# Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization

arXiv: https://arxiv.org/abs/2112.04193 · HTML: https://mlsanity.com/paper/2112.04193/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 62 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Denoising Adversarial Autoencoders](https://mlsanity.com/paper/1703.01220/) (2017)
- [Graph Regularized Autoencoder and its Application in Unsupervised Anomaly Detection](https://mlsanity.com/paper/2010.15949/) (2020)
- [The Fast Kernel Transform](https://mlsanity.com/paper/2106.04487/) (2021)
- [A Data-driven Approach to Actuator and Sensor Fault Detection, Isolation and Estimation in Discrete-Time Linear Systems](https://mlsanity.com/paper/1606.06220/) (2016)

## Built on by (most cited first, 3 of 3)

- [Principal Orthogonal Latent Components Analysis (POLCA Net)](https://mlsanity.com/paper/2410.07289/) (2024)
- [Nonlinear Principal Component Analysis with Random Bernoulli Features for Process Monitoring](https://mlsanity.com/paper/2503.12456/) (2025)
- [Orthogonal Dendritic Intrinsic Networks: An Architecture for Significance-Ordered, Orthogonal Latent Spaces](https://mlsanity.com/paper/2607.05653/) (2026)

## Abstract (arXiv)

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.