Learning locality preserving graph from data.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Graph representation is crucial for manifold learning.
• Existing methods for graph construction have limitations in preserving local data information.

Purpose of the Study:

• To propose a novel graph construction method for manifold learning.
• To directly preserve local information of the original data set during graph construction.

Main Methods:

• Formulated graph construction as an optimization problem.
• Connected the proposed objective to the Laplacian Eigenmap problem.
• Developed a cutting plane algorithm to solve the resulting quadratic programming problem efficiently, exploiting graph sparsity.

Main Results:

• The proposed method effectively preserves local data information.
• The cutting plane algorithm offers improved scalability for large datasets.
• Demonstrated advantages in clustering and semi-supervised learning tasks through experimental evaluation.

Conclusions:

• The novel graph construction method enhances manifold learning approaches.
• The efficient algorithm makes the method practical for real-world applications.
• The approach shows significant benefits for clustering and semi-supervised learning.