Interactions among large number of entities is naturally high-dimensional and
incomplete (HDI) in many big data related tasks. Behavioral characteristics of
users are hidden in these interactions, hence, effective representation of the
HDI data is a fundamental task for understanding user behaviors. Latent factor
analysis (LFA) model has proven to be effective in representing HDI data. The
performance of an LFA model relies heavily on its training process, which is a
non-convex optimization. It has been proven that incorporating local curvature
and preprocessing gradients during its training process can lead to superior
performance compared to LFA models built with first-order family methods.
However, with the escalation of data volume, the feasibility of second-order
algorithms encounters challenges. To address this pivotal issue, this paper
proposes a mini-block diagonal hessian-free (Mini-Hes) optimization for
building an LFA model. It leverages the dominant diagonal blocks in the
generalized Gauss-Newton matrix based on the analysis of the Hessian matrix of
LFA model and serves as an intermediary strategy bridging the gap between
first-order and second-order optimization methods. Experiment results indicate
that, with Mini-Hes, the LFA model outperforms several state-of-the-art models
in addressing missing data estimation task on multiple real HDI datasets from
recommender system. (The source code of Mini-Hes is available at
this https URL)

本文提出了一种使用 Mini-Hes 优化算法构建 LFA 模型的方法，通过分析 HDI 数据的 Hessian 矩阵，利用广义 Gauss-Newton 矩阵中的主对角块作为中介策略，弥合了一阶和二阶优化方法之间的差距，并在多个实际 HDI 数据集的缺失数据估计任务中证明了 Mini-Hes 使 LFA 模型超越了一些最先进的模型。