Generalized Shortest Path Kernel on Graphs

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the generalized shortest path kernel outperforms the original shortest path kernel on a number of datasets. We give a theoretical analysis for explaining our experimental results. In particular, we estimate distributions of the expected feature vectors for the shortest path kernel and the generalized shortest path kernel, and we show some evidence explaining why our graph kernel outperforms the shortest path kernel for our graph classification problem.Comment: Short version presented at Discovery Science 2015 in Banf

Significant Subgraph Mining with Multiple Testing Correction

The problem of finding itemsets that are statistically significantly enriched in a class of transactions is complicated by the need to correct for multiple hypothesis testing. Pruning untestable hypotheses was recently proposed as a strategy for this task of significant itemset mining. It was shown to lead to greater statistical power, the discovery of more truly significant itemsets, than the standard Bonferroni correction on real-world datasets. An open question, however, is whether this strategy of excluding untestable hypotheses also leads to greater statistical power in subgraph mining, in which the number of hypotheses is much larger than in itemset mining. Here we answer this question by an empirical investigation on eight popular graph benchmark datasets. We propose a new efficient search strategy, which always returns the same solution as the state-of-the-art approach and is approximately two orders of magnitude faster. Moreover, we exploit the dependence between subgraphs by considering the effective number of tests and thereby further increase the statistical power.Comment: 18 pages, 5 figure, accepted to the 2015 SIAM International Conference on Data Mining (SDM15

Mining Brain Networks using Multiple Side Views for Neurological Disorder Identification

Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information is available along with the graph data. For example, for neurological disorder identification, in addition to the brain networks derived from neuroimaging data, hundreds of clinical, immunologic, serologic and cognitive measures may also be documented for each subject. These measures compose multiple side views encoding a tremendous amount of supplemental information for diagnostic purposes, yet are often ignored. In this paper, we study the problem of discriminative subgraph selection using multiple side views and propose a novel solution to find an optimal set of subgraph features for graph classification by exploring a plurality of side views. We derive a feature evaluation criterion, named gSide, to estimate the usefulness of subgraph patterns based upon side views. Then we develop a branch-and-bound algorithm, called gMSV, to efficiently search for optimal subgraph features by integrating the subgraph mining process and the procedure of discriminative feature selection. Empirical studies on graph classification tasks for neurological disorders using brain networks demonstrate that subgraph patterns selected by the multi-side-view guided subgraph selection approach can effectively boost graph classification performances and are relevant to disease diagnosis.Comment: in Proceedings of IEEE International Conference on Data Mining (ICDM) 201

Finding the best not the most: Regularized loss minimization subgraph selection for graph classification

© 2015 Elsevier Ltd. All rights reserved. Classification on structure data, such as graphs, has drawn wide interest in recent years. Due to the lack of explicit features to represent graphs for training classification models, extensive studies have been focused on extracting the most discriminative subgraphs features from the training graph dataset to transfer graphs into vector data. However, such filter-based methods suffer from two major disadvantages: (1) the subgraph feature selection is separated from the model learning process, so the selected most discriminative subgraphs may not best fit the subsequent learning model, resulting in deteriorated classification results; (2) all these methods rely on users to specify the number of subgraph features K, and suboptimally specified K values often result in significantly reduced classification accuracy. In this paper, we propose a new graph classification paradigm which overcomes the above disadvantages by formulating subgraph feature selection as learning a K-dimensional feature space from an implicit and large subgraph space, with the optimal K value being automatically determined. To achieve the goal, we propose a regularized loss minimization-driven (RLMD) feature selection method for graph classification. RLMD integrates subgraph selection and model learning into a unified framework to find discriminative subgraphs with guaranteed minimum loss w.r.t. the objective function. To automatically determine the optimal number of subgraphs K from the exponentially large subgraph space, an effective elastic net and a subgradient method are proposed to derive the stopping criterion, so that K can be automatically obtained once RLMD converges. The proposed RLMD method enjoys gratifying property including proved convergence and applicability to various loss functions. Experimental results on real-life graph datasets demonstrate significant performance gain

Multi-graph-view subgraph mining for graph classification

© 2015, Springer-Verlag London. In this paper, we formulate a new multi-graph-view learning task, where each object to be classified contains graphs from multiple graph-views. This problem setting is essentially different from traditional single-graph-view graph classification, where graphs are collected from one single-feature view. To solve the problem, we propose a cross graph-view subgraph feature-based learning algorithm that explores an optimal set of subgraphs, across multiple graph-views, as features to represent graphs. Specifically, we derive an evaluation criterion to estimate the discriminative power and redundancy of subgraph features across all views, with a branch-and-bound algorithm being proposed to prune subgraph search space. Because graph-views may complement each other and play different roles in a learning task, we assign each view with a weight value indicating its importance to the learning task and further use an optimization process to find optimal weight values for each graph-view. The iteration between cross graph-view subgraph scoring and graph-view weight updating forms a closed loop to find optimal subgraphs to represent graphs for multi-graph-view learning. Experiments and comparisons on real-world tasks demonstrate the algorithm’s superior performance