Given nodal observations that can be limited due to sampling costs or privacy concerns, several network-science-related applications entail reconstruction of values on all network nodes by leveraging topology information. Such a semi-supervised learning (SSL) task has been tackled mainly for graphs capturing a single class of inter-dependencies (or relations) among nodal variables. Faced with multi-relational graphs (MRGs), which emerge in various real-world networks, the present work introduces a principled framework to extrapolate spatio-temporal nodal processes that could be stationary or nonstationary. Broadening the scope of graph kernel-based approaches to MRGs, stationary graph processes are modeled first using a Gaussian mixture (GM) prior, where the covariance matrix of each Gaussian component describes one of the relations in the MRG. To further cope with nonstationary nodal processes, a first-order topology-dependent Gaussian transition prior is considered per relation, what gives rise to a GM transition density that accounts for all relations. In both cases, adapting the expectation-maximization (EM) algorithm yields two novel graph-adaptive solvers that not only reconstructs nodal features over unobserved nodes, but also quantifies the contribution of each relation. To enrich expressiveness of these novel EM-based approaches, multiple kernels per relation are also explored. Experiments with real data showcase the merits of the proposed methods relative to the existing alternatives.

中文翻译：

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多重关系图的时空过程的概率重构

鉴于可能由于采样成本或隐私问题而受到限制的节点观测结果，一些与网络科学相关的应用需要利用拓扑信息在所有网络节点上重建值。这种半监督学习（SSL）任务已主要针对捕获节点变量之间的一类相互依存关系（或关系）的图形解决。面临多关系图（MRG），它出现在各种现实世界的网络中，目前的工作引入了一个有原则的框架，以推断可能是平稳的或非平稳的时空节点过程。为了拓宽基于图核的MRG方法的范围，首先先使用高斯混合（GM）对静态图过程进行建模，其中每个高斯分量的协方差矩阵描述了MRG中的一种关系。为了进一步应对非平稳节点过程，每个关系都考虑了一阶依赖于拓扑的高斯跃迁先验，这导致了考虑所有关系的GM跃迁密度。在这两种情况下，采用期望最大化（EM）算法都会产生两个新颖的图自适应求解器，它们不仅可以在未观察到的节点上重建节点特征，而且还可以量化每个关系的贡献。为了丰富这些新颖的基于EM的方法的表达能力，还探索了每个关系的多个内核。真实数据的实验证明了相对于现有替代方法而言，所提方法的优点。