laplacian
Laplacian Eigenmap. Using the notion of the Laplacian of the nearest neighbor adjacency graph, Laplacian Eigenmap compute a low dimensional representation of the dataset that optimally preserves local neighborhood information in a certain sense. The representation map generated by the algorithm may be viewed as a discrete approximation to a continuous map that naturally arises from the geometry of the manifold.
The locality preserving character of the Laplacian Eigenmap algorithm makes it relatively insensitive to outliers and noise. It is also not prone to "short circuiting" as only the local distances are used.
====References:====
Mikhail Belkin and Partha Niyogi. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. NIPS, 2001.
Parameters
the data set.
the dimension of the manifold.
k-nearest neighbor.
the smooth/width parameter of heat kernel e-||x-y||2 / t. Non-positive value means discrete weights.