Extending the Universal Approximation Theorem for a Broad Class of Hypercomplex-Valued Neural Networks

Vital, Wington L.; Vieira, Guilherme; Valle, Marcos Eduardo

doi:10.1007/978-3-031-21689-3_45

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…When compared to machine learning techniques, the BP neural network exhibits remarkable advantages in terms of nonlinear mapping capability and error tolerance. According to a theoretical proof, the BP neural network can approximate any nonlinear continuous function with arbitrary precision, 28 making it well‐suited for modelling complex respiratory motion.…”

Section: Methodsmentioning

confidence: 99%

“…This process is repeated until a complex nonlinear model is achieved, resulting in actual outputs that closely resemble the expected outputs.When compared to machine learning techniques, the BP neural network exhibits remarkable advantages in terms of nonlinear mapping capability and error tolerance. According to a theoretical proof, the BP neural network can approximate any nonlinear continuous function with arbitrary precision,28 making it well-suited for modelling complex respiratory motion. Other neural network architectures such as the Unet network, Recurrent Neural Network (RNN), and Long Short-Term Memory network (LSTM) are also under consideration.…”

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confidence: 99%

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A back propagation neural network based respiratory motion modelling method

Jiang,

Li,

Yang

et al. 2024

Robotics Computer Surgery

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BackgroundThis study presents the development of a backpropagation neural network‐based respiratory motion modelling method (BP‐RMM) for precisely tracking arbitrary points within lung tissue throughout free respiration, encompassing deep inspiration and expiration phases.MethodsInternal and external respiratory data from four‐dimensional computed tomography (4DCT) are processed using various artificial intelligence algorithms. Data augmentation through polynomial interpolation is employed to enhance dataset robustness. A BP neural network is then constructed to comprehensively track lung tissue movement.ResultsThe BP‐RMM demonstrates promising accuracy. In cases from the public 4DCT dataset, the average target registration error (TRE) between authentic deep respiration phases and those forecasted by BP‐RMM for 75 marked points is 1.819 mm. Notably, TRE for normal respiration phases is significantly lower, with a minimum error of 0.511 mm.ConclusionsThe proposed method is validated for its high accuracy and robustness, establishing it as a promising tool for surgical navigation within the lung.

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%