Function approximation using combined unsupervised and supervised learning.

Area of Science:

• Machine Learning
• Artificial Intelligence
• Data Science

Background:

• Function approximation is crucial for neural networks in engineering.
• High-dimensional data poses challenges due to the curse of dimensionality.
• Data often resides on lower-dimensional manifolds.

Purpose of the Study:

• To develop an efficient function approximation method for high-dimensional data.
• To leverage the underlying manifold structure of data.
• To improve approximation accuracy and reduce data requirements.

Main Methods:

• A two-step approach: (1) mapping high-dimensional data to a lower-dimensional manifold using over-complete self-organizing maps (SOMs) via unsupervised learning.
• (2) Function approximation on the mapped data using single hidden layer neural networks via supervised learning.
• Extensions explored using support vector machines and Bayesian SOMs for parameter optimization.

Main Results:

• The proposed two-step method, combining unsupervised and supervised learning, demonstrates superior function approximation performance.
• Outperforms traditional neural networks that approximate functions directly in high-dimensional space.
• Effectiveness shown across a set of test functions.

Conclusions:

• The proposed two-step function approximation strategy is effective for high-dimensional data.
• Mapping data to its intrinsic manifold significantly enhances approximation accuracy.
• This approach offers a more efficient and accurate solution for complex engineering problems.