A Survey on Graph Kernels

Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner's guide to kernel-based graph classification

Graph Kernels

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 fixed-point 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 d-dimensional edge kernels, and O(n^4) in the infinite-dimensional 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 R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite

Graph kernel extensions and experiments with application to molecule classification, lead hopping and multiple targets

The discovery of drugs that can effectively treat disease and alleviate pain is one of the core challenges facing modern medicine. The tools and techniques of machine learning have perhaps the greatest potential to provide a fast and efficient route toward the fabrication of novel and effective drugs. In particular, modern structured kernel methods have been successfully applied to range of problem domains and have been recently adapted for graph structures making them directly applicable to pharmaceutical drug discovery. Specifically graph structures have a natural fit with molecular data, in that a graph consists of a set of nodes that represent atoms that are connected by bonds. In this thesis we use graph kernels that utilize three different graph representations: molecular, topological pharmacophore and reduced graphs. We introduce a set of novel graph kernels which are based on a measure of the number of finite walks within a graph. To calculate this measure we employ a dynamic programming framework which allows us to extend graph kernels so they can deal with non-tottering, softmatching and allows the inclusion of gaps. In addition we review several graph colouring methods and subsequently incorporate colour into our graph kernels models. These kernels are designed for molecule classification in general, although we show how they can be adapted to other areas in drug discovery. We conduct three sets of experiments and discuss how our augmented graph kernels are designed and adapted for these areas. First, we classify molecules based on their activity in comparison to a biological target. Second, we explore the related problem of lead hopping. Here one set of chemicals is used to predict another that is structurally dissimilar. We discuss the problems that arise due to the fact that some patterns are filtered from the dataset. By analyzing lead hopping we are able to go beyond the typical cross-validation approach and construct a dataset that more accurately reflect real-world tasks. Lastly, we explore methods of integrating information from multiple targets. We test our models as a multi-response problem and later introduce a new approach that employs Kernel Canonical Correlation Analysis (KCCA) to predict the best molecules for an unseen target. Overall, we show that graph kernels achieve good results in classification, lead hopping and multiple target experiments

Graph Kernels and Applications in Bioinformatics

In recent years, machine learning has emerged as an important discipline. However, despite the popularity of machine learning techniques, data in the form of discrete structures are not fully exploited. For example, when data appear as graphs, the common choice is the transformation of such structures into feature vectors. This procedure, though convenient, does not always effectively capture topological relationships inherent to the data; therefore, the power of the learning process may be insufficient. In this context, the use of kernel functions for graphs arises as an attractive way to deal with such structured objects. On the other hand, several entities in computational biology applications, such as gene products or proteins, may be naturally represented by graphs. Hence, the demanding need for algorithms that can deal with structured data poses the question of whether the use of kernels for graphs can outperform existing methods to solve specific computational biology problems. In this dissertation, we address the challenges involved in solving two specific problems in computational biology, in which the data are represented by graphs. First, we propose a novel approach for protein function prediction by modeling proteins as graphs. For each of the vertices in a protein graph, we propose the calculation of evolutionary profiles, which are derived from multiple sequence alignments from the amino acid residues within each vertex. We then use a shortest path graph kernel in conjunction with a support vector machine to predict protein function. We evaluate our approach under two instances of protein function prediction, namely, the discrimination of proteins as enzymes, and the recognition of DNA binding proteins. In both cases, our proposed approach achieves better prediction performance than existing methods. Second, we propose two novel semantic similarity measures for proteins based on the gene ontology. The first measure directly works on the gene ontology by combining the pairwise semantic similarity scores between sets of annotating terms for a pair of input proteins. The second measure estimates protein semantic similarity using a shortest path graph kernel to take advantage of the rich semantic knowledge contained within ontologies. Our comparison with other methods shows that our proposed semantic similarity measures are highly competitive and the latter one outperforms state-of-the-art methods. Furthermore, our two methods are intrinsic to the gene ontology, in the sense that they do not rely on external sources to calculate similarities

Genome-wide Protein-chemical Interaction Prediction

The analysis of protein-chemical reactions on a large scale is critical to understanding the complex interrelated mechanisms that govern biological life at the cellular level. Chemical proteomics is a new research area aimed at genome-wide screening of such chemical-protein interactions. Traditional approaches to such screening involve in vivo or in vitro experimentation, which while becoming faster with the application of high-throughput screening technologies, remains costly and time-consuming compared to in silico methods. Early in silico methods are dependant on knowing 3D protein structures (docking) or knowing binding information for many chemicals (ligand-based approaches). Typical machine learning approaches follow a global classification approach where a single predictive model is trained for an entire data set, but such an approach is unlikely to generalize well to the protein-chemical interaction space considering its diversity and heterogeneous distribution. In response to the global approach, work on local models has recently emerged to improve generalization across the interaction space by training a series of independant models localized to each predict a single interaction. This work examines current approaches to genome-wide protein-chemical interaction prediction and explores new computational methods based on modifications to the boosting framework for ensemble learning. The methods are described and compared to several competing classification methods. Genome-wide chemical-protein interaction data sets are acquired from publicly available resources, and a series of experimental studies are performed in order to compare the the performance of each method under a variety of conditions