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A nonlinear projection method based on Kohonen's topology preserving maps.
M A Kraaijveld1, J Mao, A K Jain
1Dept. of Appl. Phys., Delft Univ. of Technol.
IEEE Transactions on Neural Networks
|January 1, 1995
Summary
This study introduces a nonlinear projection method using Kohonen
Area of Science:
- Data Visualization
- Machine Learning
- Computational Science
Background:
- High-dimensional data visualization is challenging.
- Existing methods like Sammon's projection have limitations.
Purpose of the Study:
- To present a novel nonlinear projection method for visualizing high-dimensional data in 2D.
- To introduce a metric for evaluating topology-preserving mapping quality.
- To compare the proposed method with Sammon's projection.
Main Methods:
- Utilized Kohonen's topology-preserving mapping algorithm to train a 2D network.
- Graphically displayed interpoint distances in the feature space.
- Developed a quantification method for mapping accuracy.
Main Results:
- The Kohonen projection method visualizes high-dimensional data as 2D images.
- Performance is comparable or superior to Sammon's method for clustered data classification.
- Time-complexity is independent of dataset size, depending only on output resolution.
Conclusions:
- Kohonen's method offers an effective alternative for high-dimensional data visualization and classification.
- The new quantification metric aids in evaluating projection methods.
- While computationally intensive, the method's scalability with output resolution is advantageous.
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