Nonlinear dimensionality reduction by locally linear embedding

"Nonlinear dimensionality reduction by locally linear embedding," Roweis & Saul, Science, 2000.



This paper present an unsupervised learning algorithm, locally linear embedding (LLE), which can construct a neighborhood preserving mapping based on the steps below:

1. Assign K neighbors for each data point Xi.
2. Reconstruct Xi from its neighbors with linear weight, by minimize the cost function
3. Compute the low-dimensional embedding vector Yi, by minimize the function