Paper:
A Structural Smoothing Framework For Robust Graph-Comparison
In this paper, we propose a general smoothing framework for graph kernels by taking structural similarity into account, and apply it to derive smoothed variants of popular graph kernels. Our framework is inspired by state-of-the-art smoothing techniques used in natural language processing (NLP). However, unlike NLP applications that primarily deal with strings, we show how one can apply smoothing to a richer class of inter-dependent sub-structures that naturally arise in graphs. Moreover, we discuss extensions of the Pitman-Yor process that can be adapted to smooth structured objects, thereby leading to novel graph kernels. Our kernels are able to tackle the diagonal dominance problem while respecting the structural similarity between features. Experimental evaluation shows that not only our kernels achieve statistically significant improvements over the unsmoothed variants, but also outperform several other graph kernels in the literature. Our kernels are competitive in terms of runtime, and offer a viable option for practitioners.

Review:
This paper proposes graph kernels that take smoothed matching into account when computing a structural similarity, i.e., generated by graphlet kernels, Weisfeiler-Lehman subtree kernels, and shortest-path kernels.Moreover, the paper proposes an extension of the Pitman-Yor process for smoothing subgraph distributions, which originates novel graph kernels.The empirical evaluation shows that the proposed kernels outperform their non smoothed counterpart. Additionally, they also outperform other graph kernels and are competitive in terms of runtime.The idea of using NLP smoothing for graph matching is interesting and reasonable. However, the model proposed by the authors is a subcase of a not-so-recent smoothed tree kernels. For example, see:Danilo Croce, Alessandro Moschitti, and Roberto Basili. Structured lexical similarity via convolution kernels on dependency trees. In Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, pages 1034-1046, Edinburgh, Scotland, UK., July 2011. Association for Computational Linguistics.which proposed a smoothing function in the partial tree kernel by Moschitti, ECML 2006. Such function is more general than the smoothing function proposed in the submitted paper since it can be any valid kernel similarity.Note that the smoothed partial tree kernel can be straightforwardly applied to DAG, see:Aliaksei Severyn, Alessandro Moschitti: Fast Support Vector Machines for Convolution Tree Kernels. Data Mining Knowledge Discovery 25: 325-357, 2012.Finally, there has been older work using tree kernels with similarities:Stephan Bloehdorn and Alessandro Moschitti, Exploiting Structure and Semantics for Expressive Text Kernels, Proceeding of the Conference on Information Knowledge and Management, Lisbon, Portugal, 2007