paper critique & summarization : Nonlinear Dimensionality Reduction by Locally Linear Embeddign

Title : Nonlinear Dimensionality Reduction by Locally Linear Embedding.
Author : S. T. Roweis and L. K. Saul


summarization:

This paper developed a unsupervised learning algorithm that could be used for dimension reduction.

The based ideas are:

1. Find the neighbors for each points in original coordinate system(maybe by KNN).
2. find some point in the neighbors could reconstruct the original point by linear combination.
3. map all the information above onto the low dimensions coordinate system and minimize the reconstruction error.

critique:

this approach is easy to figure out, but I like the figure 1 he draw. For PCA or MDS, they also directly project the data onto the low dimension system, so some far data would be projected into near position as the figure show. And this method use the neighbor concept to avoid this situation, it easy but make sense, I like this figure.