Hyperparameter-free and Explainable Whole Graph Embedding
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Many real-world complex systems can be described as graphs. For a large-scale graph with low sparsity, a node's adjacency vector is a long and sparse representation, limiting the practical utilization of existing machine learning methods on nodal features. In practice, graph embedding (graph representation learning) attempts to learn a lower-dimensional representation vector for each node or the whole graph while maintaining the most basic information of graph. Since various machine learning methods can efficiently process lower-dimensional vectors, graph embedding has recently attracted a lot of attention. However, most node embedding or whole graph embedding methods suffer from the problem of having more sophisticated methodology, hyperparameter optimization, and low explainability. This paper proposes a hyperparameter-free, extensible, and explainable whole graph embedding method, combining the DHC (Degree, H-index and Coreness) theorem and Shannon Entropy (E), abbreviated as DHC-E. The new whole graph embedding scheme can obtain a trade-off between the simplicity and the quality under some supervised classification learning tasks, using molecular, social, and brain networks. In addition, the proposed approach has a good performance in lower-dimensional graph visualization. The new methodology is overall simple, hyperparameter-free, extensible, and explainable for whole graph embedding with promising potential for exploring graph classification, prediction, and lower-dimensional graph visualization.
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