Stancu-Type Generalizations of Neural Network Operators with Perturbed Sampling Nodes

TL;DR

This paper introduces a flexible generalization of neural network operators with perturbed sampling nodes, providing theoretical convergence guarantees and demonstrating improved approximation and denoising performance on signals.

Contribution

It presents a novel Stancu-type generalization of neural network operators with adjustable sampling nodes, including theoretical analysis and practical applications.

Findings

Operators are well-defined and bounded.

Uniform convergence on compact domains is established.

Effective noise suppression demonstrated in ECG signal denoising.

Abstract

In this paper, we introduce a Stancu-type generalization of multivariate neural network operators by incorporating two parameters that perturb the sampling nodes. The proposed operators extend the existing neural network operator by allowing greater flexibility in the placement of sampling nodes. We establish the well-definedness and boundedness of the operators and prove uniform convergence on compact domains. Furthermore, quantitative error estimates are derived in terms of the modulus of continuity, leading to convergence rate results. Numerical experiments are presented to illustrate the approximation behavior of the proposed operators and to demonstrate the effect of the Stancu parameters on the sampling nodes and the approximation accuracy. Finally, the application of signal denoising is demonstrated using a synthetic ECG signal, showing that the proposed operators effectively suppress noise while preserving the signal's main characteristics.