Piecewise linear neural networks and deep learning

Tao, Qinghua; Li, Zhiheng; Huang, Xiaolin; Xi, Xiangming; Wang, Shuning; Suykens, Johan A. K.

doi:10.1038/s43586-022-00125-7

Cited by 18 publications

(4 citation statements)

References 133 publications

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“…As a branch of machine learning, deep learning is highly capable of modeling nonlinearities with high flexibility and performs much better in dealing with realistic and complex problems. Therefore, deep learning has been introduced into bearing fault diagnosis to obtain a higher correct rate of fault diagnosis in complex environments 12 , 13 .…”

Section: Related Workmentioning

confidence: 99%

A graph neural network-based bearing fault detection method

Xiao

Yang

2023

Sci Rep

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Bearings are very important components in mechanical equipment, and detecting bearing failures helps ensure healthy operation of mechanical equipment and can prevent catastrophic accidents. Most of the well-established detection methods do not take into account the correlation between signals and are difficult to accurately identify those fault samples that have a low degree of failure. To address this problem, we propose a graph neural network-based bearing fault detection (GNNBFD) method. The method first constructs a graph using the similarity between samples; secondly the constructed graph is fed into a graph neural network (GNN) for feature mapping, and the samples outputted by the GNN network fuse the feature information of their neighbors, which is beneficial to the downstream detection task; then the samples mapped by the GNN network are fed into base detector for fault detection; finally, the results determined by the integrated base detector algorithm are determined, and the top n samples with the highest outlier scores are the faulty samples. The experimental results with five state-of-the-art algorithms on publicly available datasets show that the GNNBFD algorithm improves the AUC by 6.4% compared to the next best algorithm, proving that the GNNBFD algorithm is effective and feasible.

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Section: Related Workmentioning

confidence: 99%

A graph neural network-based bearing fault detection method

Xiao

Yang

2023

Sci Rep

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“…This encompasses continuous and non-polynomial activation for shallow neural networks [2] and non-affine, constant, and continuously differentiable activation with nonzero derivatives for deep neural networks [3]. Consequently, neural networks utilizing the Rectified Linear Unit (ReLU) activation function have demonstrated efficacy in resolving a broad range of machine learning research problems, their solution curves corresponding to a piecewise-linear approximation [4,5].…”

Section: Introductionmentioning

confidence: 99%

Universal Approximators from Anti-Derivatives: Enhancing Neural Networks

Lee

2023

Preprint

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The existence of optimal neural networks, represented as combinations of piecewise functions, is proven by the universal approximation theorem. However, deriving this optimal solution from the training parameters of neural networks remains a challenging problem. This study proposes a novel strategy to construct an approximator for an arbitrary function, starting with a presumed optimal piecewise solution. The proposed approximation employs the anti-derivatives of a Fourier series expansion for the presumed piecewise function, leading to a remarkable feature that enables the simultaneous approximation of an arbitrary function and its anti-derivatives. Systematic experiments have demonstrated the outstanding merits of the proposed anti-derivatives-based approximator, such as the ability to solve differential equations and to enhance the capabilities of neural networks. Furthermore, the anti-derivatives approximator allows for the optimization of activation profiles within neural networks. This feature introduces a novel approach for finding unconventional activation profiles specialized for a given dataset.

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“…While CS has improved the performance of CGI through its image reconstruction algorithms, its application is constrained by strong sparsity assumptions and limitations in the reconstruction process [32][33][34]. The emergence of Deep Learning (DL) [35][36][37][38][39] presents an opportunity to relax sparsity constraints by recovering images at ultra-low sampling rates (SR) using trained data and untrained strategies [40][41][42][43]. Concurrently, ToF-based novel computational 3D imaging techniques show great promise across various imaging domains [44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Reconstructing Depth Images for Time-of-Flight Cameras Based on Second-Order Correlation Functions

Wang,

Ao,

Zheng

et al. 2023

Photonics

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Depth cameras are closely related to our daily lives and have been widely used in fields such as machine vision, autonomous driving, and virtual reality. Despite their diverse applications, depth cameras still encounter challenges like multi-path interference and mixed pixels. Compared to traditional sensors, depth cameras have lower resolution and a lower signal-to-noise ratio. Moreover, when used in environments with scattering media, object information scatters multiple times, making it difficult for time-of-flight (ToF) cameras to obtain effective object data. To tackle these issues, we propose a solution that combines ToF cameras with second-order correlation transform theory. In this article, we explore the utilization of ToF camera depth information within a computational correlated imaging system under ambient light conditions. We integrate compressed sensing and non-training neural networks with ToF technology to reconstruct depth images from a series of measurements at a low sampling rate. The research indicates that by leveraging the depth data collected by the camera, we can recover negative depth images. We analyzed and addressed the reasons behind the generation of negative depth images. Additionally, under undersampling conditions, the use of reconstruction algorithms results in a higher peak signal-to-noise ratio compared to images obtained from the original camera. The results demonstrate that the introduced second-order correlation transformation can effectively reduce noise originating from the ToF camera itself and direct ambient light, thereby enabling the use of ToF cameras in complex environments such as scattering media.

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Piecewise linear neural networks and deep learning

Abstract: For the published version, please access https://rdcu.be/cPIGw for online-reading, download the manuscript from https://www.nature.com/articles/s43586-022-00125-7#citeas, and check the supplementary information via https://www.nature.com/articles/s43586-022-00125-7#Sec38.

Cited by 18 publications

References 133 publications

A graph neural network-based bearing fault detection method

A graph neural network-based bearing fault detection method

Universal Approximators from Anti-Derivatives: Enhancing Neural Networks

Reconstructing Depth Images for Time-of-Flight Cameras Based on Second-Order Correlation Functions

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