# PI-NLF: A Proportional-Integral Approach for Non-negative Latent Factor Analysis

arXiv: https://arxiv.org/abs/2205.02591 · HTML: https://mlsanity.com/paper/2205.02591/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 10 of 10)

- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [MeLU: Meta-Learned User Preference Estimator for Cold-Start Recommendation](https://mlsanity.com/paper/1908.00413/) (2019)
- [Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints](https://mlsanity.com/paper/1408.3595/) (2014)
- [Neural Rating Regression with Abstractive Tips Generation for Recommendation](https://mlsanity.com/paper/1708.00154/) (2017)
- [AutoSVD++: An Efficient Hybrid Collaborative Filtering Model via Contractive Auto-encoders](https://mlsanity.com/paper/1704.00551/) (2017)
- [Efficient Neural Interaction Function Search for Collaborative Filtering](https://mlsanity.com/paper/1906.12091/) (2019)
- [A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples](https://mlsanity.com/paper/2106.02119/) (2021)
- [Meta Learning for Support Recovery in High-dimensional Precision Matrix Estimation](https://mlsanity.com/paper/2006.12598/) (2020)

## Abstract (arXiv)

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.