# Fast Latent Factor Analysis via a Fuzzy PID-Incorporated Stochastic Gradient Descent Algorithm

arXiv: https://arxiv.org/abs/2303.03941 · HTML: https://mlsanity.com/paper/2303.03941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 50 references that are in the map.
- First posted on arXiv 7 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [Accelerating Federated Learning via Momentum Gradient Descent](https://mlsanity.com/paper/1910.03197/) (2019)
- [A Nonlinear PID-Enhanced Adaptive Latent Factor Analysis Model](https://mlsanity.com/paper/2208.02513/) (2022)
- [Matrix Computations and Optimization in Apache Spark](https://mlsanity.com/paper/1509.02256/) (2015)

## Abstract (arXiv)

A high-dimensional and incomplete (HDI) matrix can describe the complex interactions among numerous nodes in various big data-related applications. A stochastic gradient descent (SGD)-based latent factor analysis (LFA) model is remarkably effective in extracting valuable information from an HDI matrix. However, such a model commonly encounters the problem of slow convergence because a standard SGD algorithm learns a latent factor relying on the stochastic gradient of current instance error only without considering past update information. To address this critical issue, this paper innovatively proposes a Fuzzy PID-incorporated SGD (FPS) algorithm with two-fold ideas: 1) rebuilding the instance learning error by considering the past update information in an efficient way following the principle of PID, and 2) implementing hyper-parameters and gain parameters adaptation following the fuzzy rules. With it, an FPS-incorporated LFA model is further achieved for fast processing an HDI matrix. Empirical studies on six HDI datasets demonstrate that the proposed FPS-incorporated LFA model significantly outperforms the state-of-the-art LFA models in terms of computational efficiency for predicting the missing data of an HDI matrix with competitive accuracy.