# Canonical Polyadic Decomposition and Deep Learning for Machine Fault Detection

arXiv: https://arxiv.org/abs/2107.09519 · HTML: https://mlsanity.com/paper/2107.09519/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 20 Jul 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep Learning for Audio Signal Processing](https://mlsanity.com/paper/1905.00078/) (2019)
- [MIMII Dataset: Sound Dataset for Malfunctioning Industrial Machine Investigation and Inspection](https://mlsanity.com/paper/1909.09347/) (2019)
- [Fusing Physics-based and Deep Learning Models for Prognostics](https://mlsanity.com/paper/2003.00732/) (2020)
- [Feature Learning for Fault Detection in High-Dimensional Condition-Monitoring Signals](https://mlsanity.com/paper/1810.05550/) (2018)

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

- [Robust Time Series Denoising with Learnable Wavelet Packet Transform](https://mlsanity.com/paper/2206.06126/) (2022)
- [Efficient CNN Compression via Multi-method Low Rank Factorization and Feature Map Similarity](https://mlsanity.com/paper/2510.00062/) (2025)
- [Optimizing Tensor Train Decomposition in DNNs for RISC-V Architectures Using Design Space Exploration and Compiler Optimizations](https://mlsanity.com/paper/2602.01996/) (2026)

## Abstract (arXiv)

Acoustic monitoring for machine fault detection is a recent and expanding research path that has already provided promising results for industries. However, it is impossible to collect enough data to learn all types of faults from a machine. Thus, new algorithms, trained using data from healthy conditions only, were developed to perform unsupervised anomaly detection. A key issue in the development of these algorithms is the noise in the signals, as it impacts the anomaly detection performance. In this work, we propose a powerful data-driven and quasi non-parametric denoising strategy for spectral data based on a tensor decomposition: the Non-negative Canonical Polyadic (CP) decomposition. This method is particularly adapted for machine emitting stationary sound. We demonstrate in a case study, the Malfunctioning Industrial Machine Investigation and Inspection (MIMII) baseline, how the use of our denoising strategy leads to a sensible improvement of the unsupervised anomaly detection. Such approaches are capable to make sound-based monitoring of industrial processes more reliable.