Contrary to Isomap, which works with the pairwise distances, this algorithm is based on the assumption that a high-dimensional dataset lying on a smooth manifold can have local linear structures that it tries to preserve during the dimensionality reduction process. Locally Linear Embedding (LLE), like Isomap, is based on three steps. The first one is applying the k-nearest neighbor algorithm to create a directed graph (in Isomap, it was undirected), where the vertices are the input samples and the edges represent a neighborhood relationship. As the graph is direct, a point xi can be a neighbor of xj, but the opposite could be false. It means that the weight matrix can be asymmetric.
The second step is based on the ...
