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Published on: September 17, 2019
A Riemannian distance approach for constructing principal curves
Junping Zhang1, Uwe Kruger, Xiaodan Wang
1Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai 200433, China. jpzhang@fudan.edu.cn
International Journal of Neural Systems
|June 18, 2010
Summary
This study introduces a novel principal curves algorithm that improves data distribution analysis. By incorporating Riemannian distances and sample density, it accurately captures the curve
Area of Science:
- Computational statistics
- Data analysis and visualization
- Machine learning
Background:
- Principal curves are essential for understanding data distribution.
- Traditional methods using arc-length struggle with non-constant data distributions and high curvature.
- Existing algorithms may inaccurately represent the data's middle in complex scenarios.
Purpose of the Study:
- To develop an improved principal curves algorithm.
- To address limitations of arc-length based methods in non-constant data distributions.
- To enhance the accuracy of principal curves in regions of high curvature and density.
Main Methods:
- Revisiting sample projection onto curves using Riemannian distances.
- Estimating sample density relative to neighbors.
- Developing a projection index incorporating density-weighted distances and arc-length.
- Implementing an iterative algorithm with projection and self-consistent steps.
Main Results:
- The proposed method accurately reflects the data's middle, even with non-constant distributions.
- Enhanced performance in areas of high curvature and high data density.
- Demonstrated superiority over existing algorithms in simulation and experimental datasets.
Conclusions:
- The novel approach using Riemannian distances and density improves principal curve estimation.
- This method offers a more robust solution for complex data distributions.
- The findings have implications for various data analysis and machine learning applications.
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