Neighborhood Selection and Eigenvalues for Embedding Data Complex in Low Dimension

LLE(Local linear embedding) and Isomap are widely used approaches for dimension reduction. For LLE, the neighborhood selection approach is an important research issue. For different types of datasets, we need different neighborhood selection approaches to have better chance for finding reasonable representation within the required number of dimensions. In this paper, the epsilon-distance approach and a modified version of k-nn method are introduced. For LLE and Isomap, the eigen-vectors obtained from these methods are much more discussed, but there are more information hidden in the corresponding eigenvalues which can be used for finding embeddings contains more data information.