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Orthogonal neighborhood preserving projections: a projection-based dimensionality reduction technique
Effrosyni Kokiopoulou1, Yousef Saad
1Swiss Federal Institute of Technology, Lausanne, Switzerland. effrosyni.kokiopoulou@epfl.ch
IEEE Transactions on Pattern Analysis and Machine Intelligence
|October 16, 2007
Summary
This study introduces Orthogonal Neighborhood Preserving Projections (ONPP), a novel dimensionality reduction technique. ONPP effectively preserves both local and global data geometry using an explicit linear mapping, simplifying the handling of new data points.
Area of Science:
- Machine Learning
- Data Science
- Computer Vision
Background:
- Dimensionality reduction is crucial for simplifying complex datasets.
- Existing methods like Locally Linear Embedding (LLE) often have implicit mappings.
- Preserving both local and global data geometry is a key challenge.
Purpose of the Study:
- To propose a novel dimensionality reduction technique, Orthogonal Neighborhood Preserving Projections (ONPP).
- To develop a method that preserves both intrinsic neighborhood and global data geometry.
- To enable straightforward handling of new data samples through explicit linear mapping.
Main Methods:
- Constructing an "affinity" graph for data samples, similar to LLE.
- Employing an explicit linear mapping between input and reduced spaces.
- Developing kernel variants and supervised extensions of the ONPP method.
Main Results:
- ONPP successfully preserves both local and global data geometry.
- The explicit linear mapping allows for efficient processing of new data.
- Numerical experiments demonstrate competitive performance against existing methods.
Conclusions:
- ONPP offers an effective approach to dimensionality reduction.
- The method's explicit mapping provides practical advantages for new data integration.
- ONPP shows promise for various machine learning and data analysis applications.
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