LLE

[alanyuchenhou]

paper

Nonlinear Dimensionality Reduction by Locally Linear Embedding

problem: dimensionality reduction

• given: a high dimensional datasets
• task: map all data points from the original high dimensional space to a low dimensional space

solution: locally linear embedding

• for each point, assign neighbors to it using k nearest neighbors or something similar
• produce the manifold by linear approximation of each point from its neighbors
• map each point to the manifold by minimizing the embedding cost function

comments

Locally linear embedding is a member of the family of manifold learning approach. Other members in this family should be able to substitute it in most of dimensionality reduction problem: http://scikit-learn.org/stable/modules/manifold.html

[alanyuchenhou]

application (not found in the paper): node embedding

• convert the graph to adjacency matrix
• use each row as the node vector in high dimensional space
• apply locally linear embedding to map each node to a node vector in a low dimensional space

evaluation: link weight prediction

Experiment results:

[alanyuchenhou]

I added a description of LLE embedding method and experiment for link weight prediction in the paper.