Unsupervised Adaptive Embedding for Dimensionality Reduction.

Area of Science:

• Data Science
• Machine Learning
• Computer Vision

Background:

• High-dimensional data present challenges due to high correlation and redundancy.
• Existing unsupervised dimensionality reduction (DR) methods often construct neighborhood graphs separately from projection direction selection.
• Original data can be noisy, impacting the effectiveness of DR methods.

Purpose of the Study:

• To propose an unsupervised adaptive embedding (UAE) method for dimensionality reduction.
• To address the limitations of separate graph construction and projection selection in DR.
• To develop a method that mitigates noise in high-dimensional data during DR.

Main Methods:

• Developed a linear graph-embedding method called unsupervised adaptive embedding (UAE).
• Introduced an adaptive neighbor allocation method for constructing an affinity graph.
• Integrated affinity graph construction with projection matrix calculation, considering local and global data characteristics.
• Proposed a cleaned data matrix to remove subspace noise.
• Derived an alternative iteration optimization algorithm to solve the UAE model.

Main Results:

• The proposed UAE method integrates graph construction and projection direction selection.
• The method effectively considers both local sample relationships and global high-dimensional data characteristics.
• A cleaned data matrix was introduced to reduce noise.
• Experiments demonstrated the superiority of the UAE method on synthetic and benchmark datasets.
• Analysis of convergence and computational complexity of the optimization algorithm was performed.

Conclusions:

• Unsupervised adaptive embedding (UAE) offers a superior approach to dimensionality reduction for high-dimensional data.
• Integrating graph construction with projection matrix calculation and noise reduction enhances DR performance.
• The method provides a robust solution for analyzing complex, noisy datasets.