I understand the basic principle behind the algorithm for LLE consists of three steps.
- Finding the neighborhood of each data point by some metric such as k-nn.
- Find weights for each neighbor which denote the effect the neighbor has on the data point.
- Construct the low dimensional embedding of the data based on the computed weights.
But the mathematical explanation of steps 2 and 3 are confusing in all the text books and online resources that I have read. I am not able to reason why the formulas are used.
How are these steps performed in practice? Is there any intuitive way of explaining the mathematical formulas used?