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Jackson-type inequalities for spherical neural networks with doubling weights
Shaobo Lin1, Jinshan Zeng2, Lin Xu2
1Institute of Intelligent System and Decision, Wenzhou University, Wenzhou 325035, China.
Summary
This study introduces weighted spherical neural networks (SNNs) for improved spherical data processing. These networks offer enhanced approximation capabilities for localized data analysis.
Area of Science:
- Mathematics
- Computer Science
- Data Science
Background:
- Spherical data processing is crucial in various applications.
- Spherical neural networks (SNNs) offer good approximation and localization.
- Weighted approximation can improve localized analysis on spheres.
Purpose of the Study:
- To construct well-localized spherical neural networks (SNNs).
- To study the approximation capabilities of these SNNs using weighted methods.
- To establish error estimates for weighted SNNs approximation.
Main Methods:
- Utilizing minimal Riesz energy points and spherical cap average operator.
- Developing SNNs with bounded sigmoidal activation functions.
- Establishing a Jackson-type error estimate in L(p) space for doubling weights.
Main Results:
- Construction of a class of well-localized SNNs.
- Demonstration of their approximation capabilities under weighted schemes.
- Derivation of a Jackson-type error estimate for weighted SNNs.
Conclusions:
- Weighted SNNs provide a powerful tool for localized spherical data approximation.
- The developed method offers theoretical guarantees for approximation accuracy.
- This research advances the field of spherical data analysis and machine learning.
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