffs of these kernels, as well as other proposed kernels that leverage 1D or 3D representations of molecules, are briefly discussed.
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 ..."
Abstract

Cited by 54 (10 self)
 Add to MetaCart
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.
Graph Kernels and Gaussian Processes for Relational Reinforcement Learning
 Machine Learning
, 2003
"... Relational reinforcement learning is a Qlearning technique for relational stateaction spaces. It aims to enable agents to learn how to act in an environment that has no natural representation as a tuple of constants. In this case, the learning algorithm used to approximate the mapping between stat ..."
Abstract

Cited by 46 (9 self)
 Add to MetaCart
Relational reinforcement learning is a Qlearning technique for relational stateaction spaces. It aims to enable agents to learn how to act in an environment that has no natural representation as a tuple of constants. In this case, the learning algorithm used to approximate the mapping between stateaction pairs and their so called Q(uality)value has to be not only very reliable, but it also has to be able to handle the relational representation of stateaction pairs. In this paper we investigate...
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 ..."
Abstract

Cited by 43 (3 self)
 Add to MetaCart
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:
Comparison of descriptor spaces for chemical compound retrieval and classification
 International Conference in Datamining. (ICDM
, 2006
"... Abstract. In recent years the development of computational techniques that build models to correctly assign chemical compounds to various classes or to retrieve potential druglike compounds has been an active area of research. Many of the bestperforming techniques for these tasks utilize a descript ..."
Abstract

Cited by 42 (5 self)
 Add to MetaCart
(Show Context)
Abstract. In recent years the development of computational techniques that build models to correctly assign chemical compounds to various classes or to retrieve potential druglike compounds has been an active area of research. Many of the bestperforming techniques for these tasks utilize a descriptorbased representation of the compound that captures various aspects of the underlying molecular graph’s topology. In this paper we compare five different set of descriptors that are currently used for chemical compound classification. We also introduce four different descriptors derived from all connected fragments present in the molecular graphs primarily for the purpose of comparing them to the currently used descriptor spaces and analyzing what properties of descriptor spaces are helpful in providing effective representation for molecular graphs. In addition, we introduce an extension to existing vectorbased kernel functions to take into account the length of the fragments present in the descriptors. We experimentally evaluate the performance of the previously introduced and the new descriptors in the context of SVMbased classification and rankedretrieval on 28 classification and retrieval problems derived from 18 datasets. Our experiments show that for both of these tasks, two of the four descriptors introduced in this paper along with the extended connectivity fingerprint based descriptors consistently and statistically outperform previously developed schemes based on the widely used fingerprint and Maccs keysbased descriptors, as well as recently introduced descriptors obtained by mining and analyzing the structure of the molecular graphs.
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 ..."
Abstract

Cited by 30 (3 self)
 Add to MetaCart
(Show Context)
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
Don’t be afraid of simpler patterns
 10th European Conference on Principles and Practice of Knowledge Discovery in Databases (PKDD
, 2006
"... Abstract. This paper investigates the tradeoff between the expressiveness of the pattern language and the performance of the pattern miner in structured data mining. This tradeoff is investigated in the context of correlated pattern mining, which is concerned with finding the kbest patterns accor ..."
Abstract

Cited by 27 (8 self)
 Add to MetaCart
(Show Context)
Abstract. This paper investigates the tradeoff between the expressiveness of the pattern language and the performance of the pattern miner in structured data mining. This tradeoff is investigated in the context of correlated pattern mining, which is concerned with finding the kbest patterns according to a convex criterion, for the pattern languages of itemsets, multiitemsets, sequences, trees and graphs. The criteria used in our investigation are the typical ones in data mining: computational cost and predictive accuracy and the domain is that of mining molecular graph databases. More specifically, we provide empirical answers to the following questions: how does the expressive power of the language affect the computational cost? and what is the tradeoff between expressiveness of the pattern language and the predictive accuracy of the learned model? While answering the first question, we also introduce a novel stepwise approach to correlated pattern mining in which the results of mining a simpler pattern language are employed as a starting point for mining in a more complex one. This stepwise approach typically leads to significant speedups (up to a factor 1000) for mining graphs. 1
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 ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
(Show Context)
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