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A tree-structured adaptive network for function approximation in high-dimensional spaces.

T D Sanger1

  • 1MIT, Cambridge, MA.

IEEE Transactions on Neural Networks
|January 1, 1991
PubMed
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This study introduces an adaptive nonlinear basis function technique for efficient function approximation in high-dimensional spaces. The method uses a data-driven tree structure, reducing computational complexity and measurement needs.

Area of Science:

  • Machine Learning
  • Nonlinear Dynamics
  • Robotics

Background:

  • Nonlinear function approximation typically requires numerous fixed basis functions, which becomes computationally expensive in high-dimensional spaces.
  • Existing methods often struggle with the exponential growth of basis functions as input dimensionality increases.
  • Adaptive nonlinear basis functions offer a potential solution but require iterative parameter determination.

Purpose of the Study:

  • To propose a novel adaptive nonlinear basis function technique for efficient function approximation.
  • To address the challenge of high-dimensional input spaces in nonlinear function approximation.
  • To reduce the number of required measurements in sensing-costly applications.

Main Methods:

  • Developed a learning procedure that grows a tree structure based on input data and the function to be approximated.

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  • Implemented an adaptive approach where additional input dimensions are incorporated only when necessary.
  • Utilized a technique that leverages the idea that only a few input dimensions are often sufficient for computation.

    • Main Results:

    • The proposed technique demonstrates a fast learning algorithm.
    • The method avoids local minima once the network shape is determined.
    • Successfully applied to controlling a simulated robot arm, predicting the Mackey-Glass equation, and image pixel prediction.

    Conclusions:

    • The adaptive tree-based approach offers an efficient solution for nonlinear function approximation in high-dimensional spaces.
    • This method can significantly reduce the number of required measurements, beneficial in scenarios with sensing costs.
    • The technique shows versatility across various complex dynamic systems and real-world data.