# A Proportional-Integral Controller-Incorporated SGD Algorithm for High Efficient Latent Factor Analysis

arXiv: https://arxiv.org/abs/2508.17609 · HTML: https://mlsanity.com/paper/2508.17609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 79 references that are in the map.
- First posted on arXiv 25 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Nesterov's Accelerated Gradient and Momentum as approximations to Regularised Update Descent](https://mlsanity.com/paper/1607.01981/) (2016)
- [A Nonlinear PID-Enhanced Adaptive Latent Factor Analysis Model](https://mlsanity.com/paper/2208.02513/) (2022)
- [Communication-Censored Distributed Stochastic Gradient Descent](https://mlsanity.com/paper/1909.03631/) (2019)
- [An ADRC-Incorporated Stochastic Gradient Descent Algorithm for Latent Factor Analysis](https://mlsanity.com/paper/2401.07012/) (2024)

## Abstract (arXiv)

In industrial big data scenarios, high-dimensional sparse matrices (HDI) are widely used to characterize high-order interaction relationships among massive nodes. The stochastic gradient descent-based latent factor analysis (SGD-LFA) method can effectively extract deep feature information embedded in HDI matrices. However, existing SGD-LFA methods exhibit significant limitations: their parameter update process relies solely on the instantaneous gradient information of current samples, failing to incorporate accumulated experiential knowledge from historical iterations or account for intrinsic correlations between samples, resulting in slow convergence speed and suboptimal generalization performance. Thus, this paper proposes a PILF model by developing a PI-accelerated SGD algorithm by integrating correlated instances and refining learning errors through proportional-integral (PI) control mechanism that current and historical information; Comparative experiments demonstrate the superior representation capability of the PILF model on HDI matrices