Precise representation of large-scale undirected network is the basis for understanding relations within a massive entity set. The undirected network representation task can be efficiently addressed by a symmetry non-negative latent factor (SNLF) model, whose objective is clearly non-convex. However, existing SNLF models commonly adopt a first-order optimizer that cannot well handle the non-convex objective, thereby resulting in inaccurate representation results. On the other hand, higher-order learning algorithms are expected to make a breakthrough, but their computation efficiency are greatly limited due to the direct manipulation of the Hessian matrix, which can be huge in undirected network representation tasks. Aiming at addressing this issue, this study proposes to incorporate an efficient second-order method into SNLF, thereby establishing a second-order symmetric non-negative latent factor analysis model for undirected network with two-fold ideas: a) incorporating a mapping strategy into SNLF model to form an unconstrained model, and b) training the unconstrained model with a specially designed second order method to acquire a proper second-order step efficiently. Empirical studies indicate that proposed model outperforms state-of-the-art models in representation accuracy with affordable computational burden.

中文翻译：

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二阶对称非负潜在因子分析

大规模无向网络的精确表示是理解海量实体集中关系的基础。无向网络表示任务可以通过对称非负潜在因子（SNLF）模型有效地解决，其目标显然是非凸的。然而，现有的 SNLF 模型通常采用一阶优化器，不能很好地处理非凸目标，从而导致表示结果不准确。另一方面，高阶学习算法有望取得突破，但由于直接操作 Hessian 矩阵，其计算效率受到很大限制，这在无向网络表示任务中可能是巨大的。针对这个问题，本研究提出在 SNLF 中加入一种有效的二阶方法，从而建立具有双重思想的无向网络二阶对称非负潜在因子分析模型：a）将映射策略结合到SNLF模型中以形成无约束模型，以及b）使用专门设计的第二个训练无约束模型order 方法有效地获得适当的二阶步骤。实证研究表明，所提出的模型在表示精度方面优于最先进的模型，且计算负担可承受。