用流形学习与核回归填补图中随时间变化的边流量，无需训练数据。
Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning
- 基于流形和多重核回归，结合图拓扑与特征几何结构建模
- 在真实网络数据上显著优于现有主流方法
- 适合无标签数据、低资源场景下的图动态分析
本文将最近提出的多线性核回归与流形学习插补框架（MultiL-KRIM）扩展至图中随时间变化的边流量插补任务。该方法利用单纯复形理论与霍奇拉普拉斯算子刻画图拓扑结构，并通过流形学习识别嵌入再生核希尔伯特空间（RKHS）中特征点云的潜在几何形态。基于光滑流形的切空间思想，采用线性近似片对点云进行协同过滤式逼近。结合矩阵分解，实现降维并支持高效计算，且不依赖任何训练数据或额外信息。在真实网络的时间变边流量数据上的数值实验表明，MultiL-KRIM 相较于多个先进方法展现出显著性能提升。
原文摘要 · Abstract (English)
This paper extends the recently developed framework of multilinear kernel regression and imputation via manifold learning (MultiL-KRIM) to impute time-varying edge flows in a graph. MultiL-KRIM uses simplicial-complex arguments and Hodge Laplacians to incorporate the graph topology, and exploits manifold-learning arguments to identify latent geometries within features which are modeled as a point-cloud around a smooth manifold embedded in a reproducing kernel Hilbert space (RKHS). Following the concept of tangent spaces to smooth manifolds, linear approximating patches are used to add a collaborative-filtering flavor to the point-cloud approximations. Together with matrix factorizations, MultiL-KRIM effects dimensionality reduction, and enables efficient computations, without any training data or additional information. Numerical tests on real-network time-varying edge flows demonstrate noticeable improvements of MultiL-KRIM over several state-of-the-art schemes.
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