Sylvester Tensor Equation for Multi-Way Association
Sylvester Tensor Equation for Multi-Way Association
复制标题
DOI：
10.1145/3447548.3467336
复制
发表时间：
2021-08
期刊：
影响因子：
--
通讯作者：
Boxin Du;Lihui Liu;H. Tong
中科院分区：
文献类型：
--
作者：
Boxin Du;Lihui Liu;H. Tong
我们如何从社交网络平台的集合中识别相同或相似的用户（例如，Facebook、Twitter、LinkedIn等）？我们应该在正确的时间、正确的地点向给定的用户推荐哪家餐厅？对于一种疾病，哪些基因和药物最相关？从多输入网络中识别强相关节点集的多路关联是回答这些问题的关键。尽管其重要性，但由于其高度复杂性，很少有多路关联方法存在。在本文中，我们制定的多路联想作为一个凸优化问题，其最优解可以通过一个西尔维斯特张量方程。此外，我们提出了两个快速算法来解决西尔维斯特张量方程，具有线性的时间和空间复杂度。我们进一步提供理论分析的灵敏度的西尔维斯特张量方程的解决方案。实证评估表明所提出的方法的有效性。
How can we identify the same or similar users from a collection of social network platforms (e.g., Facebook, Twitter, LinkedIn, etc.)? Which restaurant shall we recommend to a given user at the right time at the right location? Given a disease, which genes and drugs are most relevant? Multi-way association, which identifies strongly correlated node sets from multiple input networks, is the key to answering these questions. Despite its importance, very few multi-way association methods exist due to its high complexity. In this paper, we formulate multi-way association as a convex optimization problem, whose optimal solution can be obtained by a Sylvester tensor equation. Furthermore, we propose two fast algorithms to solve the Sylvester tensor equation, with a linear time and space complexity. We further provide theoretic analysis in terms of the sensitivity of the Sylvester tensor equation solution. Empirical evaluations demonstrate the efficacy of the proposed method.