Semi-Supervised Manifold Learning for Hyperspectral Data

There are real world data sets where a linear approximation like the principal components might not capture the intrinsic characteristics of the data. Nonlinear dimensionality reduction or manifold learning uses a graph-based approach to model the local structure of the data. Manifold learning algorithms assume that the data resides on a low-dimensional manifold that is embedded in a higher-dimensional space. For real world data sets this assumption might not be evident. However, using manifold learning for a classification task can reveal a better performance than using a corresponding procedure that uses the principal components of the data. We show that this is the case for our hyperspectral dataset using the two manifold learning algorithms Laplacian eigenmaps and locally linear embedding.