# Second-Order Component Analysis for Fault Detection

arXiv: https://arxiv.org/abs/2103.07303 · HTML: https://mlsanity.com/paper/2103.07303/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 44 references that are in the map.
- First posted on arXiv 12 Mar 2021.

## Builds on (most cited first, 4 of 4)

- [Quadratic Autoencoder (Q-AE) for Low-dose CT Denoising](https://mlsanity.com/paper/1901.05593/) (2019)
- [Universal Approximation with Quadratic Deep Networks](https://mlsanity.com/paper/1808.00098/) (2018)
- [An improved mixture of probabilistic PCA for nonlinear data-driven process monitoring](https://mlsanity.com/paper/2012.06830/) (2020)
- [Neural Component Analysis for Fault Detection](https://mlsanity.com/paper/1712.04118/) (2017)

## Built on by (most cited first, 2 of 2)

- [ODCR: Orthogonal Decoupling Contrastive Regularization for Unpaired Image Dehazing](https://mlsanity.com/paper/2404.17825/) (2024)
- [Luminance Component Analysis for Exposure Correction](https://mlsanity.com/paper/2411.16325/) (2024)

## Abstract (arXiv)

Process monitoring based on neural networks is getting more and more attention. Compared with classical neural networks, high-order neural networks have natural advantages in dealing with heteroscedastic data. However, high-order neural networks might bring the risk of overfitting and learning both the key information from original data and noises or anomalies. Orthogonal constraints can greatly reduce correlations between extracted features, thereby reducing the overfitting risk. This paper proposes a novel fault detection method called second-order component analysis (SCA). SCA rules out the heteroscedasticity of pro-cess data by optimizing a second-order autoencoder with orthogonal constraints. In order to deal with this constrained optimization problem, a geometric conjugate gradient algorithm is adopted in this paper, which performs geometric optimization on the combination of Stiefel manifold and Euclidean manifold. Extensive experiments on the Tennessee-Eastman benchmark pro-cess show that SCA outperforms PCA, KPCA, and autoencoder in missed detection rate (MDR) and false alarm rate (FAR).