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Related Experiment Videos

Measure fields for function approximation.

J L Marroquin1

  • 1Centro de Investigacion en Matematicas, Guanajuato.

IEEE Transactions on Neural Networks
|January 1, 1995
PubMed
Summary
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This study introduces a novel method for data approximation by segmenting data into locally smooth models and computing relative probabilities. This approach enhances accuracy in various data analysis tasks.

Area of Science:

  • Computational mathematics
  • Data science
  • Statistical modeling

Background:

  • Approximating data with piecewise smooth functions is crucial for data analysis.
  • Existing methods often struggle with complex data requiring segmentation into distinct models.
  • Decomposition into local models and probability estimation offers a promising avenue.

Purpose of the Study:

  • To develop a robust and efficient computational scheme for piecewise smooth function approximation.
  • To segment data into classes best represented by locally smooth models.
  • To compute normalized discriminant functions for relative probability estimation.

Main Methods:

  • Data segmentation using robust regression and spatial localization with Gaussian windows.
  • Fitting Gaussian mixture models for discriminant function computation within each class.

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  • An efficient procedure for computation and determining the optimal number of model components.

    • Main Results:

    • Successful segmentation of data into classes based on locally smooth models.
    • Accurate computation of normalized discriminant functions representing relative probabilities.
    • Demonstrated efficiency in determining the optimal number of components for models.

    Conclusions:

    • The proposed two-step decoupled approach provides an effective method for piecewise smooth function approximation.
    • The scheme is applicable to diverse fields including image filtering, surface reconstruction, and time series prediction.
    • Efficient computational procedures facilitate practical implementation and optimal model selection.