图机器学习是人工智能领域热点研究方向，而图核函数则是其中一类重要方法，能够针对图这类复杂且不规则的数据学习有效特征，进而为直接使用经典核机器学习方法进行图数据分析奠定了重要理论基础。然而，现有经典R-卷积（R-convolution）图核函数仍存在着一些理论难点问题，例如：忽略子结构间的位置匹配信息、忽视图结构的全局结构特征、难以捕捉多个图样本间的共性结构模式信息等，严重制约了经典图核函数的分析性能。

为克服现有经典R-卷积图核的理论局限性，本文提出了一种基于深度图自编码器的新型图核方法，即：深度层次化的可传导匹配Jensen-Shannon图核（Deep Hierarchical Transitive Aligned Jensen-Shannon Graph Kernels，DHTA-JSK）。具体而言，本文首先提出了一种逐层匹配的图自编码器（HA-GAE），能够通过逐层匹配的方式为每个原始图样本获得节点匹配的深度嵌入图结构，进而通过嵌入图的邻接矩阵获取图的层次化概率分布。然后，通过使用Jensen-Shannon散度度量上述概率分布间的相似性信息构建了DHTA-JSK图核。最后，本文基于新图核使用C-支持向量机（C-SVM）对图结构数据进行分类。经典图分类数据集上的实验证明，本文提出的新型DHTA-JSK图核具有比经典图核与图深度学习方法更好的图分类性能，具有更全面的结构信息表达能力。

Graph-based machine learning is an important aspect of artificial intelligence. One method to learn effective features in complex and irregular data such as graphs is the graph kernel method, providing theoretical basics for employing classical kernel machines for graph structural data analysis. However, most existing classical R-convolutional graph kernels have some theoretical problems, such as ignoring the locational correspondence information between substructures, paying less attention on global structural features, and being unable to capture the shared structural pattern information over multiple graph samples, influencing the effectiveness of existing R-convolution graph kernels.

In order to overcome the aforementioned limitations, we propose a family of novel Deep Hierarchical Transitive Aligned Jensen-Shannon Graph Kernels (DHTA-JSK) based on deep graph auto-encoder neural networks. Specifically, we commence by designing a Hierarchical Aligned Graph Auto-Encoder (HA-GAE), that computes the deep embedding graph for each original sample graph by gradually identifying the hierarchical transitive aligned information between graphs, and then obtains the resulting hierarchical probability distributions through the adjacency matrices of the embedding graphs. Finally, the proposed DHTA-JSK is defined by measuring the Jensen-Shannon divergence between the probability distributions. Experimental evaluations demonstrate that the proposed DHTA-JSK can outperform both the classical graph kernels and the graph deep learning approaches on graph classification tasks, providing more comprehensive structural information of graphs.