In many applications, we need to measure similarity between nodes in a large network based on features of their neighborhoods. Although in-network node similarity based on proximity has been well investigated, surprisingly, measuring in-network node similarity based on neighborhoods remains a largely untouched problem in literature. One challenge is that in different applications we may need different measurements that manifest different meanings of similarity. Furthermore, we often want to make trade-offs between specificity of neighborhood matching and efficiency. In this paper, we investigate the problem in a principled and systematic manner. We develop a unified parametric model and a series of four instance measures. Those instance similarity measures not only address a spectrum of various meanings of similarity, but also present a series of trade-offs between computational cost and strictness of matching between neighborhoods of nodes being compared. By extensive experiments and case studies, we demonstrate the effectiveness of the proposed model and its instances.
With the development of highly efficient graph data collection technology in many application fields, classification of graph data emerges as an important topic in the data mining and machine learning community. Towards building highly accurate classification models for graph data, here we present an efficient graph feature selection method. In our method, we use frequent subgraphs as features for graph classification. Different from existing methods, we consider the spatial distribution of the subgraph features in the graph data and select those ones that have consistent spatial location. We have applied our feature selection methods to several cheminformatics benchmarks. Our method demonstrates a significant improvement of prediction as compared to the state-of-the-art methods. This book addresses the question of how far it is possible to go in knowledge representation and reasoning by representing knowledge with graphs (in the graph theory sense) and reasoning with graph operations. The authors have carefully structured the book with the first part covering basic conceptual graphs, the second developing the computational aspects, and the final section pooling the kernel extensions. An appendix summarizes the basic mathematical notions. This is the first book to provide a comprehensive view on the computational facets of conceptual graphs. The mathematical prerequisites are minimal and the material presented can be used in artificial intelligence courses at graduate level upwards. As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discrete-time linear system, thus is efficiently performed by solving simultaneous linear equations. Our kernel is based on an infinite dimensional feature space, so it is fundamentally different from other string or tree kernels based on dynamic programming. We will present promising empirical results in classification of chemical compounds. State-of-the-art 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.