PI-NLF：一种非负潜在因子分析的比例积分法
PI-NLF: A Proportional-Integral Approach for Non-negative Latent Factor Analysis
摘要：
高维不完备矩阵（HDI）经常出现在各种大数据相关的应用中，它表明了众多节点之间固有的非负相互作用。非负潜在因子（NLF）模型对HDI矩阵进行有效的表示学习，其学习过程主要依赖于单个潜在因子依赖的非负乘性更新（SLF-NMU）算法。然而，SLF-NMU算法仅基于当前更新增量更新潜在因子，而没有适当考虑过去的学习信息，导致收敛缓慢。受比例积分（PI）控制器在各种应用中取得的巨大成功的启发，本文提出了一种包含PI的非负潜因子（PI-NLF）模型，该模型具有两个方面的思想：（1）根据PI控制器的原理，通过考虑过去的更新增量，建立增量细化（IR）机制;以及b）设计基于IR的SLF-NMU（ISN）算法以加速所得模型的收敛速率。对4个HDI数据集的实证研究表明，PI-NLF模型在计算效率和HDI矩阵缺失数据估计精度方面均优于现有模型。因此，本研究揭示了通过误差反馈控制器提高非负学习算法性能的可行性。
英文摘要：
A high-dimensional and incomplete (HDI) matrix frequently appears in various big-data-related applications, which demonstrates the inherently non-negative interactions among numerous nodes. A non-negative latent factor (NLF) model performs efficient representation learning to an HDI matrix, whose learning process mostly relies on a single latent factor-dependent, non-negative and multiplicative update (SLF-NMU) algorithm. However, an SLF-NMU algorithm updates a latent factor based on the current update increment only without appropriate considerations of past learning information, resulting in slow convergence. Inspired by the prominent success of a proportional-integral (PI) controller in various applications, this paper proposes a Proportional-Integral-incorporated Non-negative Latent Factor (PI-NLF) model with two-fold ideas: a) establishing an Increment Refinement (IR) mechanism via considering the past update increments following the principle of a PI controller; and b) designing an IR-based SLF-NMU (ISN) algorithm to accelerate the convergence rate of a resultant model. Empirical studies on four HDI datasets demonstrate that a PI-NLF model outperforms the state-of-the-art models in both computational efficiency and estimation accuracy for missing data of an HDI matrix. Hence, this study unveils the feasibility of boosting the performance of a non-negative learning algorithm through an error feedback controller.
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