提出自适应立方正则化模型，加速高维稀疏数据建模收敛。
Adaptive Cubic Regularized Second-Order Latent Factor Analysis Model
- 自适应立方正则化动态缓解非凸优化不稳定性
- 通过多海森向量乘积提升二阶信息精度，加快收敛
- 在工业级数据集上优于现有最优方法，适合大规模稀疏建模
高维稀疏（HDI）数据在现实应用中普遍存在，其特征为大量节点交互。二阶潜在因子模型在建模此类数据方面表现优异。然而，由于SLF模型目标函数具有双线性与非凸特性，需引入阻尼项并精细调参以保证稳定。为此，本文提出自适应立方正则化二阶潜在因子分析（ACRSLF）模型。该模型结合双重机制：1）自适应立方正则化，动态抑制非凸优化中的不稳定性；2）共轭梯度迭代中采用多海森向量乘积评估，实现更精确的二阶信息融合。在两个工业级HDI数据集上的实验表明，ACRSLF收敛速度更快，表示精度更高，优于当前基于优化器的先进潜在因子分析模型。
原文摘要 · Abstract (English)
High-dimensional and incomplete (HDI) data, characterized by massive node interactions, have become ubiquitous across various real-world applications. Second-order latent factor models have shown promising performance in modeling this type of data. Nevertheless, due to the bilinear and non-convex nature of the SLF model's objective function, incorporating a damping term into the Hessian approximation and carefully tuning associated parameters become essential. To overcome these challenges, we propose a new approach in this study, named the adaptive cubic regularized second-order latent factor analysis (ACRSLF) model. The proposed ACRSLF adopts the two-fold ideas: 1) self-tuning cubic regularization that dynamically mitigates non-convex optimization instabilities; 2) multi-Hessian-vector product evaluation during conjugate gradient iterations for precise second-order information assimilation. Comprehensive experiments on two industrial HDI datasets demonstrate that the ACRSLF converges faster and achieves higher representation accuracy than the advancing optimizer-based LFA models.
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