In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-sized aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon Divergence (QJSD) between their transitive aligned graph structures. We show that the proposed HAQJSK kernels not only reflect richer intrinsic global graph characteristics in terms of the CTQW, but also address the drawback of neglecting structural correspondence information arising in most existing R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can simultaneously guarantee the properties of permutation invariant and positive definiteness, explaining the theoretical advantages of the HAQJSK kernels. Experiments indicate the effectiveness of the proposed kernels.
翻译:在这项工作中,我们提出一组新型量子内核,即:用于无归属式图表的高级准决量Jensen-Shannon内核(HAQJSK),用于非归属式图表。与大多数现有的古典图形内核不同的是,拟议的HAQJSK内核可以将图表和随机大小的图表转换成固定尺寸一致的图形结构之间的等级一致结构信息,即:高级半轨纵向纵向横向平行矩阵和连续-时-时-量漫步(CT)的高度过渡性统一密度矩阵(HAQJJSK)。 对于将要投递的一对一对图表,HAQJSK核心内核通过测量其过渡性一致图形结构之间的量级一致结构结构图(QJSD)。我们表明,拟议的HAQJSK内核内核结构内核不仅反映CTW的更丰富的内在全球图表特征,而且还要解决连续-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时--时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-时-