A useful technique in hyperspectral data analysis is dimensionality reduction, which replaces the original high dimensional data with low dimensional representations. Usually this is done with linear techniques such as linear mixing or principal components (PCA). While often useful, there is no a priori reason for believing that the data is actually linear.
Lately there has been renewed interest in modeling high dimensional data using nonlinear techniques such as manifold learning (ML). In ML, the data is assumed to lie on a low dimensional, possibly curved surface (or manifold). The goal is to discover this manifold and therefore find the best low dimensional representation of the data.
Recently, researchers at the Naval Research Lab have begun to model hyperspectral data using ML. We continue this work by applying ML techniques to hyperspectral ocean water data. We focus on water since there are underlying physical reasons for believing that the data lies on a certain type of nonlinear manifold. In particular, ocean data is influenced by three factors: the water parameters, the bottom type, and the depth. For fixed water and bottom types, the spectra that arise by varying the depth will lie on a nonlinear, one dimensional manifold (i.e. a curve). Generally, water scenes will contain a number of different water and bottom types, each combination of which leads to a distinct curve. In this way, the scene may be modeled as a union of one dimensional curves. In this paper, we investigate the use of manifold learning techniques to separate the various curves, thus partitioning the scene into homogeneous areas. We also discuss ways in which these techniques may be able to derive various scene characteristics such as bathymetry.