Efficient Tree-SVD for Subset Node Embedding over Large Dynamic Graphs

作者：Xinyu Du, Xingyi Zhang, Sibo Wang, Zengfeng Huang · 发表于：Proceedings of the ACM on Management of Data · 年份：2023 · DOI：10.1145/3588950 · 被引用次数：13 · 研究领域：Advanced Graph Neural Networks、Recommender Systems and Techniques、Complex Network Analysis Techniques

Subset embedding is the task to learn low-dimensional representations for a subset of nodes according to the graph topology. It has applications when we focus on a subset of users, e.g., young adults, and aim to make better recommendations for these target users. In real-world scenarios, graphs are dynamically changing. Thus, it is more desirable to dynamically maintain the subset embeddings to reflect graph updates. The state-of-the-art methods, e.g., DynPPE, still adopt a hashing-based method, while hashing-based solutions are shown to be less effective than matrix factorization (MF)-based methods in existing studies. At the same time, MF-based methods in the literature are too expensive to update the embedding when the graph changes, making them inapplicable on dynamic graphs. Motivated by this, we present Tree-SVD, an efficient and effective MF-based method for dynamic subset embedding. If we simply maintain the whole proximity matrix, then we need to re-do the MF, e.g., truncated Singular Value Decomposition (SVD), on the whole matrix after graph updates, which is prohibitive. To tackle this issue, our main idea is to do hierarchical SVD (HSVD) on the proximity matrix of the given subset, which vertically divides the proximity matrix into multiple sub-matrices, and then repeatedly do SVD on sub-matrices and merge the intermediate results to obtain the final embedding. We first present Tree-SVD, which combines a sparse randomized SVD with an HSVD. Our theoretical analysis...