Nonlinear dimensionality reduction by locally linear embedding

Introduction:
The paper introduces the method of nonlinear dimension reduction.

Method:

In this figure, the middle part is the points sampled from the hyper-plane in A.

If we flatten the points in B, we could get C.



Here we have 3 steps:

1. For each point, select K neighbors.

2. Find K weights which minimize the squared error between X and WX.

3. In low-dimensional space, find Y (which is corresponding feature of X) which minimize the squared error between Y and WY.