ESammon: A Computationaly Enhanced Sammon Mapping based on Data Density

Area of Science:

• Data Visualization
• Computational Science
• Machine Learning

Background:

• Sammon mapping is a standard technique for reducing data dimensionality.
• High computational cost of conventional Sammon mapping limits its application to big data.
• Efficient visualization of large datasets remains a significant challenge.

Purpose of the Study:

• To develop a computationally efficient Sammon mapping method for big data visualization.
• To reduce the computational complexity of Sammon mapping without sacrificing projection accuracy.
• To leverage spatial data density for optimizing the Sammon mapping process.

Main Methods:

• Proposed computationally-enhanced Sammon mapping (ESammon).
• Integrated Directed-Acyclic-Graph (DAG) based data density characterization to identify critical pairwise distances.
• Modified Sammon mapping to preserve only critical distances instead of all distances.

Main Results:

• ESammon achieves comparable projection results to conventional Sammon mapping.
• Computational cost is reduced from O(N^2) to O(N).
• Demonstrated effectiveness in big data visualization scenarios.

Conclusions:

• ESammon offers a computationally efficient alternative to traditional Sammon mapping.
• The method is suitable for visualizing large and complex datasets.
• Preserving critical distances is key to achieving computational gains.