# Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring

arXiv: https://arxiv.org/abs/2503.12456 · HTML: https://mlsanity.com/paper/2503.12456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 37 references that are in the map.
- First posted on arXiv 16 Mar 2025.

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

- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Compact Random Feature Maps](https://mlsanity.com/paper/1312.4626/) (2013)
- [Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization](https://mlsanity.com/paper/2112.04193/) (2021)
- [Scalable Kernel Logistic Regression with Nystr"om Approximation: Theoretical Analysis and Application to Discrete Choice Modelling](https://mlsanity.com/paper/2402.06763/) (2024)
- [Compressed Sensing with Very Sparse Gaussian Random Projections](https://mlsanity.com/paper/1408.2504/) (2014)

## Abstract (arXiv)

The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel matrices. This dependence poses significant challenges in meeting the high computational demands and real-time responsiveness required by online monitoring systems. To alleviate the computational burden of dense large-scale matrix multiplication, we incorporate the bootstrap sampling concept into random feature mapping and propose a novel random Bernoulli principal component analysis method to efficiently capture nonlinear patterns in the process. We derive a convergence bound for the kernel matrix approximation constructed using random Bernoulli features, ensuring theoretical robustness. Subsequently, we design four fast process monitoring methods based on random Bernoulli principal component analysis to extend its nonlinear capabilities for handling diverse fault scenarios. Finally, numerical experiments and real-world data analyses are conducted to evaluate the performance of the proposed methods. Results demonstrate that the proposed methods offer excellent scalability and reduced computational complexity, achieving substantial cost savings with minimal performance loss compared to traditional kernel-based approaches.