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A new directional multi-resolution ridgelet network

  • Research Article
  • Published:
Frontiers of Electrical and Electronic Engineering in China

Abstract

In this paper, we propose a new directional multi-resolution ridgelet network (DMRN) based on the ridgelet frame theory, which uses the ridgelet as the activation function in a hidden layer. For the multi-resolution properties of the ridgelet function in the direction besides scale and position, DMRN has great capabilities in catching essential features of direction-rich data. It proves to be able to approximate any multivariate function in a more stable and efficient way, and optimal in approximating functions with spatial inhomogeneities. Besides, using binary ridgelet frame as the mathematical foundation in its construction, DMRN is more flexible with a simple structure. The construction and the learning algorithm of DMRN are given. Its approximation capacity and approximation rate are also analyzed in detail. Possibilities of applications to regression and recognition are included to demonstrate its superiority to other methods and feasibility in practice. Both theory analysis and simulation results prove its high efficiency.

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Authors and Affiliations

  1. Institute of Intelligent Information Processing, Department of Electrical Engineering, **dian University, **’an, 710071, China

    Shuyuan Yang & Licheng Jiao

  2. Key Laboratory of Radar Signal Processing, Department of Electrical Engineering, **dian University, **’an, 710071, China

    Min Wang

Authors
  1. Shuyuan Yang
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  2. Licheng Jiao
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  3. Min Wang
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Corresponding author

Correspondence to Shuyuan Yang.

Additional information

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Translated from Journal of **dian University, 2006, 33(4): 557–562 [译自: 西安电子科技大学学报(自然科学版)]

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Yang, S., Jiao, L. & Wang, M. A new directional multi-resolution ridgelet network. Front. Electr. Electron. Eng. Ch 3, 198–203 (2008). https://doi.org/10.1007/s11460-008-0026-2

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  • DOI: https://doi.org/10.1007/s11460-008-0026-2

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