Guest editors’ introduction: special issue on mining and learning with graphs

Research in machine learning and data mining acknowledges more and more the fact that most data occurring in real world problems is inherently structured. Graphs and particular subclasses of graphs are commonly used representations for such structured data. They are present in important application areas ranging from biology and chemistry to the World Wide Web and beyond. Following the ever increasing number of successful workshops on topics like mining and learning with graphs and motivated by the ever increasing amount of high quality submissions to these workshops, this special issue gathers some of the progress in the field over the recent years. One of the major trends has been to investigate how the success of kernel methods on data which is readily embedded in a Euclidean space, can be carried over to structured data. In this spirit, the paper “Graph kernels based on tree patterns for molecules” by Pierre Mahe and Jean-Philippe Vert investigates kernel functions based on co-occurrence of particular subtree patterns in graphs. They extend and use these kernels for toxicity and anti-cancer activity prediction with support vector machines on graphs representing the 2D structure of molecules. The paper “On the properties of von Neumann kernels for link analysis” by Masashi Shimbo, Takahiko Ito, Daichi Mochihashi, and Yuji Matsumoto investigates the relationship between link analysis measures and kernel functions defined on the vertices of a single huge graph. Having identified common issues of both these kernels and these link analysis measures, the authors proceed by proposing a modified kernel and demonstrate its effectiveness by analysing a citation network of scientific papers.