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

In this article, author propose a simple unsupervised algorithm that compute low dimensional embeddings of high dimensional inputs called locally linear embedding(LLE). The algorithm can be separate into three parts:

1. Assign neighbors to each data points Xi.
2. Compute the weights Wij, that best linear reconstruct Xi from its neighbors.
3. Compute low dimensional embedding vector Yi, using the wights Wij that minimize the embedding cost function.

This method find a low-dimensional representation of the data in a straight forward way and preserved the neighborhood property. There are not much math used in this article, all we need is some background in linear algebra(solving least square problem), which make this paper not hard to understand. Even though, this is still quite a innovate method and can be widely used in many applications.