Extending local features with contextual information in graph kernels

Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances, probably because the substructures can be interpreted as approximations of the subgraphs they induce. In this paper, we propose to associate to each feature a piece of information about the context in which the feature appears in the graph. A substructure appearing in two different graphs will match only if it appears with the same context in both graphs. We propose a kernel based on this idea that considers trees as substructures, and where the contexts are features too. The kernel is inspired from the framework in [6], even if it is not part of it. We give an efficient algorithm for computing the kernel and show promising results on real-world graph classification datasets.Comment: To appear in ICONIP 201

funcGNN: A Graph Neural Network Approach to Program Similarity

Program similarity is a fundamental concept, central to the solution of software engineering tasks such as software plagiarism, clone identification, code refactoring and code search. Accurate similarity estimation between programs requires an in-depth understanding of their structure, semantics and flow. A control flow graph (CFG), is a graphical representation of a program which captures its logical control flow and hence its semantics. A common approach is to estimate program similarity by analysing CFGs using graph similarity measures, e.g. graph edit distance (GED). However, graph edit distance is an NP-hard problem and computationally expensive, making the application of graph similarity techniques to complex software programs impractical. This study intends to examine the effectiveness of graph neural networks to estimate program similarity, by analysing the associated control flow graphs. We introduce funcGNN, which is a graph neural network trained on labeled CFG pairs to predict the GED between unseen program pairs by utilizing an effective embedding vector. To our knowledge, this is the first time graph neural networks have been applied on labeled CFGs for estimating the similarity between high-level language programs. Results: We demonstrate the effectiveness of funcGNN to estimate the GED between programs and our experimental analysis demonstrates how it achieves a lower error rate (0.00194), with faster (23 times faster than the quickest traditional GED approximation method) and better scalability compared with the state of the art methods. funcGNN posses the inductive learning ability to infer program structure and generalise to unseen programs. The graph embedding of a program proposed by our methodology could be applied to several related software engineering problems (such as code plagiarism and clone identification) thus opening multiple research directions.Comment: 11 pages, 8 figures, 3 table

Probabilistic Clustering of Time-Evolving Distance Data

We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichlet process prior. We validate our model on synthetic data showing that the proposed method is more accurate than state-of-the-art clustering methods. Finally, we use our dynamic clustering model to analyze and illustrate the evolution of brain cancer patients over time

Hierarchies and Ranks for Persistence Pairs

We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial relationships between features in persistence diagrams, leading to a limited expressive power. We build upon a recently-introduced hierarchy of pairs in persistence diagrams that augments the pairing stored in persistence diagrams with information about which components merge. Our proposed hierarchy captures differences in branching structure. Moreover, we show how to use our hierarchy to measure the spatial stability of a pairing and we define a rank function for persistence pairs and demonstrate different applications.Comment: Topology-based Methods in Visualization 201

Kernels on Graphs as Proximity Measures

International audienceKernels and, broadly speaking, similarity measures on graphs are extensively used in graph-based unsupervised and semi-supervised learning algorithms as well as in the link prediction problem. We analytically study proximity and distance properties of various kernels and similarity measures on graphs. This can potentially be useful for recommending the adoption of one or another similarity measure in a machine learning method. Also, we numerically compare various similarity measures in the context of spectral clustering and observe that normalized heat-type similarity measures with log modification generally perform the best