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Jointly learning relevant subgraph patterns and nonlinear models of their indicators

arXiv.org Machine Learning

Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most fundamental features, but the number of possible subgraph patterns are intractably large due to the combinatorial explosion. We propose a novel efficient algorithm to jointly learn relevant subgraph patterns and nonlinear models of their indicators. Previous methods for such joint learning of subgraph features and models are based on search for single best subgraph features with specific pruning and boosting procedures of adding their indicators one by one, which result in linear models of subgraph indicators. In contrast, the proposed approach is based on directly learning regression trees for graph inputs using a newly derived bound of the total sum of squares for data partitions by a given subgraph feature, and thus can learn nonlinear models through standard gradient boosting. An illustrative example we call the Graph-XOR problem to consider nonlinearity, numerical experiments with real datasets, and scalability comparisons to naive approaches using explicit pattern enumeration are also presented.


gRegress: Extracting Features from Graph Transactions for Regression

AAAI Conferences

In this work we propose gRegress, a new algorithm which given set of labeled graphs and a real value associated with each graph extracts the complete set of subgraphs such that a) each subgraph in this set has correlation with the real value above a user-specified threshold and b) each subgraph in this set has correlation with any other subgraph in the set below a user-specified threshold. gRegress incorporates novel pruning mechanisms based on correlation of a subgraph feature with the output and correlation with other subgraph features. These pruning mechanisms lead to significant speedup. Experimental results indicate that in terms of runtime, gRegress substantially outperforms gSpan, often by an order of magnitude while the regression models produced by both approaches have comparable accuracy.


An Application of Boosting to Graph Classification

Neural Information Processing Systems

This paper presents an application of Boosting for classifying labeled graphs, general structures for modeling a number of real-world data, such as chemical compounds, natural language texts, and bio sequences. The proposal consists of i) decision stumps that use subgraph as features, and ii) a Boosting algorithm in which subgraph-based decision stumps are used as weak learners. We also discuss the relation between our algorithm and SVMs with convolution kernels. Two experiments using natural language data and chemical compounds show that our method achieves comparable or even better performance than SVMs with convolution kernels as well as improves the testing efficiency.


An Application of Boosting to Graph Classification

Neural Information Processing Systems

This paper presents an application of Boosting for classifying labeled graphs, general structures for modeling a number of real-world data, such as chemical compounds, natural language texts, and bio sequences. The proposal consists of i) decision stumps that use subgraph as features, and ii) a Boosting algorithm in which subgraph-based decision stumps are used as weak learners. We also discuss the relation between our algorithm and SVMs with convolution kernels. Two experiments using natural language data and chemical compounds show that our method achieves comparable or even better performance than SVMs with convolution kernels as well as improves the testing efficiency.