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Methods of Obtaining Topography01:25

Methods of Obtaining Topography

Topography involves measuring and mapping land elevations, natural features, and artificial structures to create accurate representations of the terrain. Topographic surveying relies on traditional and modern methods, each with distinct advantages and limitations.Traditional Surveying Methods:Transit stadia surveys and plane table surveys were widely used traditional surveying methods. These techniques relied on instruments like theodolites and stadia rods for measuring distances and angles,...
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Related Experiment Video

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Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
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Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

Published on: October 16, 2018

Selective smoothing of the generative topographic mapping.

A Vellido1, Wael El-Deredy, P G Lisboa

  • 1Sch. of Comput. and Math. Sci., Liverpool John Moores Univ., UK.

IEEE Transactions on Neural Networks
|February 2, 2008
PubMed
Summary

This study enhances generative topographic mapping (GTM) by introducing selective map smoothing. This method improves model flexibility and prevents overfitting by adjusting mapping stiffness based on data characteristics.

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Data Science

Background:

  • Generative topographic mapping (GTM) is a probabilistic model for nonlinear dimensionality reduction.
  • Model complexity is influenced by basis functions and regularization, which can lead to overfitting.

Purpose of the Study:

  • To improve map smoothing in GTM by introducing multiple regularization terms.
  • To achieve locally controlled mapping stiffness and optimize basis function usage.

Main Methods:

  • Introduced multiple regularization terms, one per basis function.
  • Applied a technique similar to automatic relevance determination for selective map smoothing.
  • Optimized the effective number of active basis functions.

Main Results:

  • Achieved improved map smoothing through selective regularization.
  • Demonstrated local control of mapping stiffness based on manifold length scales.
  • Successfully optimized the number of active basis functions, enhancing model efficiency.

Conclusions:

  • The proposed selective map smoothing technique enhances GTM's ability to model complex data manifolds.
  • This approach offers a more flexible and robust alternative to standard GTM regularization, reducing overfitting.